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  1. C CMS3D SOURCE CHAT 05/01/12 22:11:15 5004
  2. SUBROUTINE CMS3D(NSP,JLL,JRR,WVEC_L,WVEC_R,NVECT,TVEC1,
  3. & tvec2,mpyn,lrecp,lrecv,nlcg,nlcd)
  4. C************************************************************************
  5. C
  6. C PROJET : CASTEM 2000
  7. C
  8. C NOM : CMS3D ('convection for multispecies en 3D')
  9. C
  10. C DESCRIPTION : Voir KONMS3 (appele par KONMS3.ESO)
  11. C
  12. C LANGAGE : FORTRAN 77 + ESOPE 2000 (avec estensions CISI)
  13. C
  14. C AUTEUR : S. KUDRIAKOV, DM2S/SFME/LTMF
  15. C
  16. C************************************************************************
  17. C
  18. c----------------------------------------------------------------------
  19. c GENERAL DESCRIPTION:
  20. c This subroutine provides the jacobians which are the derivatives
  21. c of the numerical flux function defined at the cell interface
  22. c with respect to the conservative variables of the left and right
  23. c cells (relative to the cell interface).
  24. c
  25. c EQUATIONS: 3D Euler equations of gas dynamics - MULTISPECIES GAS
  26. c
  27. c
  28. c REFERENCE: JCP, 129, 364-382 (1996)
  29. c " A Sequel to AUSM: AUSM+ ".
  30. c----------------------------------------------------------------------
  31. c INPUT:
  32. c
  33. c alpha -- parameter of the AUSM+ scheme in the Pressure function;
  34. c ( -3/4 <= alpha <= 3/16 ) (imposed as a parameter)
  35. c
  36. c beta -- parameter of the AUSM+ scheme in the Mach function;
  37. c ( -1/16 <= beta <= 1/2 ) (imposed as a parameter)
  38. c
  39. c nsp -- number of species (total);
  40. c
  41. c wvec_l -- vector of the primitive variables
  42. c (rho,u_x,u_y,u_z,p) at the left cell;
  43. c
  44. c wvec_r -- vector of the primitive variables
  45. c (rho,u_x,u_y,u_z,p) at the right cell;
  46. c
  47. c nvect -- normal vector to the interface (2 components in 2D);
  48. c
  49. c tvec1 -- first tangential vector to the interface;
  50. c
  51. c tvec2 -- second tangential vector to the interface;
  52. c
  53. c mpyn -- pointer to the vectors of the primitive variables
  54. c (Y_1,Y_2,...Y_(nsp-1)) at the left and the right cells;
  55. c
  56. c lrecp -- pointer to the vector of specific heats at constant pressure
  57. c (size of the vector is equal to the number of species (nsp));
  58. c
  59. c lrecv -- pointer to the vector of specific heats at constant volume
  60. c (size of the vector is equal to the number of species (nsp));
  61. c
  62. c nlcg -- "local" number corresponding to the left cell;
  63. c
  64. c nlcd -- "local" number corresponding to the right cell;
  65. c----------------------------------------------------------------------
  66. c
  67. c OUTPUT:
  68. c
  69. c jll -- jakobian matrix (4+nsp) by (4+nsp) -
  70. c derivatives of the numerical
  71. c flux function with respect to the conservative variables
  72. c from the left cell;
  73. c
  74. c jrr -- jakobian matrix (4+nsp) by (4+nsp) -
  75. c derivatives of the numerical
  76. c flux function with respect to the conservative variables
  77. c from the right cell.
  78. c----------------------------------------------------------------------
  79. IMPLICIT INTEGER(I-N)
  80. integer nsp,jll,jrr,lrecp,lrecv,nlcg,nlcd
  81. real*8 wvec_l(5),wvec_r(5)
  82. real*8 nvect(3),tvec1(3),tvec2(3)
  83. real*8 alpha,beta
  84. real*8 gal,gar,gm1l,gm1r,temph
  85. real*8 n_x,n_y,n_z,t1_x,t1_y,t1_z,t2_x,t2_y,t2_z
  86. real*8 un_l, un_r, ut1_l, ut1_r,ut2_l,ut2_r
  87. real*8 ml,mr,Mplus,Mmin,mmid
  88. real*8 mpl_m, mmin_m,am
  89. real*8 rold_l,uold_l,vold_l,wold_l,pold_l,eold_l
  90. real*8 rold_r,uold_r,vold_r,wold_r,pold_r,eold_r
  91. real*8 Pplus,Pmin,pmid
  92. real*8 hr_l,hr_r,det,c11,c12,c13,c21,c22,c23,c31,c32,c33
  93. real*8 br1,temp_l,temp_r,brac_l,brac_r,top, bot
  94. real*8 aleft, arigh
  95. real*8 damr_l,damr_r,damu_l,damu_r
  96. real*8 damv_l,damv_r,damp_l,damp_r
  97. real*8 damw_l,damw_r
  98. real*8 damg_l,damg_r
  99. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  100. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  101. real*8 dmlw_l,dmlw_r
  102. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  103. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  104. real*8 dmrw_l,dmrw_r
  105. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  106. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r
  107. real*8 dMpw_l,dMpw_r
  108. real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r
  109. real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r
  110. real*8 dMmw_l,dMmw_r
  111. real*8 dmir_l,dmir_r,dmiu_l,dmiu_r
  112. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  113. real*8 dmiw_l,dmiw_r
  114. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  115. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  116. real*8 d3mw_l,d3mw_r
  117. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  118. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  119. real*8 d2mw_l,d2mw_r
  120. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  121. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  122. real*8 dPpw_l,dPpw_r
  123. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  124. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  125. real*8 dPmw_l,dPmw_r
  126. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  127. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  128. real*8 dpiw_l,dpiw_r,ff,fs,ft,dffr,dffu,dffv,dffw,dffp
  129. real*8 dfsr,dfsu,dfsv,dfsw,dfsp,dftr,dftu,dftv,dftw,dftp
  130. integer i,j,k
  131. parameter(alpha = 0.1875D0, beta = 0.125D0)
  132. C------------------------------------------------------------
  133. -INC SMCHPOI
  134. POINTEUR MPYN.MPOVAL
  135. C-------------------------------------------------------------
  136. -INC SMLREEL
  137. POINTEUR MLRECP.MLREEL, MLRECV.MLREEL
  138. C-------------------------------------------------------------
  139. C******* Les fractionines massiques **************************
  140. C-------------------------------------------------------------
  141. SEGMENT FRAMAS
  142. REAL*8 YET(NSP)
  143. ENDSEGMENT
  144. POINTEUR YL.FRAMAS, YR.FRAMAS
  145. C-------------------------------------------------------
  146. C********** Les CP's and CV's ***********************
  147. C-------------------------------------------------------
  148. SEGMENT GCONST
  149. REAL*8 GC(NSP)
  150. ENDSEGMENT
  151. POINTEUR CP.GCONST, CV.GCONST
  152. C-------------------------------------------------------------
  153. C******** Segments for the elementary matrixes *************
  154. C-------------------------------------------------------------
  155. SEGMENT JACEL
  156. REAL*8 JAC(4+NSP,4+NSP)
  157. ENDSEGMENT
  158. POINTEUR JTL.JACEL, JTR.JACEL, JL.JACEL, JR.JACEL,
  159. & WL.JACEL, WR.JACEL
  160. c----------------------------------------
  161. SEGINI JTL
  162. SEGINI JTR
  163. SEGINI JL
  164. SEGINI JR
  165. SEGINI WL
  166. SEGINI WR
  167. C-------------------------------------------------------------
  168. C********** Segments for the vectors ***********************
  169. C-------------------------------------------------------------
  170. SEGMENT VECEL
  171. REAL*8 VV(NSP)
  172. ENDSEGMENT
  173. POINTEUR DMLY_L.VECEL, DMLY_R.VECEL,
  174. & dmry_l.vecel, dmry_r.vecel,
  175. & dMpy_l.vecel, dMpy_r.vecel,
  176. & dMmy_l.vecel, dMmy_r.vecel,
  177. & dmiy_l.vecel, dmiy_r.vecel,
  178. & d3my_l.vecel, d3my_r.vecel,
  179. & d2my_l.vecel, d2my_r.vecel,
  180. & dPpy_l.vecel, dPpy_r.vecel,
  181. & dPmy_l.vecel, dPmy_r.vecel,
  182. & dpiy_l.vecel, dpiy_r.vecel,
  183. & dgdyl.vecel, dgdyr.vecel,
  184. & dffy_l.vecel,dffy_r.vecel,
  185. & dfsy_l.vecel,dfsy_r.vecel,
  186. & dfty_l.vecel,dfty_r.vecel
  187. C----------------------------------------------
  188. SEGINI DMLY_L, DMLY_R,
  189. & dmry_l, dmry_r,
  190. & dMpy_l, dMpy_r,
  191. & dMmy_l, dMmy_r,
  192. & dmiy_l, dmiy_r,
  193. & d3my_l, d3my_r,
  194. & d2my_l, d2my_r,
  195. & dPpy_l, dPpy_r,
  196. & dPmy_l, dPmy_r,
  197. & dpiy_l, dpiy_r,
  198. & dgdyl, dgdyr,
  199. & dffy_l,dffy_r,
  200. & dfsy_l,dfsy_r,
  201. & dfty_l,dfty_r
  202. C-------------------------------------------------------------
  203. C********** Segments for the flux-vector *******************
  204. C-------------------------------------------------------------
  205. SEGMENT FUNEL
  206. REAL*8 FU(4+NSP)
  207. ENDSEGMENT
  208. POINTEUR f.funel
  209. C-------------------------
  210. SEGINI f
  211. C------------------------------------------------------------
  212. SEGINI YL, YR
  213. SEGACT MPYN
  214. DO 4 I=1,(NSP-1)
  215. YL.YET(I)=MPYN.VPOCHA(NLCG,I)
  216. YR.YET(I)=MPYN.VPOCHA(NLCD,I)
  217. 4 CONTINUE
  218. C----------------------------------------
  219. SEGINI CP, CV
  220. MLRECP = LRECP
  221. MLRECV = LRECV
  222. SEGACT MLRECP, MLRECV
  223. DO 5 I=1,(NSP-1)
  224. CP.GC(I)=MLRECP.PROG(I)
  225. CV.GC(I)=MLRECV.PROG(I)
  226. 5 CONTINUE
  227. CP.GC(NSP)=MLRECP.PROG(NSP)
  228. CV.GC(NSP)=MLRECV.PROG(NSP)
  229. c-------------------------------------------------------------
  230. c Computing GAMMA at the left cell and its derivatives
  231. c with respect to the primitive variables Y_i
  232. c-------------------------------------------------------------
  233. top=0.0D0
  234. bot=0.0D0
  235. do 40 i=1,(nsp-1)
  236. top=top+yl.yet(i)*(cp.gc(i)-cp.gc(nsp))
  237. bot=bot+yl.yet(i)*(cv.gc(i)-cv.gc(nsp))
  238. 40 continue
  239. top=cp.gc(nsp)+top
  240. bot=cv.gc(nsp)+bot
  241. gal=top/bot
  242. gm1l=gal-1.0d0
  243. c-------------------------------------------------------------
  244. do 41 i=1,(nsp-1)
  245. dgdyl.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  246. & gal*(cv.gc(i)-cv.gc(nsp)))/bot
  247. 41 continue
  248. c-------------------------------------------------------------
  249. c Computing GAMMA at the right cell and its derivatives
  250. c with respect to the primitive variables Y_i
  251. c-------------------------------------------------------------
  252. top=0.0D0
  253. bot=0.0D0
  254. do 42 i=1,(nsp-1)
  255. top=top+yr.yet(i)*(cp.gc(i)-cp.gc(nsp))
  256. bot=bot+yr.yet(i)*(cv.gc(i)-cv.gc(nsp))
  257. 42 continue
  258. top=cp.gc(nsp)+top
  259. bot=cv.gc(nsp)+bot
  260. gar=top/bot
  261. gm1r=gar-1.0d0
  262. c-------------------------------------------------------------
  263. do 43 i=1,(nsp-1)
  264. dgdyr.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  265. & gar*(cv.gc(i)-cv.gc(nsp)))/bot
  266. 43 continue
  267. c-------------------------------------------------------------
  268. n_x=nvect(1)
  269. n_y=nvect(2)
  270. n_z=nvect(3)
  271. c-------------------
  272. t1_x=tvec1(1)
  273. t1_y=tvec1(2)
  274. t1_z=tvec1(3)
  275. c-------------------
  276. t2_x=tvec2(1)
  277. t2_y=tvec2(2)
  278. t2_z=tvec2(3)
  279. c----------------------------
  280. c11=t1_y*t2_z - t1_z*t2_y
  281. c12=t1_z*t2_x - t1_x*t2_z
  282. c13=t1_x*t2_y - t1_y*t2_x
  283. det=n_x*c11 + n_y*c12 + n_z*c13
  284. c--------------------------------------
  285. c21=n_z*t2_y - n_y*t2_z
  286. c22=n_x*t2_z - n_z*t2_x
  287. c23=n_y*t2_x - n_x*t2_y
  288. c--------------------------------------
  289. c31=n_y*t1_z - n_z*t1_y
  290. c32=n_z*t1_x - n_x*t1_z
  291. c33=n_x*t1_y - n_y*t1_x
  292. c----------------------------
  293. rold_l=wvec_l(1)
  294. uold_l=wvec_l(2)
  295. vold_l=wvec_l(3)
  296. wold_l=wvec_l(4)
  297. pold_l=wvec_l(5)
  298. c-----------------------
  299. rold_r=wvec_r(1)
  300. uold_r=wvec_r(2)
  301. vold_r=wvec_r(3)
  302. wold_r=wvec_r(4)
  303. pold_r=wvec_r(5)
  304. c------------------------------------------------------------------
  305. c Computation of the specific total energy on the left and right.
  306. c------------------------------------------------------------------
  307. eold_l=(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0
  308. eold_l=eold_l+pold_l/(gm1l*rold_l)
  309. eold_r=(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0
  310. eold_r=eold_r+pold_r/(gm1r*rold_r)
  311. c-------------------------------------------------------------------
  312. c Computation of the speed of sound and its derivatives;
  313. c numerical speed of sound at the interface is taken as an average
  314. c of the speeds of sounds of the neighbouring cells
  315. c-------------------------------------------------------------------
  316. aleft=sqrt(gal*pold_l/rold_l)
  317. arigh=sqrt(gar*pold_r/rold_r)
  318. am=0.5d0*(aleft+arigh)
  319. c-------------------------------------------------------------------
  320. damr_r=-arigh/(4.0d0*rold_r)
  321. damu_r=0.0d0
  322. damv_r=0.0d0
  323. damw_r=0.0d0
  324. damp_r=gar/(4.0d0*arigh*rold_r)
  325. damg_r=arigh/(4.0d0*gar)
  326. c-----------------------
  327. damr_l=-aleft/(4.0d0*rold_l)
  328. damu_l=0.0d0
  329. damv_l=0.0d0
  330. damw_l=0.0d0
  331. damp_l=gal/(4.0d0*aleft*rold_l)
  332. damg_l=aleft/(4.0d0*gal)
  333. c-------------------------------------------------------------------
  334. c Computing numerical Mach number and its derivatives,
  335. c see p.370, under (A1).
  336. c-------------------------------------------------------------------
  337. un_l=uold_l*n_x+vold_l*n_y+wold_l*n_z
  338. un_r=uold_r*n_x+vold_r*n_y+wold_r*n_z
  339. c----------
  340. ut1_l=uold_l*t1_x+vold_l*t1_y+wold_l*t1_z
  341. ut1_r=uold_r*t1_x+vold_r*t1_y+wold_r*t1_z
  342. c----------
  343. ut2_l=uold_l*t2_x+vold_l*t2_y+wold_l*t2_z
  344. ut2_r=uold_r*t2_x+vold_r*t2_y+wold_r*t2_z
  345. c-------------------------------------------------------------------
  346. ml=un_l/am
  347. mr=un_r/am
  348. c-------------------------------------------------------------------
  349. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  350. c see (19a) and (19b), p.367.
  351. c-------------------------------------------------------------------
  352. if(abs(ml) .ge. 1.0d0) then
  353. Mplus=(ml+abs(ml))/2.0d0
  354. else
  355. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  356. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  357. endif
  358. c-------------------------------------------------------------------
  359. if(abs(mr) .ge. 1.0d0) then
  360. Mmin=(mr-abs(mr))/2.0d0
  361. else
  362. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  363. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  364. endif
  365. c-------------------------------------------------------------------
  366. c Derivatives of ml and mr with respect to both sets of primitive
  367. c variables: left and right.
  368. c-------------------------------------------------------------------
  369. temp_l=-un_l/(am*am)
  370. temp_r=-un_r/(am*am)
  371. c--------
  372. dmlr_l=temp_l*damr_l
  373. dmlr_r=temp_l*damr_r
  374. dmrr_l=temp_r*damr_l
  375. dmrr_r=temp_r*damr_r
  376. c--------
  377. dmlu_l=n_x/am+temp_l*damu_l
  378. dmlu_r=temp_l*damu_r
  379. dmru_l=temp_r*damu_l
  380. dmru_r=n_x/am+temp_r*damu_r
  381. c--------
  382. dmlv_l=n_y/am+temp_l*damv_l
  383. dmlv_r=temp_l*damv_r
  384. dmrv_l=temp_r*damv_l
  385. dmrv_r=n_y/am+temp_r*damv_r
  386. c--------
  387. dmlw_l=n_z/am+temp_l*damw_l
  388. dmlw_r=temp_l*damw_r
  389. dmrw_l=temp_r*damw_l
  390. dmrw_r=n_z/am+temp_r*damw_r
  391. c--------
  392. dmlp_l=temp_l*damp_l
  393. dmlp_r=temp_l*damp_r
  394. dmrp_l=temp_r*damp_l
  395. dmrp_r=temp_r*damp_r
  396. c--------
  397. do 44 i=1,(nsp-1)
  398. dmly_l.vv(i)=temp_l*damg_l*dgdyl.vv(i)
  399. dmly_r.vv(i)=temp_l*damg_r*dgdyr.vv(i)
  400. dmry_l.vv(i)=temp_r*damg_l*dgdyl.vv(i)
  401. dmry_r.vv(i)=temp_r*damg_r*dgdyr.vv(i)
  402. 44 continue
  403. c-----------------------------------------------------------
  404. c mmid is m_{1/2} (notation as in the paper, see (13),p.366)
  405. c-----------------------------------------------------------
  406. mmid=Mplus+Mmin
  407. c-----------------------------------------------------------
  408. c Computing the derivatives of M+ and M-
  409. c-----------------------------------------------------------
  410. if(ml .ge. 1.0d0) then
  411. dMpr_l=dmlr_l
  412. dMpu_l=dmlu_l
  413. dMpv_l=dmlv_l
  414. dMpw_l=dmlw_l
  415. dMpp_l=dmlp_l
  416. do 45 i=1,(nsp-1)
  417. dMpy_l.vv(i)=dmly_l.vv(i)
  418. 45 continue
  419. c--------------------
  420. dMpr_r=dmlr_r
  421. dMpu_r=dmlu_r
  422. dMpv_r=dmlv_r
  423. dMpw_r=dmlw_r
  424. dMpp_r=dmlp_r
  425. do 46 i=1,(nsp-1)
  426. dMpy_r.vv(i)=dmly_r.vv(i)
  427. 46 continue
  428. else
  429. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  430. temph=(ml+1.0d0)/2.0d0
  431. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  432. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  433. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  434. dMpw_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_l
  435. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  436. do 47 i=1,(nsp-1)
  437. dMpy_l.vv(i)=(temph+4.0d0*beta*ml*
  438. & (ml*ml-1.0d0))*dmly_l.vv(i)
  439. 47 continue
  440. c--------------------
  441. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  442. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  443. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  444. dMpw_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_r
  445. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  446. do 48 i=1,(nsp-1)
  447. dMpy_r.vv(i)=(temph+4.0d0*beta*ml*
  448. & (ml*ml-1.0d0))*dmly_r.vv(i)
  449. 48 continue
  450. else
  451. dMpr_l=0.0d0
  452. dMpu_l=0.0d0
  453. dMpv_l=0.0d0
  454. dMpw_l=0.0d0
  455. dMpp_l=0.0d0
  456. do 49 i=1,(nsp-1)
  457. dMpy_l.vv(i)=0.0d0
  458. 49 continue
  459. c---------------------
  460. dMpr_r=0.0d0
  461. dMpu_r=0.0d0
  462. dMpv_r=0.0d0
  463. dMpw_r=0.0d0
  464. dMpp_r=0.0d0
  465. do 50 i=1,(nsp-1)
  466. dMpy_r.vv(i)=0.0d0
  467. 50 continue
  468. endif
  469. endif
  470. c-----------------------------------------------------------
  471. if(mr .ge. 1.0d0) then
  472. dMmr_l=0.0d0
  473. dMmu_l=0.0d0
  474. dMmv_l=0.0d0
  475. dMmw_l=0.0d0
  476. dMmp_l=0.0d0
  477. do 51 i=1,(nsp-1)
  478. dMmy_l.vv(i)=0.0d0
  479. 51 continue
  480. c---------------------
  481. dMmr_r=0.0d0
  482. dMmu_r=0.0d0
  483. dMmv_r=0.0d0
  484. dMmw_r=0.0d0
  485. dMmp_r=0.0d0
  486. do 52 i=1,(nsp-1)
  487. dMmy_r.vv(i)=0.0d0
  488. 52 continue
  489. else
  490. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  491. temph=(-mr+1.0d0)/2.0d0
  492. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  493. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  494. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  495. dMmw_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_l
  496. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  497. do 53 i=1,(nsp-1)
  498. dMmy_l.vv(i)=(temph-4.0d0*beta*mr*
  499. & (mr*mr-1.0d0))*dmry_l.vv(i)
  500. 53 continue
  501. c--------------------
  502. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  503. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  504. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  505. dMmw_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_r
  506. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  507. do 54 i=1,(nsp-1)
  508. dMmy_r.vv(i)=(temph-4.0d0*beta*mr*
  509. & (mr*mr-1.0d0))*dmry_r.vv(i)
  510. 54 continue
  511. else
  512. dMmr_l=dmrr_l
  513. dMmu_l=dmru_l
  514. dMmv_l=dmrv_l
  515. dMmw_l=dmrw_l
  516. dMmp_l=dmrp_l
  517. do 55 i=1,(nsp-1)
  518. dMmy_l.vv(i)=dmry_l.vv(i)
  519. 55 continue
  520. c--------------------
  521. dMmr_r=dmrr_r
  522. dMmu_r=dmru_r
  523. dMmv_r=dmrv_r
  524. dMmw_r=dmrw_r
  525. dMmp_r=dmrp_r
  526. do 56 i=1,(nsp-1)
  527. dMmy_r.vv(i)=dmry_r.vv(i)
  528. 56 continue
  529. endif
  530. endif
  531. c-----------------------------------------------------------------
  532. c computing the derivatives of m_{1/2} (notation as in the paper)
  533. c-----------------------------------------------------------------
  534. dmir_l=dMpr_l+dMmr_l
  535. dmir_r=dMpr_r+dMmr_r
  536. c-------------
  537. dmiu_l=dMpu_l+dMmu_l
  538. dmiu_r=dMpu_r+dMmu_r
  539. c-------------
  540. dmiv_l=dMpv_l+dMmv_l
  541. dmiv_r=dMpv_r+dMmv_r
  542. c-------------
  543. dmiw_l=dMpw_l+dMmw_l
  544. dmiw_r=dMpw_r+dMmw_r
  545. c-------------
  546. dmip_l=dMpp_l+dMmp_l
  547. dmip_r=dMpp_r+dMmp_r
  548. c-------------
  549. do 57 i=1,(nsp-1)
  550. dmiy_l.vv(i)=dMpy_l.vv(i)+dMmy_l.vv(i)
  551. dmiy_r.vv(i)=dMpy_r.vv(i)+dMmy_r.vv(i)
  552. 57 continue
  553. c----------------------------------------------------------------
  554. c computing the main convective variables and their derivatives
  555. c mpl_m is m^{+}_{1/2} (paper's notation) and
  556. c mmin_m is m^{-}_{1/2} (paper's notation), see (A2) on p.370.
  557. c----------------------------------------------------------------
  558. if(mmid .ge. 0.0d0) then
  559. mpl_m = mmid
  560. d2mr_l=dmir_l
  561. d2mu_l=dmiu_l
  562. d2mv_l=dmiv_l
  563. d2mw_l=dmiw_l
  564. d2mp_l=dmip_l
  565. do 58 i=1,(nsp-1)
  566. d2my_l.vv(i)=dmiy_l.vv(i)
  567. 58 continue
  568. c------------
  569. d2mr_r=dmir_r
  570. d2mu_r=dmiu_r
  571. d2mv_r=dmiv_r
  572. d2mw_r=dmiw_r
  573. d2mp_r=dmip_r
  574. do 59 i=1,(nsp-1)
  575. d2my_r.vv(i)=dmiy_r.vv(i)
  576. 59 continue
  577. c------------
  578. else
  579. mpl_m = 0.0d0
  580. d2mr_l=0.0d0
  581. d2mu_l=0.0d0
  582. d2mv_l=0.0d0
  583. d2mw_l=0.0d0
  584. d2mp_l=0.0d0
  585. do 60 i=1,(nsp-1)
  586. d2my_l.vv(i)=0.0d0
  587. 60 continue
  588. c------------
  589. d2mr_r=0.0d0
  590. d2mu_r=0.0d0
  591. d2mv_r=0.0d0
  592. d2mw_r=0.0d0
  593. d2mp_r=0.0d0
  594. do 61 i=1,(nsp-1)
  595. d2my_r.vv(i)=0.0d0
  596. 61 continue
  597. endif
  598. c---------------------------------------------
  599. if(mmid .le. 0.0d0) then
  600. mmin_m = mmid
  601. d3mr_l=dmir_l
  602. d3mu_l=dmiu_l
  603. d3mv_l=dmiv_l
  604. d3mw_l=dmiw_l
  605. d3mp_l=dmip_l
  606. do 62 i=1,(nsp-1)
  607. d3my_l.vv(i)=dmiy_l.vv(i)
  608. 62 continue
  609. c------------
  610. d3mr_r=dmir_r
  611. d3mu_r=dmiu_r
  612. d3mv_r=dmiv_r
  613. d3mw_r=dmiw_r
  614. d3mp_r=dmip_r
  615. do 63 i=1,(nsp-1)
  616. d3my_r.vv(i)=dmiy_r.vv(i)
  617. 63 continue
  618. c------------
  619. else
  620. mmin_m = 0.0d0
  621. d3mr_l=0.0d0
  622. d3mu_l=0.0d0
  623. d3mv_l=0.0d0
  624. d3mw_l=0.0d0
  625. d3mp_l=0.0d0
  626. do 64 i=1,(nsp-1)
  627. d3my_l.vv(i)=0.0d0
  628. 64 continue
  629. c------------
  630. d3mr_r=0.0d0
  631. d3mu_r=0.0d0
  632. d3mv_r=0.0d0
  633. d3mw_r=0.0d0
  634. d3mp_r=0.0d0
  635. do 65 i=1,(nsp-1)
  636. d3my_r.vv(i)=0.0d0
  637. 65 continue
  638. endif
  639. c---------------------------------------------------------------
  640. c Computing the calligraphic P+ and P- with their derivatives,
  641. c see (21a) & (21b) on p.368.
  642. c---------------------------------------------------------------
  643. if(ml .ge. 1.0d0) then
  644. Pplus = 1.0d0
  645. else
  646. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  647. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  648. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  649. else
  650. Pplus = 0.0d0
  651. endif
  652. endif
  653. c---------------------------------------------------------------
  654. if(mr .ge. 1.0d0) then
  655. Pmin = 0.0d0
  656. else
  657. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  658. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  659. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  660. else
  661. Pmin = 1.0d0
  662. endif
  663. endif
  664. c---------------------------------------------------------------
  665. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  666. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  667. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  668. c--------------
  669. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  670. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  671. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  672. c---------------------------------------------------------------
  673. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  674. dPpr_l=brac_l*dmlr_l
  675. dPpr_r=brac_l*dmlr_r
  676. c------------
  677. dPpu_l=brac_l*dmlu_l
  678. dPpu_r=brac_l*dmlu_r
  679. c------------
  680. dPpv_l=brac_l*dmlv_l
  681. dPpv_r=brac_l*dmlv_r
  682. c------------
  683. dPpw_l=brac_l*dmlw_l
  684. dPpw_r=brac_l*dmlw_r
  685. c------------
  686. dPpp_l=brac_l*dmlp_l
  687. dPpp_r=brac_l*dmlp_r
  688. c------------
  689. do 66 i=1,(nsp-1)
  690. dPpy_l.vv(i)=brac_l*dmly_l.vv(i)
  691. dPpy_r.vv(i)=brac_l*dmly_r.vv(i)
  692. 66 continue
  693. c------------
  694. else
  695. dPpr_l=0.0d0
  696. dPpr_r=0.0d0
  697. c-----------
  698. dPpu_l=0.0d0
  699. dPpu_r=0.0d0
  700. c-----------
  701. dPpv_l=0.0d0
  702. dPpv_r=0.0d0
  703. c-----------
  704. dPpw_l=0.0d0
  705. dPpw_r=0.0d0
  706. c-----------
  707. dPpp_l=0.0d0
  708. dPpp_r=0.0d0
  709. c-----------
  710. do 67 i=1,(nsp-1)
  711. dPpy_l.vv(i)=0.0d0
  712. dPpy_r.vv(i)=0.0d0
  713. 67 continue
  714. c-----------
  715. endif
  716. c---------------------------------------------------------------
  717. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  718. dPmr_l=brac_r*dmrr_l
  719. dPmr_r=brac_r*dmrr_r
  720. c------------
  721. dPmu_l=brac_r*dmru_l
  722. dPmu_r=brac_r*dmru_r
  723. c------------
  724. dPmv_l=brac_r*dmrv_l
  725. dPmv_r=brac_r*dmrv_r
  726. c------------
  727. dPmw_l=brac_r*dmrw_l
  728. dPmw_r=brac_r*dmrw_r
  729. c------------
  730. dPmp_l=brac_r*dmrp_l
  731. dPmp_r=brac_r*dmrp_r
  732. c------------
  733. do 68 i=1,(nsp-1)
  734. dPmy_l.vv(i)=brac_r*dmry_l.vv(i)
  735. dPmy_r.vv(i)=brac_r*dmry_r.vv(i)
  736. 68 continue
  737. c------------
  738. else
  739. dPmr_l=0.0d0
  740. dPmr_r=0.0d0
  741. c-----------
  742. dPmu_l=0.0d0
  743. dPmu_r=0.0d0
  744. c-----------
  745. dPmv_l=0.0d0
  746. dPmv_r=0.0d0
  747. c-----------
  748. dPmw_l=0.0d0
  749. dPmw_r=0.0d0
  750. c-----------
  751. dPmp_l=0.0d0
  752. dPmp_r=0.0d0
  753. c-----------
  754. do 69 i=1,(nsp-1)
  755. dPmy_l.vv(i)=0.0d0
  756. dPmy_r.vv(i)=0.0d0
  757. 69 continue
  758. c-----------
  759. endif
  760. c-------------------------------------------------------------------
  761. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  762. c-------------------------------------------------------------------
  763. pmid=Pplus*pold_l + Pmin*pold_r
  764. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  765. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  766. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  767. dpiw_l=dPpw_l*pold_l+dPmw_l*pold_r
  768. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  769. do 70 i=1,(nsp-1)
  770. dpiy_l.vv(i)=dPpy_l.vv(i)*pold_l+dPmy_l.vv(i)*pold_r
  771. 70 continue
  772. c----------------------------
  773. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  774. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  775. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  776. dpiw_r=dPpw_r*pold_l+dPmw_r*pold_r
  777. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  778. do 71 i=1,(nsp-1)
  779. dpiy_r.vv(i)=dPpy_r.vv(i)*pold_l+dPmy_r.vv(i)*pold_r
  780. 71 continue
  781. c---------------------------------------------------------------------
  782. c computing JACOBIAN as a derivative of the numerical flux function
  783. c with respect to the primitive variables.
  784. c Notation: jl(i,j) --- is the derivative of the i-component of the
  785. c flux function with respect to the j-component of the
  786. c vector of primitive variables of the left state.
  787. c jr(i,j) --- is the derivative of the i-component of the
  788. c flux function with respect to the j-component of the
  789. c vector of primitive variables of the right state.
  790. c---------------------------------------------------------------------
  791. f.fu(1)=am*(mpl_m*rold_l+mmin_m*rold_r)
  792. c---------------------------------------------------------------------
  793. jl.jac(1,1)=damr_l*f.fu(1)/am+am*(d2mr_l*rold_l+mpl_m)
  794. jl.jac(1,1)=jl.jac(1,1)+am*d3mr_l*rold_r
  795. jl.jac(1,2)=damu_l*f.fu(1)/am+am*(d2mu_l*rold_l+d3mu_l*rold_r)
  796. jl.jac(1,3)=damv_l*f.fu(1)/am+am*(d2mv_l*rold_l+d3mv_l*rold_r)
  797. jl.jac(1,4)=damw_l*f.fu(1)/am+am*(d2mw_l*rold_l+d3mw_l*rold_r)
  798. jl.jac(1,5)=damp_l*f.fu(1)/am+am*(d2mp_l*rold_l+d3mp_l*rold_r)
  799. do 72 i=1,(nsp-1)
  800. jl.jac(1,5+i)=damg_l*dgdyl.vv(i)*f.fu(1)/am+
  801. & am*(d2my_l.vv(i)*rold_l+d3my_l.vv(i)*rold_r)
  802. 72 continue
  803. c------------------------------------
  804. jr.jac(1,1)=damr_r*f.fu(1)/am+am*(d2mr_r*rold_l+mmin_m)
  805. jr.jac(1,1)=jr.jac(1,1)+am*d3mr_r*rold_r
  806. jr.jac(1,2)=damu_r*f.fu(1)/am+am*(d2mu_r*rold_l+d3mu_r*rold_r)
  807. jr.jac(1,3)=damv_r*f.fu(1)/am+am*(d2mv_r*rold_l+d3mv_r*rold_r)
  808. jr.jac(1,4)=damw_r*f.fu(1)/am+am*(d2mw_r*rold_l+d3mw_r*rold_r)
  809. jr.jac(1,5)=damp_r*f.fu(1)/am+am*(d2mp_r*rold_l+d3mp_r*rold_r)
  810. do 73 i=1,(nsp-1)
  811. jr.jac(1,5+i)=damg_r*dgdyr.vv(i)*f.fu(1)/am+
  812. & am*(d2my_r.vv(i)*rold_l+d3my_r.vv(i)*rold_r)
  813. 73 continue
  814. c------------------------------------------------------
  815. c-------------------- f2 ---------------------------
  816. c------------------------------------------------------
  817. ff=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  818. dffr=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  819. dffu=d2mu_l*rold_l*un_l+mpl_m*rold_l*c11/det
  820. dffu=dffu+d3mu_l*rold_r*un_r
  821. dffv=d2mv_l*rold_l*un_l+mpl_m*rold_l*c12/det
  822. dffv=dffv+d3mv_l*rold_r*un_r
  823. dffw=d2mw_l*rold_l*un_l+mpl_m*rold_l*c13/det
  824. dffw=dffw+d3mw_l*rold_r*un_r
  825. dffp=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  826. do 74 i=1,(nsp-1)
  827. dffy_l.vv(i)=d2my_l.vv(i)*rold_l*un_l
  828. & +d3my_l.vv(i)*rold_r*un_r
  829. 74 continue
  830. c------------------------------------------------
  831. fs=mpl_m*rold_l*ut1_l+mmin_m*rold_r*ut1_r
  832. dfsr=d2mr_l*rold_l*ut1_l+mpl_m*ut1_l
  833. dfsr=dfsr+d3mr_l*rold_r*ut1_r
  834. dfsu=d2mu_l*rold_l*ut1_l+mpl_m*rold_l*c21/det
  835. dfsu=dfsu+d3mu_l*rold_r*ut1_r
  836. dfsv=d2mv_l*rold_l*ut1_l+mpl_m*rold_l*c22/det
  837. dfsv=dfsv+d3mv_l*rold_r*ut1_r
  838. dfsw=d2mw_l*rold_l*ut1_l+mpl_m*rold_l*c23/det
  839. dfsw=dfsw+d3mw_l*rold_r*ut1_r
  840. dfsp=d2mp_l*rold_l*ut1_l+d3mp_l*rold_r*ut1_r
  841. do 75 i=1,(nsp-1)
  842. dfsy_l.vv(i)=d2my_l.vv(i)*rold_l*ut1_l+
  843. & d3my_l.vv(i)*rold_r*ut1_r
  844. 75 continue
  845. c------------------------------------------------
  846. ft=mpl_m*rold_l*ut2_l+mmin_m*rold_r*ut2_r
  847. dftr=d2mr_l*rold_l*ut2_l+mpl_m*ut2_l
  848. dftr=dftr+d3mr_l*rold_r*ut2_r
  849. dftu=d2mu_l*rold_l*ut2_l+mpl_m*rold_l*c31/det
  850. dftu=dftu+d3mu_l*rold_r*ut2_r
  851. dftv=d2mv_l*rold_l*ut2_l+mpl_m*rold_l*c32/det
  852. dftv=dftv+d3mv_l*rold_r*ut2_r
  853. dftw=d2mw_l*rold_l*ut2_l+mpl_m*rold_l*c33/det
  854. dftw=dftw+d3mw_l*rold_r*ut2_r
  855. dftp=d2mp_l*rold_l*ut2_l+d3mp_l*rold_r*ut2_r
  856. do 76 i=1,(nsp-1)
  857. dfty_l.vv(i)=d2my_l.vv(i)*rold_l*ut2_l+
  858. & d3my_l.vv(i)*rold_r*ut2_r
  859. 76 continue
  860. c------------------------------------------------
  861. f.fu(2)=am*(ff*n_x+fs*t1_x+ft*t2_x)+pmid*n_x
  862. c---------------------------------------------------------
  863. jl.jac(2,1)=damr_l*(f.fu(2)-pmid*n_x)/am+dpir_l*n_x
  864. jl.jac(2,1)=jl.jac(2,1)+am*(dffr*n_x+dfsr*t1_x+dftr*t2_x)
  865. jl.jac(2,2)=damu_l*(f.fu(2)-pmid*n_x)/am+dpiu_l*n_x
  866. jl.jac(2,2)=jl.jac(2,2)+am*(dffu*n_x+dfsu*t1_x+dftu*t2_x)
  867. jl.jac(2,3)=damv_l*(f.fu(2)-pmid*n_x)/am+dpiv_l*n_x
  868. jl.jac(2,3)=jl.jac(2,3)+am*(dffv*n_x+dfsv*t1_x+dftv*t2_x)
  869. jl.jac(2,4)=damw_l*(f.fu(2)-pmid*n_x)/am+dpiw_l*n_x
  870. jl.jac(2,4)=jl.jac(2,4)+am*(dffw*n_x+dfsw*t1_x+dftw*t2_x)
  871. jl.jac(2,5)=damp_l*(f.fu(2)-pmid*n_x)/am+dpip_l*n_x
  872. jl.jac(2,5)=jl.jac(2,5)+am*(dffp*n_x+dfsp*t1_x+dftp*t2_x)
  873. do 77 i=1,(nsp-1)
  874. jl.jac(2,5+i)=damg_l*dgdyl.vv(i)*(f.fu(2)-pmid*n_x)/am+
  875. & dpiy_l.vv(i)*n_x
  876. jl.jac(2,5+i)=jl.jac(2,5+i)+
  877. & am*(dffy_l.vv(i)*n_x+dfsy_l.vv(i)*t1_x)
  878. jl.jac(2,5+i)=jl.jac(2,5+i)+am*(dfty_l.vv(i)*t2_x)
  879. 77 continue
  880. c---------------------------------------------------------
  881. f.fu(3)=am*(ff*n_y+fs*t1_y+ft*t2_y)+pmid*n_y
  882. c-------------------------------------------------
  883. jl.jac(3,1)=damr_l*(f.fu(3)-pmid*n_y)/am+dpir_l*n_y
  884. jl.jac(3,1)=jl.jac(3,1)+am*(dffr*n_y+dfsr*t1_y+dftr*t2_y)
  885. jl.jac(3,2)=damu_l*(f.fu(3)-pmid*n_y)/am+dpiu_l*n_y
  886. jl.jac(3,2)=jl.jac(3,2)+am*(dffu*n_y+dfsu*t1_y+dftu*t2_y)
  887. jl.jac(3,3)=damv_l*(f.fu(3)-pmid*n_y)/am+dpiv_l*n_y
  888. jl.jac(3,3)=jl.jac(3,3)+am*(dffv*n_y+dfsv*t1_y+dftv*t2_y)
  889. jl.jac(3,4)=damw_l*(f.fu(3)-pmid*n_y)/am+dpiw_l*n_y
  890. jl.jac(3,4)=jl.jac(3,4)+am*(dffw*n_y+dfsw*t1_y+dftw*t2_y)
  891. jl.jac(3,5)=damp_l*(f.fu(3)-pmid*n_y)/am+dpip_l*n_y
  892. jl.jac(3,5)=jl.jac(3,5)+am*(dffp*n_y+dfsp*t1_y+dftp*t2_y)
  893. do 78 i=1,(nsp-1)
  894. jl.jac(3,5+i)=damg_l*dgdyl.vv(i)*(f.fu(3)-pmid*n_y)/am+
  895. & dpiy_l.vv(i)*n_y
  896. jl.jac(3,5+i)=jl.jac(3,5+i)+
  897. & am*(dffy_l.vv(i)*n_y+dfsy_l.vv(i)*t1_y)
  898. jl.jac(3,5+i)=jl.jac(3,5+i)+am*(dfty_l.vv(i)*t2_y)
  899. 78 continue
  900. c-------------------------------------------------
  901. f.fu(4)=am*(ff*n_z+fs*t1_z+ft*t2_z)+pmid*n_z
  902. c-------------------------------------------------
  903. jl.jac(4,1)=damr_l*(f.fu(4)-pmid*n_z)/am+dpir_l*n_z
  904. jl.jac(4,1)=jl.jac(4,1)+am*(dffr*n_z+dfsr*t1_z+dftr*t2_z)
  905. jl.jac(4,2)=damu_l*(f.fu(4)-pmid*n_z)/am+dpiu_l*n_z
  906. jl.jac(4,2)=jl.jac(4,2)+am*(dffu*n_z+dfsu*t1_z+dftu*t2_z)
  907. jl.jac(4,3)=damv_l*(f.fu(4)-pmid*n_z)/am+dpiv_l*n_z
  908. jl.jac(4,3)=jl.jac(4,3)+am*(dffv*n_z+dfsv*t1_z+dftv*t2_z)
  909. jl.jac(4,4)=damw_l*(f.fu(4)-pmid*n_z)/am+dpiw_l*n_z
  910. jl.jac(4,4)=jl.jac(4,4)+am*(dffw*n_z+dfsw*t1_z+dftw*t2_z)
  911. jl.jac(4,5)=damp_l*(f.fu(4)-pmid*n_z)/am+dpip_l*n_z
  912. jl.jac(4,5)=jl.jac(4,5)+am*(dffp*n_z+dfsp*t1_z+dftp*t2_z)
  913. do 79 i=1,(nsp-1)
  914. jl.jac(4,5+i)=damg_l*dgdyl.vv(i)*(f.fu(4)-pmid*n_z)/am+
  915. & dpiy_l.vv(i)*n_z
  916. jl.jac(4,5+i)=jl.jac(4,5+i)+
  917. & am*(dffy_l.vv(i)*n_z+dfsy_l.vv(i)*t1_z)
  918. jl.jac(4,5+i)=jl.jac(4,5+i)+am*(dfty_l.vv(i)*t2_z)
  919. 79 continue
  920. c---------------------------------------------------
  921. c derivatives with respect to the right
  922. c set of the primitive variables
  923. c-------------------------------------------------------
  924. dffr=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  925. dffu=d2mu_r*rold_l*un_l+mmin_m*rold_r*c11/det
  926. dffu=dffu+d3mu_r*rold_r*un_r
  927. dffv=d2mv_r*rold_l*un_l+mmin_m*rold_r*c12/det
  928. dffv=dffv+d3mv_r*rold_r*un_r
  929. dffw=d2mw_r*rold_l*un_l+mmin_m*rold_r*c13/det
  930. dffw=dffw+d3mw_r*rold_r*un_r
  931. dffp=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  932. do 80 i=1,(nsp-1)
  933. dffy_r.vv(i)=d2my_r.vv(i)*rold_l*un_l+
  934. & d3my_r.vv(i)*rold_r*un_r
  935. 80 continue
  936. c------------------------------------------------------
  937. dfsr=d2mr_r*rold_l*ut1_l+mmin_m*ut1_r
  938. dfsr=dfsr+d3mr_r*rold_r*ut1_r
  939. dfsu=d2mu_r*rold_l*ut1_l+mmin_m*rold_r*c21/det
  940. dfsu=dfsu+d3mu_r*rold_r*ut1_r
  941. dfsv=d2mv_r*rold_l*ut1_l+mmin_m*rold_r*c22/det
  942. dfsv=dfsv+d3mv_r*rold_r*ut1_r
  943. dfsw=d2mw_r*rold_l*ut1_l+mmin_m*rold_r*c23/det
  944. dfsw=dfsw+d3mw_r*rold_r*ut1_r
  945. dfsp=d2mp_r*rold_l*ut1_l+d3mp_r*rold_r*ut1_r
  946. do 81 i=1,(nsp-1)
  947. dfsy_r.vv(i)=d2my_r.vv(i)*rold_l*ut1_l+
  948. & d3my_r.vv(i)*rold_r*ut1_r
  949. 81 continue
  950. c------------------------------------------------------
  951. dftr=d2mr_r*rold_l*ut2_l+mmin_m*ut2_r
  952. dftr=dftr+d3mr_r*rold_r*ut2_r
  953. dftu=d2mu_r*rold_l*ut2_l+mmin_m*rold_r*c31/det
  954. dftu=dftu+d3mu_r*rold_r*ut2_r
  955. dftv=d2mv_r*rold_l*ut2_l+mmin_m*rold_r*c32/det
  956. dftv=dftv+d3mv_r*rold_r*ut2_r
  957. dftw=d2mw_r*rold_l*ut2_l+mmin_m*rold_r*c33/det
  958. dftw=dftw+d3mw_r*rold_r*ut2_r
  959. dftp=d2mp_r*rold_l*ut2_l+d3mp_r*rold_r*ut2_r
  960. do 83 i=1,(nsp-1)
  961. dfty_r.vv(i)=d2my_r.vv(i)*rold_l*ut2_l+
  962. & d3my_r.vv(i)*rold_r*ut2_r
  963. 83 continue
  964. c-------------------------------------------------------
  965. jr.jac(2,1)=damr_r*(f.fu(2)-pmid*n_x)/am+dpir_r*n_x
  966. jr.jac(2,1)=jr.jac(2,1)+am*(dffr*n_x+dfsr*t1_x+dftr*t2_x)
  967. jr.jac(2,2)=damu_r*(f.fu(2)-pmid*n_x)/am+dpiu_r*n_x
  968. jr.jac(2,2)=jr.jac(2,2)+am*(dffu*n_x+dfsu*t1_x+dftu*t2_x)
  969. jr.jac(2,3)=damv_r*(f.fu(2)-pmid*n_x)/am+dpiv_r*n_x
  970. jr.jac(2,3)=jr.jac(2,3)+am*(dffv*n_x+dfsv*t1_x+dftv*t2_x)
  971. jr.jac(2,4)=damw_r*(f.fu(2)-pmid*n_x)/am+dpiw_r*n_x
  972. jr.jac(2,4)=jr.jac(2,4)+am*(dffw*n_x+dfsw*t1_x+dftw*t2_x)
  973. jr.jac(2,5)=damp_r*(f.fu(2)-pmid*n_x)/am+dpip_r*n_x
  974. jr.jac(2,5)=jr.jac(2,5)+am*(dffp*n_x+dfsp*t1_x+dftp*t2_x)
  975. do 84 i=1,(nsp-1)
  976. jr.jac(2,5+i)=damg_r*dgdyr.vv(i)*(f.fu(2)-pmid*n_x)/am+
  977. & dpiy_r.vv(i)*n_x
  978. jr.jac(2,5+i)=jr.jac(2,5+i)+am*(dffy_r.vv(i)*n_x+
  979. & dfsy_r.vv(i)*t1_x)
  980. jr.jac(2,5+i)=jr.jac(2,5+i)+am*(dfty_r.vv(i)*t2_x)
  981. 84 continue
  982. c-------------------------------------------------------
  983. jr.jac(3,1)=damr_r*(f.fu(3)-pmid*n_y)/am+dpir_r*n_y
  984. jr.jac(3,1)=jr.jac(3,1)+am*(dffr*n_y+dfsr*t1_y+dftr*t2_y)
  985. jr.jac(3,2)=damu_r*(f.fu(3)-pmid*n_y)/am+dpiu_r*n_y
  986. jr.jac(3,2)=jr.jac(3,2)+am*(dffu*n_y+dfsu*t1_y+dftu*t2_y)
  987. jr.jac(3,3)=damv_r*(f.fu(3)-pmid*n_y)/am+dpiv_r*n_y
  988. jr.jac(3,3)=jr.jac(3,3)+am*(dffv*n_y+dfsv*t1_y+dftv*t2_y)
  989. jr.jac(3,4)=damw_r*(f.fu(3)-pmid*n_y)/am+dpiw_r*n_y
  990. jr.jac(3,4)=jr.jac(3,4)+am*(dffw*n_y+dfsw*t1_y+dftw*t2_y)
  991. jr.jac(3,5)=damp_r*(f.fu(3)-pmid*n_y)/am+dpip_r*n_y
  992. jr.jac(3,5)=jr.jac(3,5)+am*(dffp*n_y+dfsp*t1_y+dftp*t2_y)
  993. do 85 i=1,(nsp-1)
  994. jr.jac(3,5+i)=damg_r*dgdyr.vv(i)*(f.fu(3)-pmid*n_y)/am+
  995. & dpiy_r.vv(i)*n_y
  996. jr.jac(3,5+i)=jr.jac(3,5+i)+am*(dffy_r.vv(i)*n_y+
  997. & dfsy_r.vv(i)*t1_y)
  998. jr.jac(3,5+i)=jr.jac(3,5+i)+am*(dfty_r.vv(i)*t2_y)
  999. 85 continue
  1000. c--------------------------------------------------------
  1001. jr.jac(4,1)=damr_r*(f.fu(4)-pmid*n_z)/am+dpir_r*n_z
  1002. jr.jac(4,1)=jr.jac(4,1)+am*(dffr*n_z+dfsr*t1_z+dftr*t2_z)
  1003. jr.jac(4,2)=damu_r*(f.fu(4)-pmid*n_z)/am+dpiu_r*n_z
  1004. jr.jac(4,2)=jr.jac(4,2)+am*(dffu*n_z+dfsu*t1_z+dftu*t2_z)
  1005. jr.jac(4,3)=damv_r*(f.fu(4)-pmid*n_z)/am+dpiv_r*n_z
  1006. jr.jac(4,3)=jr.jac(4,3)+am*(dffv*n_z+dfsv*t1_z+dftv*t2_z)
  1007. jr.jac(4,4)=damw_r*(f.fu(4)-pmid*n_z)/am+dpiw_r*n_z
  1008. jr.jac(4,4)=jr.jac(4,4)+am*(dffw*n_z+dfsw*t1_z+dftw*t2_z)
  1009. jr.jac(4,5)=damp_r*(f.fu(4)-pmid*n_z)/am+dpip_r*n_z
  1010. jr.jac(4,5)=jr.jac(4,5)+am*(dffp*n_z+dfsp*t1_z+dftp*t2_z)
  1011. do 86 i=1,(nsp-1)
  1012. jr.jac(4,5+i)=damg_r*dgdyr.vv(i)*(f.fu(4)-pmid*n_z)/am+
  1013. & dpiy_r.vv(i)*n_z
  1014. jr.jac(4,5+i)=jr.jac(4,5+i)+am*(dffy_r.vv(i)*n_z+
  1015. & dfsy_r.vv(i)*t1_z)
  1016. jr.jac(4,5+i)=jr.jac(4,5+i)+am*(dfty_r.vv(i)*t2_z)
  1017. 86 continue
  1018. c-------------------------------------------------------
  1019. c-------------------------------------------------------
  1020. c-------------------------------------------------------
  1021. hr_l=(eold_l+pold_l/rold_l)*rold_l
  1022. hr_r=(eold_r+pold_r/rold_r)*rold_r
  1023. f.fu(5)=am*(mpl_m*hr_l+mmin_m*hr_r)
  1024. c-------------------------------------------------
  1025. br1=d2mr_l*hr_l+d3mr_l*hr_r
  1026. br1=br1+mpl_m*(uold_l*uold_l+vold_l*vold_l+
  1027. & wold_l*wold_l)/2.0d0
  1028. jl.jac(5,1)=damr_l*f.fu(5)/am+am*br1
  1029. c-------------------------------------------------
  1030. br1=d2mu_l*hr_l+mpl_m*uold_l*rold_l
  1031. br1=br1+d3mu_l*hr_r
  1032. jl.jac(5,2)=damu_l*f.fu(5)/am+am*br1
  1033. c-------------------------------------------------
  1034. br1=d2mv_l*hr_l+mpl_m*vold_l*rold_l
  1035. br1=br1+d3mv_l*hr_r
  1036. jl.jac(5,3)=damv_l*f.fu(5)/am+am*br1
  1037. c-------------------------------------------------
  1038. br1=d2mw_l*hr_l+mpl_m*wold_l*rold_l
  1039. br1=br1+d3mw_l*hr_r
  1040. jl.jac(5,4)=damw_l*f.fu(5)/am+am*br1
  1041. c-------------------------------------------------
  1042. br1=d2mp_l*hr_l+mpl_m*gal/gm1l
  1043. br1=br1+d3mp_l*hr_r
  1044. jl.jac(5,5)=damp_l*f.fu(5)/am+am*br1
  1045. c-------------------------------------------------
  1046. do 87 i=1,(nsp-1)
  1047. br1=d2my_l.vv(i)*hr_l+mpl_m*(-pold_l)*
  1048. & dgdyl.vv(i)/(gm1l*gm1l)
  1049. br1=br1+d3my_l.vv(i)*hr_r
  1050. jl.jac(5,5+i)=damg_l*dgdyl.vv(i)*f.fu(5)/am+am*br1
  1051. 87 continue
  1052. c-------------------------------------------------------------
  1053. c------------------------- f5 ------------------------------
  1054. c-------------------------------------------------------------
  1055. do 180 i=1,(nsp-1)
  1056. f.fu(5+i)=am*(mpl_m*rold_l*yl.yet(i)+mmin_m*rold_r*yr.yet(i))
  1057. c---------------------
  1058. jl.jac(5+i,1)=damr_l*f.fu(5+i)/am+
  1059. & am*(d2mr_l*rold_l*yl.yet(i)+mpl_m*yl.yet(i))
  1060. jl.jac(5+i,1)=jl.jac(5+i,1)+am*d3mr_l*rold_r*yr.yet(i)
  1061. jl.jac(5+i,2)=damu_l*f.fu(5+i)/am+am*(d2mu_l*rold_l*yl.yet(i)+
  1062. & d3mu_l*rold_r*yr.yet(i))
  1063. jl.jac(5+i,3)=damv_l*f.fu(5+i)/am+am*(d2mv_l*rold_l*yl.yet(i)+
  1064. & d3mv_l*rold_r*yr.yet(i))
  1065. jl.jac(5+i,4)=damw_l*f.fu(5+i)/am+am*(d2mw_l*rold_l*yl.yet(i)+
  1066. & d3mw_l*rold_r*yr.yet(i))
  1067. jl.jac(5+i,5)=damp_l*f.fu(5+i)/am+am*(d2mp_l*rold_l*yl.yet(i)+
  1068. & d3mp_l*rold_r*yr.yet(i))
  1069. do 181 j=6,(4+nsp)
  1070. if((5+i).eq.j) then
  1071. jl.jac(5+i,j)=damg_l*dgdyl.vv(j-5)*f.fu(5+i)/am+
  1072. & am*(d2my_l.vv(j-5)*rold_l*yl.yet(i)+mpl_m*rold_l+
  1073. & d3my_l.vv(j-5)*rold_r*yr.yet(i))
  1074. else
  1075. jl.jac(5+i,j)=damg_l*dgdyl.vv(j-5)*f.fu(5+i)/am+
  1076. & am*(d2my_l.vv(j-5)*rold_l*yl.yet(i)+
  1077. & d3my_l.vv(j-5)*rold_r*yr.yet(i))
  1078. endif
  1079. 181 continue
  1080. 180 continue
  1081. c-------------------------------------------------
  1082. br1=d2mr_r*hr_l+d3mr_r*hr_r
  1083. br1=br1+mmin_m*(uold_r*uold_r+vold_r*vold_r+
  1084. & wold_r*wold_r)/2.0d0
  1085. jr.jac(5,1)=damr_r*f.fu(5)/am+am*br1
  1086. c---------------------
  1087. br1=d2mu_r*hr_l+mmin_m*uold_r*rold_r
  1088. br1=br1+d3mu_r*hr_r
  1089. jr.jac(5,2)=damu_r*f.fu(5)/am+am*br1
  1090. c---------------------
  1091. br1=d2mv_r*hr_l+mmin_m*vold_r*rold_r
  1092. br1=br1+d3mv_r*hr_r
  1093. jr.jac(5,3)=damv_r*f.fu(5)/am+am*br1
  1094. c---------------------
  1095. br1=d2mw_r*hr_l+mmin_m*wold_r*rold_r
  1096. br1=br1+d3mw_r*hr_r
  1097. jr.jac(5,4)=damw_r*f.fu(5)/am+am*br1
  1098. c---------------------
  1099. br1=d2mp_r*hr_l+mmin_m*gar/gm1r
  1100. br1=br1+d3mp_r*hr_r
  1101. jr.jac(5,5)=damp_r*f.fu(5)/am+am*br1
  1102. c---------------------
  1103. do 88 i=1,(nsp-1)
  1104. br1=d2my_r.vv(i)*hr_l+mmin_m*(-pold_r)*
  1105. & dgdyr.vv(i)/(gm1r*gm1r)
  1106. br1=br1+d3my_r.vv(i)*hr_r
  1107. jr.jac(5,5+i)=damg_r*dgdyr.vv(i)*f.fu(5)/am+am*br1
  1108. 88 continue
  1109. c----------------------------------------------------------------
  1110. do 182 i=1,(nsp-1)
  1111. jr.jac(5+i,1)=damr_r*f.fu(5+i)/am+am*(d2mr_r*rold_l*yl.yet(i)+
  1112. & mmin_m*yr.yet(i))
  1113. jr.jac(5+i,1)=jr.jac(5+i,1)+am*d3mr_r*rold_r*yr.yet(i)
  1114. jr.jac(5+i,2)=damu_r*f.fu(5+i)/am+am*(d2mu_r*rold_l*yl.yet(i)+
  1115. & d3mu_r*rold_r*yr.yet(i))
  1116. jr.jac(5+i,3)=damv_r*f.fu(5+i)/am+am*(d2mv_r*rold_l*yl.yet(i)+
  1117. & d3mv_r*rold_r*yr.yet(i))
  1118. jr.jac(5+i,4)=damw_r*f.fu(5+i)/am+am*(d2mw_r*rold_l*yl.yet(i)+
  1119. & d3mw_r*rold_r*yr.yet(i))
  1120. jr.jac(5+i,5)=damp_r*f.fu(5+i)/am+am*(d2mp_r*rold_l*yl.yet(i)+
  1121. & d3mp_r*rold_r*yr.yet(i))
  1122. do 183 j=1,(nsp-1)
  1123. if(i.eq.j) then
  1124. jr.jac(5+i,5+j)=damg_r*dgdyr.vv(j)*f.fu(5+i)/am+
  1125. & am*(d2my_r.vv(j)*rold_l*yl.yet(i)+mmin_m*rold_r+
  1126. & d3my_r.vv(j)*rold_r*yr.yet(i))
  1127. else
  1128. jr.jac(5+i,5+j)=damg_r*dgdyr.vv(j)*f.fu(5+i)/am+
  1129. & am*(d2my_r.vv(j)*rold_l*yl.yet(i)+
  1130. & d3my_r.vv(j)*rold_r*yr.yet(i))
  1131. endif
  1132. 183 continue
  1133. 182 continue
  1134. c------------------------------------------------------------
  1135. c matrix wl(i,j) represents the derivative of the i-component
  1136. c of the vector of primitive variables of the left state with
  1137. c respect to the j-component of the vector of the conservative
  1138. c variables of the left state.
  1139. c
  1140. c Here: (rho, ux, uy, uz, p, Y_1,...,Y_(nsp-1)) -
  1141. c vector of primitive variables;
  1142. c (rho, rho ux, rho uy, rho uz, rho e, rho Y_1,..., rho Y_(nsp-1))
  1143. c vector of conservative variables.
  1144. c------------------------------------------------------------
  1145. wl.jac(1,1)=1.0d0
  1146. wl.jac(1,2)=0.0d0
  1147. wl.jac(1,3)=0.0d0
  1148. wl.jac(1,4)=0.0d0
  1149. wl.jac(1,5)=0.0d0
  1150. do 89 i=1,(nsp-1)
  1151. wl.jac(1,5+i)=0.0d0
  1152. 89 continue
  1153. c------------------------------
  1154. wl.jac(2,1)=-uold_l/rold_l
  1155. wl.jac(2,2)=1.0d0/rold_l
  1156. wl.jac(2,3)=0.0d0
  1157. wl.jac(2,4)=0.0d0
  1158. wl.jac(2,5)=0.0d0
  1159. do 90 i=1,(nsp-1)
  1160. wl.jac(2,5+i)=0.0d0
  1161. 90 continue
  1162. c------------------------------
  1163. wl.jac(3,1)=-vold_l/rold_l
  1164. wl.jac(3,2)=0.0d0
  1165. wl.jac(3,3)=1.0d0/rold_l
  1166. wl.jac(3,4)=0.0d0
  1167. wl.jac(3,5)=0.0d0
  1168. do 91 i=1,(nsp-1)
  1169. wl.jac(3,5+i)=0.0d0
  1170. 91 continue
  1171. c------------------------------
  1172. wl.jac(4,1)=-wold_l/rold_l
  1173. wl.jac(4,2)=0.0d0
  1174. wl.jac(4,3)=0.0d0
  1175. wl.jac(4,4)=1.0d0/rold_l
  1176. wl.jac(4,5)=0.0d0
  1177. do 92 i=1,(nsp-1)
  1178. wl.jac(4,5+i)=0.0d0
  1179. 92 continue
  1180. c------------------------------
  1181. br1=0.0d0
  1182. do 93 i=1,(nsp-1)
  1183. br1=br1+dgdyl.vv(i)*yl.yet(i)
  1184. 93 continue
  1185. br1=br1*pold_l/(rold_l*gm1l)
  1186. wl.jac(5,1)=gm1l*(uold_l*uold_l+vold_l*vold_l+
  1187. & wold_l*wold_l)/2.0d0
  1188. wl.jac(5,1)=wl.jac(5,1)-br1
  1189. wl.jac(5,2)=-uold_l*gm1l
  1190. wl.jac(5,3)=-vold_l*gm1l
  1191. wl.jac(5,4)=-wold_l*gm1l
  1192. wl.jac(5,5)=gm1l
  1193. do 94 i=1,(nsp-1)
  1194. wl.jac(5,5+i)=dgdyl.vv(i)*pold_l/(rold_l*gm1l)
  1195. 94 continue
  1196. c------------------------------
  1197. do 95 i=1,(nsp-1)
  1198. do 96 j=1,5
  1199. wl.jac(5+i,j)=0.0d0
  1200. if(j.eq.1) wl.jac(5+i,j)=-yl.yet(i)/rold_l
  1201. 96 continue
  1202. c---------------------
  1203. do 960 j=6,(4+nsp)
  1204. wl.jac(5+i,j)=0.0d0
  1205. if(5+i.eq.j) then
  1206. wl.jac(5+i,j)=1.0d0/rold_l
  1207. endif
  1208. 960 continue
  1209. 95 continue
  1210. c------------------------------
  1211. wr.jac(1,1)=1.0d0
  1212. wr.jac(1,2)=0.0d0
  1213. wr.jac(1,3)=0.0d0
  1214. wr.jac(1,4)=0.0d0
  1215. wr.jac(1,5)=0.0d0
  1216. do 97 i=1,(nsp-1)
  1217. wr.jac(1,5+i)=0.0d0
  1218. 97 continue
  1219. c------------------------------
  1220. wr.jac(2,1)=-uold_r/rold_r
  1221. wr.jac(2,2)=1.0d0/rold_r
  1222. wr.jac(2,3)=0.0d0
  1223. wr.jac(2,4)=0.0d0
  1224. wr.jac(2,5)=0.0d0
  1225. do 98 i=1,(nsp-1)
  1226. wr.jac(2,5+i)=0.0d0
  1227. 98 continue
  1228. c------------------------------
  1229. wr.jac(3,1)=-vold_r/rold_r
  1230. wr.jac(3,2)=0.0d0
  1231. wr.jac(3,3)=1.0d0/rold_r
  1232. wr.jac(3,4)=0.0d0
  1233. wr.jac(3,5)=0.0d0
  1234. do 99 i=1,(nsp-1)
  1235. wr.jac(3,5+i)=0.0d0
  1236. 99 continue
  1237. c------------------------------
  1238. wr.jac(4,1)=-wold_r/rold_r
  1239. wr.jac(4,2)=0.0d0
  1240. wr.jac(4,3)=0.0d0
  1241. wr.jac(4,4)=1.0d0/rold_r
  1242. wr.jac(4,5)=0.0d0
  1243. do 100 i=1,(nsp-1)
  1244. wr.jac(4,5+i)=0.0d0
  1245. 100 continue
  1246. c------------------------------
  1247. br1=0.0d0
  1248. do 101 i=1,(nsp-1)
  1249. br1=br1+dgdyr.vv(i)*yr.yet(i)
  1250. 101 continue
  1251. br1=br1*pold_r/(rold_r*gm1r)
  1252. wr.jac(5,1)=gm1r*(uold_r*uold_r+vold_r*vold_r+
  1253. & wold_r*wold_r)/2.0d0
  1254. wr.jac(5,1)=wr.jac(5,1)-br1
  1255. wr.jac(5,2)=-uold_r*gm1r
  1256. wr.jac(5,3)=-vold_r*gm1r
  1257. wr.jac(5,4)=-wold_r*gm1r
  1258. wr.jac(5,5)=gm1r
  1259. do 102 i=1,(nsp-1)
  1260. wr.jac(5,5+i)=dgdyr.vv(i)*pold_r/(rold_r*gm1r)
  1261. 102 continue
  1262. c----------------------------------------------
  1263. do 103 i=1,(nsp-1)
  1264. do 104 j=1,5
  1265. wr.jac(5+i,j)=0.0d0
  1266. if(j.eq.1) wr.jac(5+i,j)=-yr.yet(i)/rold_r
  1267. 104 continue
  1268. c---------------------
  1269. do 1040 j=6,(4+nsp)
  1270. wr.jac(5+i,j)=0.0d0
  1271. if(5+i.eq.j) wr.jac(5+i,j)=1.0d0/rold_r
  1272. 1040 continue
  1273. 103 continue
  1274. c----------------------------------------------
  1275. c----------------------------------------------
  1276. do 1 i=1,(4+nsp)
  1277. do 2 j=1,(4+nsp)
  1278. jtl.jac(i,j)=0.0d0
  1279. jtr.jac(i,j)=0.0d0
  1280. do 3 k=1,(4+nsp)
  1281. jtl.jac(i,j)=jtl.jac(i,j)+jl.jac(i,k)*wl.jac(k,j)
  1282. jtr.jac(i,j)=jtr.jac(i,j)+jr.jac(i,k)*wr.jac(k,j)
  1283. 3 continue
  1284. 2 continue
  1285. 1 continue
  1286. c----------------------------------------------------------------------
  1287. SEGSUP DMLY_L, DMLY_R,
  1288. & dmry_l, dmry_r,
  1289. & dMpy_l, dMpy_r,
  1290. & dMmy_l, dMmy_r,
  1291. & dmiy_l, dmiy_r,
  1292. & d3my_l, d3my_r,
  1293. & d2my_l, d2my_r,
  1294. & dPpy_l, dPpy_r,
  1295. & dPmy_l, dPmy_r,
  1296. & dpiy_l, dpiy_r,
  1297. & dgdyl, dgdyr,
  1298. & dffy_l,dffy_r,
  1299. & dfsy_l,dfsy_r,
  1300. & dfty_l,dfty_r
  1301. C--------------------------------------------
  1302. SEGSUP f
  1303. C--------------------------------------------
  1304. SEGSUP JL
  1305. SEGSUP JR
  1306. SEGSUP WL
  1307. SEGSUP WR
  1308. C--------------------------------------------
  1309. jll=jtl
  1310. SEGDES JTL
  1311. jrr=jtr
  1312. SEGDES JTR
  1313. SEGDES YL
  1314. SEGDES YR
  1315. SEGDES CP
  1316. SEGDES CV
  1317. SEGDES MLRECP, MLRECV
  1318. C--------------------------------------------
  1319. return
  1320. end
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