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  1. C COPMS2 SOURCE HP1 07/12/05 21:15:11 5991
  2. SUBROUTINE COPMS2(NSP,JLL,JRR,WVEC_L,WVEC_R,NVECT,TVECT,
  3. & yh,mpyn,lrecp,lrecv,nlcd)
  4. C************************************************************************
  5. C
  6. C PROJET : CASTEM 2000
  7. C
  8. C NOM : COPMS2 ('convection for multispecies')
  9. C
  10. C DESCRIPTION : (appele par CLI262) - jacobian
  11. C wrt primitive variables for multiespeces
  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 primitive variables of the left and right
  23. c cells (relative to the cell interface).
  24. c
  25. c EQUATIONS: 2D 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,p) at the left cell;
  43. c
  44. c wvec_r -- vector of the primitive variables
  45. c (rho,u_x,u_y,p) at the right cell;
  46. c
  47. c nvect -- normal vector to the interface (2 components in 2D);
  48. c
  49. c tvect -- tangential vector to the interface;
  50. c
  51. c mpyn -- pointer to the vectors of the primitive variables
  52. c (Y_1,Y_2,...Y_(nsp-1)) at the left and the right cells;
  53. c
  54. c lrecp -- pointer to the vector of specific heats at constant pressure
  55. c (size of the vector is equal to number of species (nsp));
  56. c
  57. c lrecv -- pointer to the vector of specific heats at constant volume
  58. c (size of the vector is equal to number of species (nsp));
  59. c
  60. c nlcd -- "local" number corresponding to the right cell;
  61. c----------------------------------------------------------------------
  62. c
  63. c OUTPUT:
  64. c
  65. c jll -- jakobian matrix (3+nsp) by (3+nsp) -
  66. c derivatives of the numerical
  67. c flux function with respect to the primitive variables
  68. c from the left cell;
  69. c
  70. c jrr -- jakobian matrix (3+nsp) by (3+nsp) -
  71. c derivatives of the numerical
  72. c flux function with respect to the primitive variables
  73. c from the right cell.
  74. c----------------------------------------------------------------------
  75. IMPLICIT INTEGER(I-N)
  76. integer nsp,jll,jrr,lrecp,lrecv,nlcd
  77. real*8 wvec_l(4),wvec_r(4)
  78. real*8 nvect(2),tvect(2)
  79. real*8 alpha,beta
  80. real*8 gal,gar,gm1l,gm1r,temph
  81. real*8 n_x,n_y,t_x,t_y
  82. real*8 un_l, un_r, ut_l, ut_r
  83. real*8 ml,mr,Mplus,Mmin,mmid
  84. real*8 mpl_m, mmin_m,am
  85. real*8 rold_l,uold_l,vold_l,pold_l,eold_l
  86. real*8 rold_r,uold_r,vold_r,pold_r,eold_r
  87. real*8 Pplus,Pmin,pmid
  88. real*8 hr_l,hr_r,det,top,bot
  89. real*8 br1,br2,br3,br4,temp_l,temp_r,brac_l,brac_r
  90. real*8 aleft, arigh
  91. real*8 damr_l,damr_r,damu_l,damu_r
  92. real*8 damv_l,damv_r,damp_l,damp_r
  93. real*8 damg_l,damg_r
  94. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  95. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  96. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  97. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  98. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  99. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r
  100. real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r
  101. real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r
  102. real*8 dmir_l,dmir_r,dmiu_l,dmiu_r
  103. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  104. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  105. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  106. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  107. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  108. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  109. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  110. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  111. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  112. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  113. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  114. integer i,j
  115. parameter(alpha = 0.1875D0, beta = 0.125D0)
  116. C------------------------------------------------------------
  117. -INC SMCHPOI
  118. POINTEUR MPYN.MPOVAL
  119. C-------------------------------------------------------------
  120. -INC SMLREEL
  121. POINTEUR MLRECP.MLREEL, MLRECV.MLREEL
  122. C-------------------------------------------------------------
  123. C******* Les fractionines massiques **************************
  124. C-------------------------------------------------------------
  125. SEGMENT FRAMAS
  126. REAL*8 YET(NSP)
  127. ENDSEGMENT
  128. POINTEUR YL.FRAMAS, YR.FRAMAS, YH.FRAMAS
  129. C-------------------------------------------------------
  130. C********** Les CP's and CV's ***********************
  131. C-------------------------------------------------------
  132. SEGMENT GCONST
  133. REAL*8 GC(NSP)
  134. ENDSEGMENT
  135. POINTEUR CP.GCONST, CV.GCONST
  136. C-------------------------------------------------------------
  137. C******** Segments for the elementary matrixes *************
  138. C-------------------------------------------------------------
  139. SEGMENT JACEL
  140. REAL*8 JAC(3+NSP,3+NSP)
  141. ENDSEGMENT
  142. POINTEUR JL.JACEL, JR.JACEL
  143. c----------------------------------------
  144. SEGINI JL
  145. SEGINI JR
  146. C-------------------------------------------------------------
  147. C********** Segments for the vectors ***********************
  148. C-------------------------------------------------------------
  149. SEGMENT VECEL
  150. REAL*8 VV(NSP)
  151. ENDSEGMENT
  152. POINTEUR DMLY_L.VECEL, DMLY_R.VECEL,
  153. & dmry_l.vecel, dmry_r.vecel,
  154. & dMpy_l.vecel, dMpy_r.vecel,
  155. & dMmy_l.vecel, dMmy_r.vecel,
  156. & dmiy_l.vecel, dmiy_r.vecel,
  157. & d3my_l.vecel, d3my_r.vecel,
  158. & d2my_l.vecel, d2my_r.vecel,
  159. & dPpy_l.vecel, dPpy_r.vecel,
  160. & dPmy_l.vecel, dPmy_r.vecel,
  161. & dpiy_l.vecel, dpiy_r.vecel,
  162. & dgdyl.vecel, dgdyr.vecel
  163. C----------------------------------------------
  164. SEGINI DMLY_L, DMLY_R,
  165. & dmry_l, dmry_r,
  166. & dMpy_l, dMpy_r,
  167. & dMmy_l, dMmy_r,
  168. & dmiy_l, dmiy_r,
  169. & d3my_l, d3my_r,
  170. & d2my_l, d2my_r,
  171. & dPpy_l, dPpy_r,
  172. & dPmy_l, dPmy_r,
  173. & dpiy_l, dpiy_r,
  174. & dgdyl, dgdyr
  175. C-------------------------------------------------------------
  176. C********** Segments for the flux-vector *******************
  177. C-------------------------------------------------------------
  178. SEGMENT FUNEL
  179. REAL*8 FU(3+NSP)
  180. ENDSEGMENT
  181. POINTEUR f.funel
  182. C-------------------------
  183. SEGINI f
  184. C------------------------------------------------------------
  185. SEGINI YL, YR
  186. SEGACT MPYN
  187. c SEGACT MPLIN
  188. DO 100 I=1,(NSP-1)
  189. YL.YET(I)=YH.YET(I)
  190. YR.YET(I)=MPYN.VPOCHA(NLCD,I)
  191. 100 CONTINUE
  192. C----------------------------------------
  193. SEGINI CP, CV
  194. MLRECP = LRECP
  195. MLRECV = LRECV
  196. SEGACT MLRECP, MLRECV
  197. DO 101 I=1,(NSP-1)
  198. CP.GC(I)=MLRECP.PROG(I)
  199. CV.GC(I)=MLRECV.PROG(I)
  200. 101 CONTINUE
  201. CP.GC(NSP)=MLRECP.PROG(NSP)
  202. CV.GC(NSP)=MLRECV.PROG(NSP)
  203. c-------------------------------------------------------------
  204. c Computing GAMMA at the left cell and its derivatives
  205. c with respect to the primitive variables Y_i
  206. c-------------------------------------------------------------
  207. top=0.0D0
  208. bot=0.0D0
  209. do 40 i=1,(nsp-1)
  210. top=top+yl.yet(i)*(cp.gc(i)-cp.gc(nsp))
  211. bot=bot+yl.yet(i)*(cv.gc(i)-cv.gc(nsp))
  212. 40 continue
  213. top=cp.gc(nsp)+top
  214. bot=cv.gc(nsp)+bot
  215. gal=top/bot
  216. gm1l=gal-1.0d0
  217. c-------------------------------------------------------------
  218. do 41 i=1,(nsp-1)
  219. dgdyl.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  220. & gal*(cv.gc(i)-cv.gc(nsp)))/bot
  221. 41 continue
  222. c-------------------------------------------------------------
  223. c Computing GAMMA at the right cell and its derivatives
  224. c with respect to the primitive variables Y_i
  225. c-------------------------------------------------------------
  226. top=0.0D0
  227. bot=0.0D0
  228. do 42 i=1,(nsp-1)
  229. top=top+yr.yet(i)*(cp.gc(i)-cp.gc(nsp))
  230. bot=bot+yr.yet(i)*(cv.gc(i)-cv.gc(nsp))
  231. 42 continue
  232. top=cp.gc(nsp)+top
  233. bot=cv.gc(nsp)+bot
  234. gar=top/bot
  235. gm1r=gar-1.0d0
  236. c-------------------------------------------------------------
  237. do 43 i=1,(nsp-1)
  238. dgdyr.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  239. & gar*(cv.gc(i)-cv.gc(nsp)))/bot
  240. 43 continue
  241. c-------------------------------------------------------------
  242. n_x=nvect(1)
  243. n_y=nvect(2)
  244. t_x=tvect(1)
  245. t_y=tvect(2)
  246. c----------------------------
  247. c----------------------------
  248. rold_l=wvec_l(1)
  249. uold_l=wvec_l(2)
  250. vold_l=wvec_l(3)
  251. pold_l=wvec_l(4)
  252. c-----------------------
  253. rold_r=wvec_r(1)
  254. uold_r=wvec_r(2)
  255. vold_r=wvec_r(3)
  256. pold_r=wvec_r(4)
  257. c------------------------------------------------------------------
  258. c Computation of the specific total energy on the left and right.
  259. c------------------------------------------------------------------
  260. eold_l=(uold_l*uold_l+vold_l*vold_l)/2.0d0
  261. eold_l=eold_l+pold_l/(gm1l*rold_l)
  262. eold_r=(uold_r*uold_r+vold_r*vold_r)/2.0d0
  263. eold_r=eold_r+pold_r/(gm1r*rold_r)
  264. c-------------------------------------------------------------------
  265. c Computation of the speed of sound and its derivatives;
  266. c numerical speed of sound at the interface is taken as an average
  267. c of the speeds of sounds of the neighbouring cells
  268. c-------------------------------------------------------------------
  269. aleft=sqrt(gal*pold_l/rold_l)
  270. arigh=sqrt(gar*pold_r/rold_r)
  271. am=0.5d0*(aleft+arigh)
  272. c-------------------------------------------------------------------
  273. damr_r=-arigh/(4.0d0*rold_r)
  274. damu_r=0.0d0
  275. damv_r=0.0d0
  276. damp_r=gar/(4.0d0*arigh*rold_r)
  277. damg_r=arigh/(4.0d0*gar)
  278. c-----------------------
  279. damr_l=-aleft/(4.0d0*rold_l)
  280. damu_l=0.0d0
  281. damv_l=0.0d0
  282. damp_l=gal/(4.0d0*aleft*rold_l)
  283. damg_l=aleft/(4.0d0*gal)
  284. c-------------------------------------------------------------------
  285. c Computing numerical Mach number and its derivatives,
  286. c see p.370, under (A1).
  287. c-------------------------------------------------------------------
  288. un_l=uold_l*n_x+vold_l*n_y
  289. un_r=uold_r*n_x+vold_r*n_y
  290. ut_l=uold_l*t_x+vold_l*t_y
  291. ut_r=uold_r*t_x+vold_r*t_y
  292. c-------------------------------------------------------------------
  293. ml=un_l/am
  294. mr=un_r/am
  295. c-------------------------------------------------------------------
  296. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  297. c see (19a) and (19b), p.367.
  298. c-------------------------------------------------------------------
  299. if(abs(ml) .ge. 1.0d0) then
  300. Mplus=(ml+abs(ml))/2.0d0
  301. else
  302. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  303. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  304. endif
  305. c-------------------------------------------------------------------
  306. if(abs(mr) .ge. 1.0d0) then
  307. Mmin=(mr-abs(mr))/2.0d0
  308. else
  309. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  310. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  311. endif
  312. c-------------------------------------------------------------------
  313. c Derivatives of ml and mr with respect to both sets of primitive
  314. c variables: left and right.
  315. c-------------------------------------------------------------------
  316. temp_l=-un_l/(am*am)
  317. temp_r=-un_r/(am*am)
  318. c--------
  319. dmlr_l=temp_l*damr_l
  320. dmlr_r=temp_l*damr_r
  321. dmrr_l=temp_r*damr_l
  322. dmrr_r=temp_r*damr_r
  323. c--------
  324. dmlu_l=n_x/am+temp_l*damu_l
  325. dmlu_r=temp_l*damu_r
  326. dmru_l=temp_r*damu_l
  327. dmru_r=n_x/am+temp_r*damu_r
  328. c--------
  329. dmlv_l=n_y/am+temp_l*damv_l
  330. dmlv_r=temp_l*damv_r
  331. dmrv_l=temp_r*damv_l
  332. dmrv_r=n_y/am+temp_r*damv_r
  333. c--------
  334. dmlp_l=temp_l*damp_l
  335. dmlp_r=temp_l*damp_r
  336. dmrp_l=temp_r*damp_l
  337. dmrp_r=temp_r*damp_r
  338. c--------
  339. do 44 i=1,(nsp-1)
  340. dmly_l.vv(i)=temp_l*damg_l*dgdyl.vv(i)
  341. dmly_r.vv(i)=temp_l*damg_r*dgdyr.vv(i)
  342. dmry_l.vv(i)=temp_r*damg_l*dgdyl.vv(i)
  343. dmry_r.vv(i)=temp_r*damg_r*dgdyr.vv(i)
  344. 44 continue
  345. c-----------------------------------------------------------
  346. c mmid is m_{1/2} (notation as in the paper, see (13),p.366)
  347. c-----------------------------------------------------------
  348. mmid=Mplus+Mmin
  349. c-----------------------------------------------------------
  350. c Computing the derivatives of M+ and M-
  351. c-----------------------------------------------------------
  352. if(ml .ge. 1.0d0) then
  353. dMpr_l=dmlr_l
  354. dMpu_l=dmlu_l
  355. dMpv_l=dmlv_l
  356. dMpp_l=dmlp_l
  357. do 45 i=1,(nsp-1)
  358. dMpy_l.vv(i)=dmly_l.vv(i)
  359. 45 continue
  360. c--------------------
  361. dMpr_r=dmlr_r
  362. dMpu_r=dmlu_r
  363. dMpv_r=dmlv_r
  364. dMpp_r=dmlp_r
  365. do 46 i=1,(nsp-1)
  366. dMpy_r.vv(i)=dmly_r.vv(i)
  367. 46 continue
  368. else
  369. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  370. temph=(ml+1.0d0)/2.0d0
  371. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  372. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  373. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  374. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  375. do 47 i=1,(nsp-1)
  376. dMpy_l.vv(i)=(temph+4.0d0*beta*ml*
  377. & (ml*ml-1.0d0))*dmly_l.vv(i)
  378. 47 continue
  379. c--------------------
  380. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  381. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  382. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  383. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  384. do 48 i=1,(nsp-1)
  385. dMpy_r.vv(i)=(temph+4.0d0*beta*ml*
  386. & (ml*ml-1.0d0))*dmly_r.vv(i)
  387. 48 continue
  388. else
  389. dMpr_l=0.0d0
  390. dMpu_l=0.0d0
  391. dMpv_l=0.0d0
  392. dMpp_l=0.0d0
  393. do 49 i=1,(nsp-1)
  394. dMpy_l.vv(i)=0.0d0
  395. 49 continue
  396. c---------------------
  397. dMpr_r=0.0d0
  398. dMpu_r=0.0d0
  399. dMpv_r=0.0d0
  400. dMpp_r=0.0d0
  401. do 50 i=1,(nsp-1)
  402. dMpy_r.vv(i)=0.0d0
  403. 50 continue
  404. endif
  405. endif
  406. c-----------------------------------------------------------
  407. if(mr .ge. 1.0d0) then
  408. dMmr_l=0.0d0
  409. dMmu_l=0.0d0
  410. dMmv_l=0.0d0
  411. dMmp_l=0.0d0
  412. do 51 i=1,(nsp-1)
  413. dMmy_l.vv(i)=0.0d0
  414. 51 continue
  415. c---------------------
  416. dMmr_r=0.0d0
  417. dMmu_r=0.0d0
  418. dMmv_r=0.0d0
  419. dMmp_r=0.0d0
  420. do 52 i=1,(nsp-1)
  421. dMmy_r.vv(i)=0.0d0
  422. 52 continue
  423. else
  424. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  425. temph=(-mr+1.0d0)/2.0d0
  426. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  427. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  428. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  429. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  430. do 53 i=1,(nsp-1)
  431. dMmy_l.vv(i)=(temph-4.0d0*beta*mr*
  432. & (mr*mr-1.0d0))*dmry_l.vv(i)
  433. 53 continue
  434. c--------------------
  435. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  436. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  437. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  438. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  439. do 54 i=1,(nsp-1)
  440. dMmy_r.vv(i)=(temph-4.0d0*beta*mr*
  441. & (mr*mr-1.0d0))*dmry_r.vv(i)
  442. 54 continue
  443. else
  444. dMmr_l=dmrr_l
  445. dMmu_l=dmru_l
  446. dMmv_l=dmrv_l
  447. dMmp_l=dmrp_l
  448. do 55 i=1,(nsp-1)
  449. dMmy_l.vv(i)=dmry_l.vv(i)
  450. 55 continue
  451. c--------------------
  452. dMmr_r=dmrr_r
  453. dMmu_r=dmru_r
  454. dMmv_r=dmrv_r
  455. dMmp_r=dmrp_r
  456. do 56 i=1,(nsp-1)
  457. dMmy_r.vv(i)=dmry_r.vv(i)
  458. 56 continue
  459. endif
  460. endif
  461. c-----------------------------------------------------------------
  462. c computing the derivatives of m_{1/2} (notation as in the paper)
  463. c-----------------------------------------------------------------
  464. dmir_l=dMpr_l+dMmr_l
  465. dmir_r=dMpr_r+dMmr_r
  466. c-------------
  467. dmiu_l=dMpu_l+dMmu_l
  468. dmiu_r=dMpu_r+dMmu_r
  469. c-------------
  470. dmiv_l=dMpv_l+dMmv_l
  471. dmiv_r=dMpv_r+dMmv_r
  472. c-------------
  473. dmip_l=dMpp_l+dMmp_l
  474. dmip_r=dMpp_r+dMmp_r
  475. c-------------
  476. do 57 i=1,(nsp-1)
  477. dmiy_l.vv(i)=dMpy_l.vv(i)+dMmy_l.vv(i)
  478. dmiy_r.vv(i)=dMpy_r.vv(i)+dMmy_r.vv(i)
  479. 57 continue
  480. c----------------------------------------------------------------
  481. c computing the main convective variables and their derivatives
  482. c mpl_m is m^{+}_{1/2} (paper's notation) and
  483. c mmin_m is m^{-}_{1/2} (paper's notation), see (A2) on p.370.
  484. c----------------------------------------------------------------
  485. if(mmid .ge. 0.0d0) then
  486. mpl_m = mmid
  487. d2mr_l=dmir_l
  488. d2mu_l=dmiu_l
  489. d2mv_l=dmiv_l
  490. d2mp_l=dmip_l
  491. do 58 i=1,(nsp-1)
  492. d2my_l.vv(i)=dmiy_l.vv(i)
  493. 58 continue
  494. c------------
  495. d2mr_r=dmir_r
  496. d2mu_r=dmiu_r
  497. d2mv_r=dmiv_r
  498. d2mp_r=dmip_r
  499. do 59 i=1,(nsp-1)
  500. d2my_r.vv(i)=dmiy_r.vv(i)
  501. 59 continue
  502. c------------
  503. else
  504. mpl_m = 0.0d0
  505. d2mr_l=0.0d0
  506. d2mu_l=0.0d0
  507. d2mv_l=0.0d0
  508. d2mp_l=0.0d0
  509. do 60 i=1,(nsp-1)
  510. d2my_l.vv(i)=0.0d0
  511. 60 continue
  512. c------------
  513. d2mr_r=0.0d0
  514. d2mu_r=0.0d0
  515. d2mv_r=0.0d0
  516. d2mp_r=0.0d0
  517. do 61 i=1,(nsp-1)
  518. d2my_r.vv(i)=0.0d0
  519. 61 continue
  520. endif
  521. c---------------------------------------------
  522. if(mmid .le. 0.0d0) then
  523. mmin_m = mmid
  524. d3mr_l=dmir_l
  525. d3mu_l=dmiu_l
  526. d3mv_l=dmiv_l
  527. d3mp_l=dmip_l
  528. do 62 i=1,(nsp-1)
  529. d3my_l.vv(i)=dmiy_l.vv(i)
  530. 62 continue
  531. c------------
  532. d3mr_r=dmir_r
  533. d3mu_r=dmiu_r
  534. d3mv_r=dmiv_r
  535. d3mp_r=dmip_r
  536. do 63 i=1,(nsp-1)
  537. d3my_r.vv(i)=dmiy_r.vv(i)
  538. 63 continue
  539. c------------
  540. else
  541. mmin_m = 0.0d0
  542. d3mr_l=0.0d0
  543. d3mu_l=0.0d0
  544. d3mv_l=0.0d0
  545. d3mp_l=0.0d0
  546. do 64 i=1,(nsp-1)
  547. d3my_l.vv(i)=0.0d0
  548. 64 continue
  549. c------------
  550. d3mr_r=0.0d0
  551. d3mu_r=0.0d0
  552. d3mv_r=0.0d0
  553. d3mp_r=0.0d0
  554. do 65 i=1,(nsp-1)
  555. d3my_r.vv(i)=0.0d0
  556. 65 continue
  557. endif
  558. c---------------------------------------------------------------
  559. c Computing the calligraphic P+ and P- with their derivatives,
  560. c see (21a) & (21b) on p.368.
  561. c---------------------------------------------------------------
  562. if(ml .ge. 1.0d0) then
  563. Pplus = 1.0d0
  564. else
  565. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  566. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  567. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  568. else
  569. Pplus = 0.0d0
  570. endif
  571. endif
  572. c---------------------------------------------------------------
  573. if(mr .ge. 1.0d0) then
  574. Pmin = 0.0d0
  575. else
  576. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  577. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  578. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  579. else
  580. Pmin = 1.0d0
  581. endif
  582. endif
  583. c---------------------------------------------------------------
  584. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  585. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  586. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  587. c--------------
  588. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  589. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  590. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  591. c---------------------------------------------------------------
  592. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  593. dPpr_l=brac_l*dmlr_l
  594. dPpr_r=brac_l*dmlr_r
  595. c------------
  596. dPpu_l=brac_l*dmlu_l
  597. dPpu_r=brac_l*dmlu_r
  598. c------------
  599. dPpv_l=brac_l*dmlv_l
  600. dPpv_r=brac_l*dmlv_r
  601. c------------
  602. dPpp_l=brac_l*dmlp_l
  603. dPpp_r=brac_l*dmlp_r
  604. c------------
  605. do 66 i=1,(nsp-1)
  606. dPpy_l.vv(i)=brac_l*dmly_l.vv(i)
  607. dPpy_r.vv(i)=brac_l*dmly_r.vv(i)
  608. 66 continue
  609. c------------
  610. else
  611. dPpr_l=0.0d0
  612. dPpr_r=0.0d0
  613. c-----------
  614. dPpu_l=0.0d0
  615. dPpu_r=0.0d0
  616. c-----------
  617. dPpv_l=0.0d0
  618. dPpv_r=0.0d0
  619. c-----------
  620. dPpp_l=0.0d0
  621. dPpp_r=0.0d0
  622. c-----------
  623. do 67 i=1,(nsp-1)
  624. dPpy_l.vv(i)=0.0d0
  625. dPpy_r.vv(i)=0.0d0
  626. 67 continue
  627. c-----------
  628. endif
  629. c---------------------------------------------------------------
  630. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  631. dPmr_l=brac_r*dmrr_l
  632. dPmr_r=brac_r*dmrr_r
  633. c------------
  634. dPmu_l=brac_r*dmru_l
  635. dPmu_r=brac_r*dmru_r
  636. c------------
  637. dPmv_l=brac_r*dmrv_l
  638. dPmv_r=brac_r*dmrv_r
  639. c------------
  640. dPmp_l=brac_r*dmrp_l
  641. dPmp_r=brac_r*dmrp_r
  642. c------------
  643. do 68 i=1,(nsp-1)
  644. dPmy_l.vv(i)=brac_r*dmry_l.vv(i)
  645. dPmy_r.vv(i)=brac_r*dmry_r.vv(i)
  646. 68 continue
  647. c------------
  648. else
  649. dPmr_l=0.0d0
  650. dPmr_r=0.0d0
  651. c-----------
  652. dPmu_l=0.0d0
  653. dPmu_r=0.0d0
  654. c-----------
  655. dPmv_l=0.0d0
  656. dPmv_r=0.0d0
  657. c-----------
  658. dPmp_l=0.0d0
  659. dPmp_r=0.0d0
  660. c-----------
  661. do 69 i=1,(nsp-1)
  662. dPmy_l.vv(i)=0.0d0
  663. dPmy_r.vv(i)=0.0d0
  664. 69 continue
  665. c-----------
  666. endif
  667. c-------------------------------------------------------------------
  668. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  669. c-------------------------------------------------------------------
  670. pmid=Pplus*pold_l + Pmin*pold_r
  671. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  672. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  673. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  674. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  675. do 70 i=1,(nsp-1)
  676. dpiy_l.vv(i)=dPpy_l.vv(i)*pold_l+dPmy_l.vv(i)*pold_r
  677. 70 continue
  678. c----------------------------
  679. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  680. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  681. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  682. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  683. do 71 i=1,(nsp-1)
  684. dpiy_r.vv(i)=dPpy_r.vv(i)*pold_l+dPmy_r.vv(i)*pold_r
  685. 71 continue
  686. c---------------------------------------------------------------------
  687. c computing JACOBIAN as a derivative of the numerical flux function
  688. c with respect to the primitive variables.
  689. c Notation: jl(i,j) --- is the derivative of the i-component of the
  690. c flux function with respect to the j-component of the
  691. c vector of primitive variables of the left state.
  692. c jr(i,j) --- is the derivative of the i-component of the
  693. c flux function with respect to the j-component of the
  694. c vector of primitive variables of the right state.
  695. c---------------------------------------------------------------------
  696. f.fu(1)=am*(mpl_m*rold_l+mmin_m*rold_r)
  697. c---------------------------------------------------------------------
  698. jl.jac(1,1)=damr_l*f.fu(1)/am+am*(d2mr_l*rold_l+mpl_m)
  699. jl.jac(1,1)=jl.jac(1,1)+am*d3mr_l*rold_r
  700. jl.jac(1,2)=damu_l*f.fu(1)/am+am*(d2mu_l*rold_l+d3mu_l*rold_r)
  701. jl.jac(1,3)=damv_l*f.fu(1)/am+am*(d2mv_l*rold_l+d3mv_l*rold_r)
  702. jl.jac(1,4)=damp_l*f.fu(1)/am+am*(d2mp_l*rold_l+d3mp_l*rold_r)
  703. do 72 i=1,(nsp-1)
  704. jl.jac(1,4+i)=damg_l*dgdyl.vv(i)*f.fu(1)/am+
  705. & am*(d2my_l.vv(i)*rold_l+d3my_l.vv(i)*rold_r)
  706. 72 continue
  707. c------------------------------------
  708. jr.jac(1,1)=damr_r*f.fu(1)/am+am*(d2mr_r*rold_l+mmin_m)
  709. jr.jac(1,1)=jr.jac(1,1)+am*d3mr_r*rold_r
  710. jr.jac(1,2)=damu_r*f.fu(1)/am+am*(d2mu_r*rold_l+d3mu_r*rold_r)
  711. jr.jac(1,3)=damv_r*f.fu(1)/am+am*(d2mv_r*rold_l+d3mv_r*rold_r)
  712. jr.jac(1,4)=damp_r*f.fu(1)/am+am*(d2mp_r*rold_l+d3mp_r*rold_r)
  713. do 73 i=1,(nsp-1)
  714. jr.jac(1,4+i)=damg_r*dgdyr.vv(i)*f.fu(1)/am+
  715. & am*(d2my_r.vv(i)*rold_l+d3my_r.vv(i)*rold_r)
  716. 73 continue
  717. c------------------------------------
  718. c------------------------------------
  719. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  720. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  721. f.fu(2)=n_x*(am*br1+pmid)+am*t_x*br2
  722. c------------------
  723. det=n_x*t_y-n_y*t_x
  724. c---------------------------------------------------------
  725. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  726. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  727. jl.jac(2,1)=n_x*(damr_l*br1+am*br3+dpir_l)
  728. jl.jac(2,1)=jl.jac(2,1)+t_x*damr_l*br2+am*t_x*br4
  729. c-------------------
  730. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  731. br3=br3+d3mu_l*rold_r*un_r
  732. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y)/det
  733. br4=br4+d3mu_l*rold_r*ut_r
  734. jl.jac(2,2)=n_x*(damu_l*br1+am*br3+dpiu_l)
  735. jl.jac(2,2)=jl.jac(2,2)+t_x*damu_l*br2+am*t_x*br4
  736. c-------------------
  737. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x)/det
  738. br3=br3+d3mv_l*rold_r*un_r
  739. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  740. br4=br4+d3mv_l*rold_r*ut_r
  741. jl.jac(2,3)=n_x*(damv_l*br1+am*br3+dpiv_l)
  742. jl.jac(2,3)=jl.jac(2,3)+t_x*damv_l*br2+am*t_x*br4
  743. c-------------------
  744. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  745. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  746. jl.jac(2,4)=n_x*(damp_l*br1+am*br3+dpip_l)
  747. jl.jac(2,4)=jl.jac(2,4)+t_x*damp_l*br2+am*t_x*br4
  748. c-------------------
  749. do 74 i=1,(nsp-1)
  750. br3=d2my_l.vv(i)*rold_l*un_l+d3my_l.vv(i)*rold_r*un_r
  751. br4=d2my_l.vv(i)*rold_l*ut_l+d3my_l.vv(i)*rold_r*ut_r
  752. jl.jac(2,4+i)=n_x*(damg_l*dgdyl.vv(i)*br1+
  753. & am*br3+dpiy_l.vv(i))
  754. jl.jac(2,4+i)=jl.jac(2,4+i)+
  755. & t_x*damg_l*dgdyl.vv(i)*br2+am*t_x*br4
  756. 74 continue
  757. c-------------------------------------------------------------
  758. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  759. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  760. jr.jac(2,1)=n_x*(damr_r*br1+am*br3+dpir_r)
  761. jr.jac(2,1)=jr.jac(2,1)+t_x*damr_r*br2+am*t_x*br4
  762. c-------------------
  763. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  764. br3=br3+d3mu_r*rold_r*un_r
  765. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  766. br4=br4+d3mu_r*rold_r*ut_r
  767. jr.jac(2,2)=n_x*(damu_r*br1+am*br3+dpiu_r)
  768. jr.jac(2,2)=jr.jac(2,2)+t_x*damu_r*br2+am*t_x*br4
  769. c-------------------
  770. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  771. br3=br3+d3mv_r*rold_r*un_r
  772. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  773. br4=br4+d3mv_r*rold_r*ut_r
  774. jr.jac(2,3)=n_x*(damv_r*br1+am*br3+dpiv_r)
  775. jr.jac(2,3)=jr.jac(2,3)+t_x*damv_r*br2+am*t_x*br4
  776. c-------------------
  777. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  778. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  779. jr.jac(2,4)=n_x*(damp_r*br1+am*br3+dpip_r)
  780. jr.jac(2,4)=jr.jac(2,4)+t_x*damp_r*br2+am*t_x*br4
  781. c-------------------
  782. do 75 i=1,(nsp-1)
  783. br3=d2my_r.vv(i)*rold_l*un_l+d3my_r.vv(i)*rold_r*un_r
  784. br4=d2my_r.vv(i)*rold_l*ut_l+d3my_r.vv(i)*rold_r*ut_r
  785. jr.jac(2,4+i)=n_x*(damg_r*dgdyr.vv(i)*br1+
  786. & am*br3+dpiy_r.vv(i))
  787. jr.jac(2,4+i)=jr.jac(2,4+i)+
  788. & t_x*damg_r*dgdyr.vv(i)*br2+am*t_x*br4
  789. 75 continue
  790. c-------------------------------------------------------------
  791. c-------------------------------------------------------------
  792. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  793. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  794. f.fu(3)=n_y*(am*br1+pmid)+am*t_y*br2
  795. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  796. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  797. jl.jac(3,1)=n_y*(damr_l*br1+am*br3+dpir_l)
  798. jl.jac(3,1)=jl.jac(3,1)+t_y*damr_l*br2+am*t_y*br4
  799. c-------------------
  800. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  801. br3=br3+d3mu_l*rold_r*un_r
  802. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y/det)
  803. br4=br4+d3mu_l*rold_r*ut_r
  804. jl.jac(3,2)=n_y*(damu_l*br1+am*br3+dpiu_l)
  805. jl.jac(3,2)=jl.jac(3,2)+t_y*damu_l*br2+am*t_y*br4
  806. c-------------------
  807. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x/det)
  808. br3=br3+d3mv_l*rold_r*un_r
  809. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  810. br4=br4+d3mv_l*rold_r*ut_r
  811. jl.jac(3,3)=n_y*(damv_l*br1+am*br3+dpiv_l)
  812. jl.jac(3,3)=jl.jac(3,3)+t_y*damv_l*br2+am*t_y*br4
  813. c-------------------
  814. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  815. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  816. jl.jac(3,4)=n_y*(damp_l*br1+am*br3+dpip_l)
  817. jl.jac(3,4)=jl.jac(3,4)+t_y*damp_l*br2+am*t_y*br4
  818. c-------------------
  819. do 76 i=1,(nsp-1)
  820. br3=d2my_l.vv(i)*rold_l*un_l+d3my_l.vv(i)*rold_r*un_r
  821. br4=d2my_l.vv(i)*rold_l*ut_l+d3my_l.vv(i)*rold_r*ut_r
  822. jl.jac(3,4+i)=n_y*(damg_l*dgdyl.vv(i)*br1+
  823. & am*br3+dpiy_l.vv(i))
  824. jl.jac(3,4+i)=jl.jac(3,4+i)+
  825. & t_y*damg_l*dgdyl.vv(i)*br2+am*t_y*br4
  826. 76 continue
  827. c-------------------------------------------------------------
  828. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  829. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  830. jr.jac(3,1)=n_y*(damr_r*br1+am*br3+dpir_r)
  831. jr.jac(3,1)=jr.jac(3,1)+t_y*damr_r*br2+am*t_y*br4
  832. c-------------------
  833. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  834. br3=br3+d3mu_r*rold_r*un_r
  835. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  836. br4=br4+d3mu_r*rold_r*ut_r
  837. jr.jac(3,2)=n_y*(damu_r*br1+am*br3+dpiu_r)
  838. jr.jac(3,2)=jr.jac(3,2)+t_y*damu_r*br2+am*t_y*br4
  839. c-------------------
  840. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  841. br3=br3+d3mv_r*rold_r*un_r
  842. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  843. br4=br4+d3mv_r*rold_r*ut_r
  844. jr.jac(3,3)=n_y*(damv_r*br1+am*br3+dpiv_r)
  845. jr.jac(3,3)=jr.jac(3,3)+t_y*damv_r*br2+am*t_y*br4
  846. c-------------------
  847. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  848. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  849. jr.jac(3,4)=n_y*(damp_r*br1+am*br3+dpip_r)
  850. jr.jac(3,4)=jr.jac(3,4)+t_y*damp_r*br2+am*t_y*br4
  851. c-------------------
  852. do 77 i=1,(nsp-1)
  853. br3=d2my_r.vv(i)*rold_l*un_l+d3my_r.vv(i)*rold_r*un_r
  854. br4=d2my_r.vv(i)*rold_l*ut_l+d3my_r.vv(i)*rold_r*ut_r
  855. jr.jac(3,4+i)=n_y*(damg_r*dgdyr.vv(i)*br1+
  856. & am*br3+dpiy_r.vv(i))
  857. jr.jac(3,4+i)=jr.jac(3,4+i)+
  858. & t_y*damg_r*dgdyr.vv(i)*br2+am*t_y*br4
  859. 77 continue
  860. c-------------------------------------------------------------
  861. c --------------------- f4 ----------------------------
  862. c-------------------------------------------------------------
  863. hr_l=rold_l*(uold_l*uold_l+vold_l*vold_l)/2.0d0+gal*pold_l/gm1l
  864. hr_r=rold_r*(uold_r*uold_r+vold_r*vold_r)/2.0d0+gar*pold_r/gm1r
  865. f.fu(4)=am*(mpl_m*hr_l+mmin_m*hr_r)
  866. c---------------------
  867. br1=d2mr_l*hr_l+mpl_m*(uold_l*uold_l+vold_l*vold_l)/2.0d0
  868. br1=br1+d3mr_l*hr_r
  869. jl.jac(4,1)=damr_l*f.fu(4)/am+am*br1
  870. c---------------------
  871. br1=d2mu_l*hr_l+mpl_m*uold_l*rold_l
  872. br1=br1+d3mu_l*hr_r
  873. jl.jac(4,2)=damu_l*f.fu(4)/am+am*br1
  874. c---------------------
  875. br1=d2mv_l*hr_l+mpl_m*vold_l*rold_l
  876. br1=br1+d3mv_l*hr_r
  877. jl.jac(4,3)=damv_l*f.fu(4)/am+am*br1
  878. c---------------------
  879. br1=d2mp_l*hr_l+mpl_m*gal/gm1l
  880. br1=br1+d3mp_l*hr_r
  881. jl.jac(4,4)=damp_l*f.fu(4)/am+am*br1
  882. c---------------------
  883. do 78 i=1,(nsp-1)
  884. br1=d2my_l.vv(i)*hr_l+mpl_m*(-pold_l)*dgdyl.vv(i)/(gm1l*gm1l)
  885. br1=br1+d3my_l.vv(i)*hr_r
  886. jl.jac(4,4+i)=damg_l*dgdyl.vv(i)*f.fu(4)/am+am*br1
  887. 78 continue
  888. c----------------------------------------------------------
  889. c----------------------------------------------------------
  890. br1=d2mr_r*hr_l+mmin_m*(uold_r*uold_r+vold_r*vold_r)/2.0d0
  891. br1=br1+d3mr_r*hr_r
  892. jr.jac(4,1)=damr_r*f.fu(4)/am+am*br1
  893. c---------------------
  894. br1=d2mu_r*hr_l+mmin_m*uold_r*rold_r
  895. br1=br1+d3mu_r*hr_r
  896. jr.jac(4,2)=damu_r*f.fu(4)/am+am*br1
  897. c---------------------
  898. br1=d2mv_r*hr_l+mmin_m*vold_r*rold_r
  899. br1=br1+d3mv_r*hr_r
  900. jr.jac(4,3)=damv_r*f.fu(4)/am+am*br1
  901. c---------------------
  902. br1=d2mp_r*hr_l+mmin_m*gar/gm1r
  903. br1=br1+d3mp_r*hr_r
  904. jr.jac(4,4)=damp_r*f.fu(4)/am+am*br1
  905. c---------------------
  906. do 79 i=1,(nsp-1)
  907. br1=d2my_r.vv(i)*hr_l+mmin_m*
  908. & (-pold_r)*dgdyr.vv(i)/(gm1r*gm1r)
  909. br1=br1+d3my_r.vv(i)*hr_r
  910. jr.jac(4,4+i)=damg_r*dgdyr.vv(i)*f.fu(4)/am+am*br1
  911. 79 continue
  912. c-------------------------------------------------------------
  913. c ------------------ f5++ ------------------------------------
  914. c-------------------------------------------------------------
  915. do 80 i=1,(nsp-1)
  916. f.fu(4+i)=am*(mpl_m*rold_l*yl.yet(i)+mmin_m*rold_r*yr.yet(i))
  917. c---------------------
  918. jl.jac(4+i,1)=damr_l*f.fu(4+i)/am+
  919. & am*(d2mr_l*rold_l*yl.yet(i)+mpl_m*yl.yet(i))
  920. jl.jac(4+i,1)=jl.jac(4+i,1)+am*d3mr_l*rold_r*yr.yet(i)
  921. jl.jac(4+i,2)=damu_l*f.fu(4+i)/am+am*(d2mu_l*rold_l*yl.yet(i)+
  922. & d3mu_l*rold_r*yr.yet(i))
  923. jl.jac(4+i,3)=damv_l*f.fu(4+i)/am+am*(d2mv_l*rold_l*yl.yet(i)+
  924. & d3mv_l*rold_r*yr.yet(i))
  925. jl.jac(4+i,4)=damp_l*f.fu(4+i)/am+am*(d2mp_l*rold_l*yl.yet(i)+
  926. & d3mp_l*rold_r*yr.yet(i))
  927. do 81 j=5,(4+nsp-1)
  928. if((4+i).eq.j) then
  929. jl.jac(4+i,j)=damg_l*dgdyl.vv(j-4)*f.fu(4+i)/am+
  930. & am*(d2my_l.vv(j-4)*rold_l*yl.yet(i)+mpl_m*rold_l+
  931. & d3my_l.vv(j-4)*rold_r*yr.yet(i))
  932. else
  933. jl.jac(4+i,j)=damg_l*dgdyl.vv(j-4)*f.fu(4+i)/am+
  934. & am*(d2my_l.vv(j-4)*rold_l*yl.yet(i)+
  935. & d3my_l.vv(j-4)*rold_r*yr.yet(i))
  936. endif
  937. 81 continue
  938. c------------------------------------
  939. jr.jac(4+i,1)=damr_r*f.fu(4+i)/am+
  940. & am*(d2mr_r*rold_l*yl.yet(i)+mmin_m*yr.yet(i))
  941. jr.jac(4+i,1)=jr.jac(4+i,1)+am*d3mr_r*rold_r*yr.yet(i)
  942. jr.jac(4+i,2)=damu_r*f.fu(4+i)/am+am*(d2mu_r*rold_l*yl.yet(i)+
  943. & d3mu_r*rold_r*yr.yet(i))
  944. jr.jac(4+i,3)=damv_r*f.fu(4+i)/am+am*(d2mv_r*rold_l*yl.yet(i)+
  945. & d3mv_r*rold_r*yr.yet(i))
  946. jr.jac(4+i,4)=damp_r*f.fu(4+i)/am+am*(d2mp_r*rold_l*yl.yet(i)+
  947. & d3mp_r*rold_r*yr.yet(i))
  948. do 82 j=1,(nsp-1)
  949. if(i.eq.j) then
  950. jr.jac(4+i,4+j)=damg_r*dgdyr.vv(j)*f.fu(4+i)/am+
  951. & am*(d2my_r.vv(j)*rold_l*yl.yet(i)+mmin_m*rold_r+
  952. & d3my_r.vv(j)*rold_r*yr.yet(i))
  953. else
  954. jr.jac(4+i,4+j)=damg_r*dgdyr.vv(j)*f.fu(4+i)/am+
  955. & am*(d2my_r.vv(j)*rold_l*yl.yet(i)+
  956. & d3my_r.vv(j)*rold_r*yr.yet(i))
  957. endif
  958. 82 continue
  959. 80 continue
  960. c-------------------------------------------------------------
  961. SEGSUP DMLY_L, DMLY_R,
  962. & dmry_l, dmry_r,
  963. & dMpy_l, dMpy_r,
  964. & dMmy_l, dMmy_r,
  965. & dmiy_l, dmiy_r,
  966. & d3my_l, d3my_r,
  967. & d2my_l, d2my_r,
  968. & dPpy_l, dPpy_r,
  969. & dPmy_l, dPmy_r,
  970. & dpiy_l, dpiy_r,
  971. & dgdyl, dgdyr
  972. C--------------------------------------------
  973. SEGSUP f
  974. C--------------------------------------------
  975. jll=jl
  976. SEGDES JL
  977. jrr=jr
  978. SEGDES JR
  979. SEGDES YL
  980. SEGDES YR
  981. SEGDES CP
  982. SEGDES CV
  983. SEGDES MLRECP, MLRECV
  984. C--------------------------------------------
  985. return
  986. end
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