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  1. C COPMSP SOURCE CHAT 05/01/12 22:20:44 5004
  2. SUBROUTINE COPMSP(NSP,JPL,JLL,WVEC_L,WVEC_R,NVECT,TVECT,
  3. & mpyn,lrecp,lrecv,nlcg,nlcd)
  4. C************************************************************************
  5. C
  6. C PROJET : CASTEM 2000
  7. C
  8. C NOM : COPMSP ('convection for multispecies')
  9. C
  10. C DESCRIPTION : Voir CLI252 (appele par CLI252)
  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: 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 nlcg -- "local" number corresponding to the left cell;
  61. c
  62. c nlcd -- "local" number corresponding to the right cell;
  63. c----------------------------------------------------------------------
  64. c
  65. c OUTPUT:
  66. c
  67. c jll -- jakobian matrix (3+nsp) by (3+nsp) -
  68. c derivatives of the numerical
  69. c flux function with respect to the conservative variables
  70. c from the left cell;
  71. c
  72. c jpl -- jakobian matrix (3+nsp) by (3+nsp) -
  73. c derivatives of the numerical
  74. c flux function with respect to the primitive variables
  75. c from the left cell.
  76. c----------------------------------------------------------------------
  77. IMPLICIT INTEGER(I-N)
  78. integer nsp,jll,jpl,lrecp,lrecv,nlcg,nlcd
  79. real*8 wvec_l(4),wvec_r(4)
  80. real*8 nvect(2),tvect(2)
  81. real*8 alpha,beta
  82. real*8 gal,gar,gm1l,gm1r,temph
  83. real*8 n_x,n_y,t_x,t_y
  84. real*8 un_l, un_r, ut_l, ut_r
  85. real*8 ml,mr,Mplus,Mmin,mmid
  86. real*8 mpl_m, mmin_m,am
  87. real*8 rold_l,uold_l,vold_l,pold_l,eold_l
  88. real*8 rold_r,uold_r,vold_r,pold_r,eold_r
  89. real*8 Pplus,Pmin,pmid
  90. real*8 hr_l,hr_r,det,top,bot
  91. real*8 br1,br2,br3,br4,temp_l,temp_r,brac_l,brac_r
  92. real*8 aleft, arigh
  93. real*8 damr_l,damr_r,damu_l,damu_r
  94. real*8 damv_l,damv_r,damp_l,damp_r
  95. real*8 damg_l,damg_r
  96. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  97. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  98. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  99. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  100. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  101. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r
  102. real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r
  103. real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r
  104. real*8 dmir_l,dmir_r,dmiu_l,dmiu_r
  105. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  106. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  107. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  108. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  109. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  110. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  111. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  112. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  113. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  114. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  115. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  116. integer i,j,k
  117. parameter(alpha = 0.1875D0, beta = 0.125D0)
  118. C------------------------------------------------------------
  119. -INC SMCHPOI
  120. POINTEUR MPYN.MPOVAL
  121. C-------------------------------------------------------------
  122. -INC SMLREEL
  123. POINTEUR MLRECP.MLREEL, MLRECV.MLREEL
  124. C-------------------------------------------------------------
  125. C******* Les fractionines massiques **************************
  126. C-------------------------------------------------------------
  127. SEGMENT FRAMAS
  128. REAL*8 YET(NSP)
  129. ENDSEGMENT
  130. POINTEUR YL.FRAMAS, YR.FRAMAS
  131. C-------------------------------------------------------
  132. C********** Les CP's and CV's ***********************
  133. C-------------------------------------------------------
  134. SEGMENT GCONST
  135. REAL*8 GC(NSP)
  136. ENDSEGMENT
  137. POINTEUR CP.GCONST, CV.GCONST
  138. C-------------------------------------------------------------
  139. C******** Segments for the elementary matrixes *************
  140. C-------------------------------------------------------------
  141. SEGMENT JACEL
  142. REAL*8 JAC(3+NSP,3+NSP)
  143. ENDSEGMENT
  144. POINTEUR JTL.JACEL, JL.JACEL, JR.JACEL,
  145. & WL.JACEL
  146. c----------------------------------------
  147. SEGINI JTL
  148. SEGINI JL
  149. SEGINI JR
  150. SEGINI WL
  151. C-------------------------------------------------------------
  152. C********** Segments for the vectors ***********************
  153. C-------------------------------------------------------------
  154. SEGMENT VECEL
  155. REAL*8 VV(NSP)
  156. ENDSEGMENT
  157. POINTEUR DMLY_L.VECEL, DMLY_R.VECEL,
  158. & dmry_l.vecel, dmry_r.vecel,
  159. & dMpy_l.vecel, dMpy_r.vecel,
  160. & dMmy_l.vecel, dMmy_r.vecel,
  161. & dmiy_l.vecel, dmiy_r.vecel,
  162. & d3my_l.vecel, d3my_r.vecel,
  163. & d2my_l.vecel, d2my_r.vecel,
  164. & dPpy_l.vecel, dPpy_r.vecel,
  165. & dPmy_l.vecel, dPmy_r.vecel,
  166. & dpiy_l.vecel, dpiy_r.vecel,
  167. & dgdyl.vecel, dgdyr.vecel
  168. C----------------------------------------------
  169. SEGINI DMLY_L, DMLY_R,
  170. & dmry_l, dmry_r,
  171. & dMpy_l, dMpy_r,
  172. & dMmy_l, dMmy_r,
  173. & dmiy_l, dmiy_r,
  174. & d3my_l, d3my_r,
  175. & d2my_l, d2my_r,
  176. & dPpy_l, dPpy_r,
  177. & dPmy_l, dPmy_r,
  178. & dpiy_l, dpiy_r,
  179. & dgdyl, dgdyr
  180. C-------------------------------------------------------------
  181. C********** Segments for the flux-vector *******************
  182. C-------------------------------------------------------------
  183. SEGMENT FUNEL
  184. REAL*8 FU(3+NSP)
  185. ENDSEGMENT
  186. POINTEUR f.funel
  187. C-------------------------
  188. SEGINI f
  189. C------------------------------------------------------------
  190. SEGINI YL, YR
  191. SEGACT MPYN
  192. DO 100 I=1,(NSP-1)
  193. YL.YET(I)=MPYN.VPOCHA(NLCG,I)
  194. YR.YET(I)=MPYN.VPOCHA(NLCD,I)
  195. 100 CONTINUE
  196. C----------------------------------------
  197. SEGINI CP, CV
  198. MLRECP = LRECP
  199. MLRECV = LRECV
  200. SEGACT MLRECP, MLRECV
  201. DO 101 I=1,(NSP-1)
  202. CP.GC(I)=MLRECP.PROG(I)
  203. CV.GC(I)=MLRECV.PROG(I)
  204. 101 CONTINUE
  205. CP.GC(NSP)=MLRECP.PROG(NSP)
  206. CV.GC(NSP)=MLRECV.PROG(NSP)
  207. c-------------------------------------------------------------
  208. c Computing GAMMA at the left cell and its derivatives
  209. c with respect to the primitive variables Y_i
  210. c-------------------------------------------------------------
  211. top=0.0D0
  212. bot=0.0D0
  213. do 40 i=1,(nsp-1)
  214. top=top+yl.yet(i)*(cp.gc(i)-cp.gc(nsp))
  215. bot=bot+yl.yet(i)*(cv.gc(i)-cv.gc(nsp))
  216. 40 continue
  217. top=cp.gc(nsp)+top
  218. bot=cv.gc(nsp)+bot
  219. gal=top/bot
  220. gm1l=gal-1.0d0
  221. c-------------------------------------------------------------
  222. do 41 i=1,(nsp-1)
  223. dgdyl.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  224. & gal*(cv.gc(i)-cv.gc(nsp)))/bot
  225. 41 continue
  226. c-------------------------------------------------------------
  227. c Computing GAMMA at the right cell and its derivatives
  228. c with respect to the primitive variables Y_i
  229. c-------------------------------------------------------------
  230. top=0.0D0
  231. bot=0.0D0
  232. do 42 i=1,(nsp-1)
  233. top=top+yr.yet(i)*(cp.gc(i)-cp.gc(nsp))
  234. bot=bot+yr.yet(i)*(cv.gc(i)-cv.gc(nsp))
  235. 42 continue
  236. top=cp.gc(nsp)+top
  237. bot=cv.gc(nsp)+bot
  238. gar=top/bot
  239. gm1r=gar-1.0d0
  240. c-------------------------------------------------------------
  241. do 43 i=1,(nsp-1)
  242. dgdyr.vv(i)=(cp.gc(i)-cp.gc(nsp)-
  243. & gar*(cv.gc(i)-cv.gc(nsp)))/bot
  244. 43 continue
  245. c-------------------------------------------------------------
  246. n_x=nvect(1)
  247. n_y=nvect(2)
  248. t_x=tvect(1)
  249. t_y=tvect(2)
  250. c----------------------------
  251. c----------------------------
  252. rold_l=wvec_l(1)
  253. uold_l=wvec_l(2)
  254. vold_l=wvec_l(3)
  255. pold_l=wvec_l(4)
  256. c-----------------------
  257. rold_r=wvec_r(1)
  258. uold_r=wvec_r(2)
  259. vold_r=wvec_r(3)
  260. pold_r=wvec_r(4)
  261. c------------------------------------------------------------------
  262. c Computation of the specific total energy on the left and right.
  263. c------------------------------------------------------------------
  264. eold_l=(uold_l*uold_l+vold_l*vold_l)/2.0d0
  265. eold_l=eold_l+pold_l/(gm1l*rold_l)
  266. eold_r=(uold_r*uold_r+vold_r*vold_r)/2.0d0
  267. eold_r=eold_r+pold_r/(gm1r*rold_r)
  268. c-------------------------------------------------------------------
  269. c Computation of the speed of sound and its derivatives;
  270. c numerical speed of sound at the interface is taken as an average
  271. c of the speeds of sounds of the neighbouring cells
  272. c-------------------------------------------------------------------
  273. aleft=sqrt(gal*pold_l/rold_l)
  274. arigh=sqrt(gar*pold_r/rold_r)
  275. am=0.5d0*(aleft+arigh)
  276. c-------------------------------------------------------------------
  277. damr_r=-arigh/(4.0d0*rold_r)
  278. damu_r=0.0d0
  279. damv_r=0.0d0
  280. damp_r=gar/(4.0d0*arigh*rold_r)
  281. damg_r=arigh/(4.0d0*gar)
  282. c-----------------------
  283. damr_l=-aleft/(4.0d0*rold_l)
  284. damu_l=0.0d0
  285. damv_l=0.0d0
  286. damp_l=gal/(4.0d0*aleft*rold_l)
  287. damg_l=aleft/(4.0d0*gal)
  288. c-------------------------------------------------------------------
  289. c Computing numerical Mach number and its derivatives,
  290. c see p.370, under (A1).
  291. c-------------------------------------------------------------------
  292. un_l=uold_l*n_x+vold_l*n_y
  293. un_r=uold_r*n_x+vold_r*n_y
  294. ut_l=uold_l*t_x+vold_l*t_y
  295. ut_r=uold_r*t_x+vold_r*t_y
  296. c-------------------------------------------------------------------
  297. ml=un_l/am
  298. mr=un_r/am
  299. c-------------------------------------------------------------------
  300. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  301. c see (19a) and (19b), p.367.
  302. c-------------------------------------------------------------------
  303. if(abs(ml) .ge. 1.0d0) then
  304. Mplus=(ml+abs(ml))/2.0d0
  305. else
  306. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  307. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  308. endif
  309. c-------------------------------------------------------------------
  310. if(abs(mr) .ge. 1.0d0) then
  311. Mmin=(mr-abs(mr))/2.0d0
  312. else
  313. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  314. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  315. endif
  316. c-------------------------------------------------------------------
  317. c Derivatives of ml and mr with respect to both sets of primitive
  318. c variables: left and right.
  319. c-------------------------------------------------------------------
  320. temp_l=-un_l/(am*am)
  321. temp_r=-un_r/(am*am)
  322. c--------
  323. dmlr_l=temp_l*damr_l
  324. dmlr_r=temp_l*damr_r
  325. dmrr_l=temp_r*damr_l
  326. dmrr_r=temp_r*damr_r
  327. c--------
  328. dmlu_l=n_x/am+temp_l*damu_l
  329. dmlu_r=temp_l*damu_r
  330. dmru_l=temp_r*damu_l
  331. dmru_r=n_x/am+temp_r*damu_r
  332. c--------
  333. dmlv_l=n_y/am+temp_l*damv_l
  334. dmlv_r=temp_l*damv_r
  335. dmrv_l=temp_r*damv_l
  336. dmrv_r=n_y/am+temp_r*damv_r
  337. c--------
  338. dmlp_l=temp_l*damp_l
  339. dmlp_r=temp_l*damp_r
  340. dmrp_l=temp_r*damp_l
  341. dmrp_r=temp_r*damp_r
  342. c--------
  343. do 44 i=1,(nsp-1)
  344. dmly_l.vv(i)=temp_l*damg_l*dgdyl.vv(i)
  345. dmly_r.vv(i)=temp_l*damg_r*dgdyr.vv(i)
  346. dmry_l.vv(i)=temp_r*damg_l*dgdyl.vv(i)
  347. dmry_r.vv(i)=temp_r*damg_r*dgdyr.vv(i)
  348. 44 continue
  349. c-----------------------------------------------------------
  350. c mmid is m_{1/2} (notation as in the paper, see (13),p.366)
  351. c-----------------------------------------------------------
  352. mmid=Mplus+Mmin
  353. c-----------------------------------------------------------
  354. c Computing the derivatives of M+ and M-
  355. c-----------------------------------------------------------
  356. if(ml .ge. 1.0d0) then
  357. dMpr_l=dmlr_l
  358. dMpu_l=dmlu_l
  359. dMpv_l=dmlv_l
  360. dMpp_l=dmlp_l
  361. do 45 i=1,(nsp-1)
  362. dMpy_l.vv(i)=dmly_l.vv(i)
  363. 45 continue
  364. c--------------------
  365. dMpr_r=dmlr_r
  366. dMpu_r=dmlu_r
  367. dMpv_r=dmlv_r
  368. dMpp_r=dmlp_r
  369. do 46 i=1,(nsp-1)
  370. dMpy_r.vv(i)=dmly_r.vv(i)
  371. 46 continue
  372. else
  373. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  374. temph=(ml+1.0d0)/2.0d0
  375. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  376. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  377. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  378. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  379. do 47 i=1,(nsp-1)
  380. dMpy_l.vv(i)=(temph+4.0d0*beta*ml*
  381. & (ml*ml-1.0d0))*dmly_l.vv(i)
  382. 47 continue
  383. c--------------------
  384. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  385. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  386. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  387. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  388. do 48 i=1,(nsp-1)
  389. dMpy_r.vv(i)=(temph+4.0d0*beta*ml*
  390. & (ml*ml-1.0d0))*dmly_r.vv(i)
  391. 48 continue
  392. else
  393. dMpr_l=0.0d0
  394. dMpu_l=0.0d0
  395. dMpv_l=0.0d0
  396. dMpp_l=0.0d0
  397. do 49 i=1,(nsp-1)
  398. dMpy_l.vv(i)=0.0d0
  399. 49 continue
  400. c---------------------
  401. dMpr_r=0.0d0
  402. dMpu_r=0.0d0
  403. dMpv_r=0.0d0
  404. dMpp_r=0.0d0
  405. do 50 i=1,(nsp-1)
  406. dMpy_r.vv(i)=0.0d0
  407. 50 continue
  408. endif
  409. endif
  410. c-----------------------------------------------------------
  411. if(mr .ge. 1.0d0) then
  412. dMmr_l=0.0d0
  413. dMmu_l=0.0d0
  414. dMmv_l=0.0d0
  415. dMmp_l=0.0d0
  416. do 51 i=1,(nsp-1)
  417. dMmy_l.vv(i)=0.0d0
  418. 51 continue
  419. c---------------------
  420. dMmr_r=0.0d0
  421. dMmu_r=0.0d0
  422. dMmv_r=0.0d0
  423. dMmp_r=0.0d0
  424. do 52 i=1,(nsp-1)
  425. dMmy_r.vv(i)=0.0d0
  426. 52 continue
  427. else
  428. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  429. temph=(-mr+1.0d0)/2.0d0
  430. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  431. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  432. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  433. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  434. do 53 i=1,(nsp-1)
  435. dMmy_l.vv(i)=(temph-4.0d0*beta*mr*
  436. & (mr*mr-1.0d0))*dmry_l.vv(i)
  437. 53 continue
  438. c--------------------
  439. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  440. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  441. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  442. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  443. do 54 i=1,(nsp-1)
  444. dMmy_r.vv(i)=(temph-4.0d0*beta*mr*
  445. & (mr*mr-1.0d0))*dmry_r.vv(i)
  446. 54 continue
  447. else
  448. dMmr_l=dmrr_l
  449. dMmu_l=dmru_l
  450. dMmv_l=dmrv_l
  451. dMmp_l=dmrp_l
  452. do 55 i=1,(nsp-1)
  453. dMmy_l.vv(i)=dmry_l.vv(i)
  454. 55 continue
  455. c--------------------
  456. dMmr_r=dmrr_r
  457. dMmu_r=dmru_r
  458. dMmv_r=dmrv_r
  459. dMmp_r=dmrp_r
  460. do 56 i=1,(nsp-1)
  461. dMmy_r.vv(i)=dmry_r.vv(i)
  462. 56 continue
  463. endif
  464. endif
  465. c-----------------------------------------------------------------
  466. c computing the derivatives of m_{1/2} (notation as in the paper)
  467. c-----------------------------------------------------------------
  468. dmir_l=dMpr_l+dMmr_l
  469. dmir_r=dMpr_r+dMmr_r
  470. c-------------
  471. dmiu_l=dMpu_l+dMmu_l
  472. dmiu_r=dMpu_r+dMmu_r
  473. c-------------
  474. dmiv_l=dMpv_l+dMmv_l
  475. dmiv_r=dMpv_r+dMmv_r
  476. c-------------
  477. dmip_l=dMpp_l+dMmp_l
  478. dmip_r=dMpp_r+dMmp_r
  479. c-------------
  480. do 57 i=1,(nsp-1)
  481. dmiy_l.vv(i)=dMpy_l.vv(i)+dMmy_l.vv(i)
  482. dmiy_r.vv(i)=dMpy_r.vv(i)+dMmy_r.vv(i)
  483. 57 continue
  484. c----------------------------------------------------------------
  485. c computing the main convective variables and their derivatives
  486. c mpl_m is m^{+}_{1/2} (paper's notation) and
  487. c mmin_m is m^{-}_{1/2} (paper's notation), see (A2) on p.370.
  488. c----------------------------------------------------------------
  489. if(mmid .ge. 0.0d0) then
  490. mpl_m = mmid
  491. d2mr_l=dmir_l
  492. d2mu_l=dmiu_l
  493. d2mv_l=dmiv_l
  494. d2mp_l=dmip_l
  495. do 58 i=1,(nsp-1)
  496. d2my_l.vv(i)=dmiy_l.vv(i)
  497. 58 continue
  498. c------------
  499. d2mr_r=dmir_r
  500. d2mu_r=dmiu_r
  501. d2mv_r=dmiv_r
  502. d2mp_r=dmip_r
  503. do 59 i=1,(nsp-1)
  504. d2my_r.vv(i)=dmiy_r.vv(i)
  505. 59 continue
  506. c------------
  507. else
  508. mpl_m = 0.0d0
  509. d2mr_l=0.0d0
  510. d2mu_l=0.0d0
  511. d2mv_l=0.0d0
  512. d2mp_l=0.0d0
  513. do 60 i=1,(nsp-1)
  514. d2my_l.vv(i)=0.0d0
  515. 60 continue
  516. c------------
  517. d2mr_r=0.0d0
  518. d2mu_r=0.0d0
  519. d2mv_r=0.0d0
  520. d2mp_r=0.0d0
  521. do 61 i=1,(nsp-1)
  522. d2my_r.vv(i)=0.0d0
  523. 61 continue
  524. endif
  525. c---------------------------------------------
  526. if(mmid .le. 0.0d0) then
  527. mmin_m = mmid
  528. d3mr_l=dmir_l
  529. d3mu_l=dmiu_l
  530. d3mv_l=dmiv_l
  531. d3mp_l=dmip_l
  532. do 62 i=1,(nsp-1)
  533. d3my_l.vv(i)=dmiy_l.vv(i)
  534. 62 continue
  535. c------------
  536. d3mr_r=dmir_r
  537. d3mu_r=dmiu_r
  538. d3mv_r=dmiv_r
  539. d3mp_r=dmip_r
  540. do 63 i=1,(nsp-1)
  541. d3my_r.vv(i)=dmiy_r.vv(i)
  542. 63 continue
  543. c------------
  544. else
  545. mmin_m = 0.0d0
  546. d3mr_l=0.0d0
  547. d3mu_l=0.0d0
  548. d3mv_l=0.0d0
  549. d3mp_l=0.0d0
  550. do 64 i=1,(nsp-1)
  551. d3my_l.vv(i)=0.0d0
  552. 64 continue
  553. c------------
  554. d3mr_r=0.0d0
  555. d3mu_r=0.0d0
  556. d3mv_r=0.0d0
  557. d3mp_r=0.0d0
  558. do 65 i=1,(nsp-1)
  559. d3my_r.vv(i)=0.0d0
  560. 65 continue
  561. endif
  562. c---------------------------------------------------------------
  563. c Computing the calligraphic P+ and P- with their derivatives,
  564. c see (21a) & (21b) on p.368.
  565. c---------------------------------------------------------------
  566. if(ml .ge. 1.0d0) then
  567. Pplus = 1.0d0
  568. else
  569. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  570. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  571. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  572. else
  573. Pplus = 0.0d0
  574. endif
  575. endif
  576. c---------------------------------------------------------------
  577. if(mr .ge. 1.0d0) then
  578. Pmin = 0.0d0
  579. else
  580. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  581. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  582. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  583. else
  584. Pmin = 1.0d0
  585. endif
  586. endif
  587. c---------------------------------------------------------------
  588. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  589. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  590. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  591. c--------------
  592. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  593. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  594. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  595. c---------------------------------------------------------------
  596. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  597. dPpr_l=brac_l*dmlr_l
  598. dPpr_r=brac_l*dmlr_r
  599. c------------
  600. dPpu_l=brac_l*dmlu_l
  601. dPpu_r=brac_l*dmlu_r
  602. c------------
  603. dPpv_l=brac_l*dmlv_l
  604. dPpv_r=brac_l*dmlv_r
  605. c------------
  606. dPpp_l=brac_l*dmlp_l
  607. dPpp_r=brac_l*dmlp_r
  608. c------------
  609. do 66 i=1,(nsp-1)
  610. dPpy_l.vv(i)=brac_l*dmly_l.vv(i)
  611. dPpy_r.vv(i)=brac_l*dmly_r.vv(i)
  612. 66 continue
  613. c------------
  614. else
  615. dPpr_l=0.0d0
  616. dPpr_r=0.0d0
  617. c-----------
  618. dPpu_l=0.0d0
  619. dPpu_r=0.0d0
  620. c-----------
  621. dPpv_l=0.0d0
  622. dPpv_r=0.0d0
  623. c-----------
  624. dPpp_l=0.0d0
  625. dPpp_r=0.0d0
  626. c-----------
  627. do 67 i=1,(nsp-1)
  628. dPpy_l.vv(i)=0.0d0
  629. dPpy_r.vv(i)=0.0d0
  630. 67 continue
  631. c-----------
  632. endif
  633. c---------------------------------------------------------------
  634. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  635. dPmr_l=brac_r*dmrr_l
  636. dPmr_r=brac_r*dmrr_r
  637. c------------
  638. dPmu_l=brac_r*dmru_l
  639. dPmu_r=brac_r*dmru_r
  640. c------------
  641. dPmv_l=brac_r*dmrv_l
  642. dPmv_r=brac_r*dmrv_r
  643. c------------
  644. dPmp_l=brac_r*dmrp_l
  645. dPmp_r=brac_r*dmrp_r
  646. c------------
  647. do 68 i=1,(nsp-1)
  648. dPmy_l.vv(i)=brac_r*dmry_l.vv(i)
  649. dPmy_r.vv(i)=brac_r*dmry_r.vv(i)
  650. 68 continue
  651. c------------
  652. else
  653. dPmr_l=0.0d0
  654. dPmr_r=0.0d0
  655. c-----------
  656. dPmu_l=0.0d0
  657. dPmu_r=0.0d0
  658. c-----------
  659. dPmv_l=0.0d0
  660. dPmv_r=0.0d0
  661. c-----------
  662. dPmp_l=0.0d0
  663. dPmp_r=0.0d0
  664. c-----------
  665. do 69 i=1,(nsp-1)
  666. dPmy_l.vv(i)=0.0d0
  667. dPmy_r.vv(i)=0.0d0
  668. 69 continue
  669. c-----------
  670. endif
  671. c-------------------------------------------------------------------
  672. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  673. c-------------------------------------------------------------------
  674. pmid=Pplus*pold_l + Pmin*pold_r
  675. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  676. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  677. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  678. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  679. do 70 i=1,(nsp-1)
  680. dpiy_l.vv(i)=dPpy_l.vv(i)*pold_l+dPmy_l.vv(i)*pold_r
  681. 70 continue
  682. c----------------------------
  683. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  684. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  685. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  686. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  687. do 71 i=1,(nsp-1)
  688. dpiy_r.vv(i)=dPpy_r.vv(i)*pold_l+dPmy_r.vv(i)*pold_r
  689. 71 continue
  690. c---------------------------------------------------------------------
  691. c computing JACOBIAN as a derivative of the numerical flux function
  692. c with respect to the primitive variables.
  693. c Notation: jl(i,j) --- is the derivative of the i-component of the
  694. c flux function with respect to the j-component of the
  695. c vector of primitive variables of the left state.
  696. c jr(i,j) --- is the derivative of the i-component of the
  697. c flux function with respect to the j-component of the
  698. c vector of primitive variables of the right state.
  699. c---------------------------------------------------------------------
  700. f.fu(1)=am*(mpl_m*rold_l+mmin_m*rold_r)
  701. c---------------------------------------------------------------------
  702. jl.jac(1,1)=damr_l*f.fu(1)/am+am*(d2mr_l*rold_l+mpl_m)
  703. jl.jac(1,1)=jl.jac(1,1)+am*d3mr_l*rold_r
  704. jl.jac(1,2)=damu_l*f.fu(1)/am+am*(d2mu_l*rold_l+d3mu_l*rold_r)
  705. jl.jac(1,3)=damv_l*f.fu(1)/am+am*(d2mv_l*rold_l+d3mv_l*rold_r)
  706. jl.jac(1,4)=damp_l*f.fu(1)/am+am*(d2mp_l*rold_l+d3mp_l*rold_r)
  707. do 72 i=1,(nsp-1)
  708. jl.jac(1,4+i)=damg_l*dgdyl.vv(i)*f.fu(1)/am+
  709. & am*(d2my_l.vv(i)*rold_l+d3my_l.vv(i)*rold_r)
  710. 72 continue
  711. c------------------------------------
  712. jr.jac(1,1)=damr_r*f.fu(1)/am+am*(d2mr_r*rold_l+mmin_m)
  713. jr.jac(1,1)=jr.jac(1,1)+am*d3mr_r*rold_r
  714. jr.jac(1,2)=damu_r*f.fu(1)/am+am*(d2mu_r*rold_l+d3mu_r*rold_r)
  715. jr.jac(1,3)=damv_r*f.fu(1)/am+am*(d2mv_r*rold_l+d3mv_r*rold_r)
  716. jr.jac(1,4)=damp_r*f.fu(1)/am+am*(d2mp_r*rold_l+d3mp_r*rold_r)
  717. do 73 i=1,(nsp-1)
  718. jr.jac(1,4+i)=damg_r*dgdyr.vv(i)*f.fu(1)/am+
  719. & am*(d2my_r.vv(i)*rold_l+d3my_r.vv(i)*rold_r)
  720. 73 continue
  721. c------------------------------------
  722. c------------------------------------
  723. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  724. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  725. f.fu(2)=n_x*(am*br1+pmid)+am*t_x*br2
  726. c------------------
  727. det=n_x*t_y-n_y*t_x
  728. c---------------------------------------------------------
  729. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  730. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  731. jl.jac(2,1)=n_x*(damr_l*br1+am*br3+dpir_l)
  732. jl.jac(2,1)=jl.jac(2,1)+t_x*damr_l*br2+am*t_x*br4
  733. c-------------------
  734. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  735. br3=br3+d3mu_l*rold_r*un_r
  736. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y)/det
  737. br4=br4+d3mu_l*rold_r*ut_r
  738. jl.jac(2,2)=n_x*(damu_l*br1+am*br3+dpiu_l)
  739. jl.jac(2,2)=jl.jac(2,2)+t_x*damu_l*br2+am*t_x*br4
  740. c-------------------
  741. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x)/det
  742. br3=br3+d3mv_l*rold_r*un_r
  743. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  744. br4=br4+d3mv_l*rold_r*ut_r
  745. jl.jac(2,3)=n_x*(damv_l*br1+am*br3+dpiv_l)
  746. jl.jac(2,3)=jl.jac(2,3)+t_x*damv_l*br2+am*t_x*br4
  747. c-------------------
  748. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  749. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  750. jl.jac(2,4)=n_x*(damp_l*br1+am*br3+dpip_l)
  751. jl.jac(2,4)=jl.jac(2,4)+t_x*damp_l*br2+am*t_x*br4
  752. c-------------------
  753. do 74 i=1,(nsp-1)
  754. br3=d2my_l.vv(i)*rold_l*un_l+d3my_l.vv(i)*rold_r*un_r
  755. br4=d2my_l.vv(i)*rold_l*ut_l+d3my_l.vv(i)*rold_r*ut_r
  756. jl.jac(2,4+i)=n_x*(damg_l*dgdyl.vv(i)*br1+
  757. & am*br3+dpiy_l.vv(i))
  758. jl.jac(2,4+i)=jl.jac(2,4+i)+
  759. & t_x*damg_l*dgdyl.vv(i)*br2+am*t_x*br4
  760. 74 continue
  761. c-------------------------------------------------------------
  762. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  763. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  764. jr.jac(2,1)=n_x*(damr_r*br1+am*br3+dpir_r)
  765. jr.jac(2,1)=jr.jac(2,1)+t_x*damr_r*br2+am*t_x*br4
  766. c-------------------
  767. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  768. br3=br3+d3mu_r*rold_r*un_r
  769. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  770. br4=br4+d3mu_r*rold_r*ut_r
  771. jr.jac(2,2)=n_x*(damu_r*br1+am*br3+dpiu_r)
  772. jr.jac(2,2)=jr.jac(2,2)+t_x*damu_r*br2+am*t_x*br4
  773. c-------------------
  774. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  775. br3=br3+d3mv_r*rold_r*un_r
  776. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  777. br4=br4+d3mv_r*rold_r*ut_r
  778. jr.jac(2,3)=n_x*(damv_r*br1+am*br3+dpiv_r)
  779. jr.jac(2,3)=jr.jac(2,3)+t_x*damv_r*br2+am*t_x*br4
  780. c-------------------
  781. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  782. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  783. jr.jac(2,4)=n_x*(damp_r*br1+am*br3+dpip_r)
  784. jr.jac(2,4)=jr.jac(2,4)+t_x*damp_r*br2+am*t_x*br4
  785. c-------------------
  786. do 75 i=1,(nsp-1)
  787. br3=d2my_r.vv(i)*rold_l*un_l+d3my_r.vv(i)*rold_r*un_r
  788. br4=d2my_r.vv(i)*rold_l*ut_l+d3my_r.vv(i)*rold_r*ut_r
  789. jr.jac(2,4+i)=n_x*(damg_r*dgdyr.vv(i)*br1+
  790. & am*br3+dpiy_r.vv(i))
  791. jr.jac(2,4+i)=jr.jac(2,4+i)+
  792. & t_x*damg_r*dgdyr.vv(i)*br2+am*t_x*br4
  793. 75 continue
  794. c-------------------------------------------------------------
  795. c-------------------------------------------------------------
  796. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  797. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  798. f.fu(3)=n_y*(am*br1+pmid)+am*t_y*br2
  799. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  800. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  801. jl.jac(3,1)=n_y*(damr_l*br1+am*br3+dpir_l)
  802. jl.jac(3,1)=jl.jac(3,1)+t_y*damr_l*br2+am*t_y*br4
  803. c-------------------
  804. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  805. br3=br3+d3mu_l*rold_r*un_r
  806. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y/det)
  807. br4=br4+d3mu_l*rold_r*ut_r
  808. jl.jac(3,2)=n_y*(damu_l*br1+am*br3+dpiu_l)
  809. jl.jac(3,2)=jl.jac(3,2)+t_y*damu_l*br2+am*t_y*br4
  810. c-------------------
  811. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x/det)
  812. br3=br3+d3mv_l*rold_r*un_r
  813. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  814. br4=br4+d3mv_l*rold_r*ut_r
  815. jl.jac(3,3)=n_y*(damv_l*br1+am*br3+dpiv_l)
  816. jl.jac(3,3)=jl.jac(3,3)+t_y*damv_l*br2+am*t_y*br4
  817. c-------------------
  818. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  819. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  820. jl.jac(3,4)=n_y*(damp_l*br1+am*br3+dpip_l)
  821. jl.jac(3,4)=jl.jac(3,4)+t_y*damp_l*br2+am*t_y*br4
  822. c-------------------
  823. do 76 i=1,(nsp-1)
  824. br3=d2my_l.vv(i)*rold_l*un_l+d3my_l.vv(i)*rold_r*un_r
  825. br4=d2my_l.vv(i)*rold_l*ut_l+d3my_l.vv(i)*rold_r*ut_r
  826. jl.jac(3,4+i)=n_y*(damg_l*dgdyl.vv(i)*br1+
  827. & am*br3+dpiy_l.vv(i))
  828. jl.jac(3,4+i)=jl.jac(3,4+i)+
  829. & t_y*damg_l*dgdyl.vv(i)*br2+am*t_y*br4
  830. 76 continue
  831. c-------------------------------------------------------------
  832. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  833. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  834. jr.jac(3,1)=n_y*(damr_r*br1+am*br3+dpir_r)
  835. jr.jac(3,1)=jr.jac(3,1)+t_y*damr_r*br2+am*t_y*br4
  836. c-------------------
  837. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  838. br3=br3+d3mu_r*rold_r*un_r
  839. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  840. br4=br4+d3mu_r*rold_r*ut_r
  841. jr.jac(3,2)=n_y*(damu_r*br1+am*br3+dpiu_r)
  842. jr.jac(3,2)=jr.jac(3,2)+t_y*damu_r*br2+am*t_y*br4
  843. c-------------------
  844. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  845. br3=br3+d3mv_r*rold_r*un_r
  846. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  847. br4=br4+d3mv_r*rold_r*ut_r
  848. jr.jac(3,3)=n_y*(damv_r*br1+am*br3+dpiv_r)
  849. jr.jac(3,3)=jr.jac(3,3)+t_y*damv_r*br2+am*t_y*br4
  850. c-------------------
  851. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  852. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  853. jr.jac(3,4)=n_y*(damp_r*br1+am*br3+dpip_r)
  854. jr.jac(3,4)=jr.jac(3,4)+t_y*damp_r*br2+am*t_y*br4
  855. c-------------------
  856. do 77 i=1,(nsp-1)
  857. br3=d2my_r.vv(i)*rold_l*un_l+d3my_r.vv(i)*rold_r*un_r
  858. br4=d2my_r.vv(i)*rold_l*ut_l+d3my_r.vv(i)*rold_r*ut_r
  859. jr.jac(3,4+i)=n_y*(damg_r*dgdyr.vv(i)*br1+
  860. & am*br3+dpiy_r.vv(i))
  861. jr.jac(3,4+i)=jr.jac(3,4+i)+
  862. & t_y*damg_r*dgdyr.vv(i)*br2+am*t_y*br4
  863. 77 continue
  864. c-------------------------------------------------------------
  865. c --------------------- f4 ----------------------------
  866. c-------------------------------------------------------------
  867. hr_l=rold_l*(uold_l*uold_l+vold_l*vold_l)/2.0d0+gal*pold_l/gm1l
  868. hr_r=rold_r*(uold_r*uold_r+vold_r*vold_r)/2.0d0+gar*pold_r/gm1r
  869. f.fu(4)=am*(mpl_m*hr_l+mmin_m*hr_r)
  870. c---------------------
  871. br1=d2mr_l*hr_l+mpl_m*(uold_l*uold_l+vold_l*vold_l)/2.0d0
  872. br1=br1+d3mr_l*hr_r
  873. jl.jac(4,1)=damr_l*f.fu(4)/am+am*br1
  874. c---------------------
  875. br1=d2mu_l*hr_l+mpl_m*uold_l*rold_l
  876. br1=br1+d3mu_l*hr_r
  877. jl.jac(4,2)=damu_l*f.fu(4)/am+am*br1
  878. c---------------------
  879. br1=d2mv_l*hr_l+mpl_m*vold_l*rold_l
  880. br1=br1+d3mv_l*hr_r
  881. jl.jac(4,3)=damv_l*f.fu(4)/am+am*br1
  882. c---------------------
  883. br1=d2mp_l*hr_l+mpl_m*gal/gm1l
  884. br1=br1+d3mp_l*hr_r
  885. jl.jac(4,4)=damp_l*f.fu(4)/am+am*br1
  886. c---------------------
  887. do 78 i=1,(nsp-1)
  888. br1=d2my_l.vv(i)*hr_l+mpl_m*(-pold_l)*dgdyl.vv(i)/(gm1l*gm1l)
  889. br1=br1+d3my_l.vv(i)*hr_r
  890. jl.jac(4,4+i)=damg_l*dgdyl.vv(i)*f.fu(4)/am+am*br1
  891. 78 continue
  892. c----------------------------------------------------------
  893. c----------------------------------------------------------
  894. br1=d2mr_r*hr_l+mmin_m*(uold_r*uold_r+vold_r*vold_r)/2.0d0
  895. br1=br1+d3mr_r*hr_r
  896. jr.jac(4,1)=damr_r*f.fu(4)/am+am*br1
  897. c---------------------
  898. br1=d2mu_r*hr_l+mmin_m*uold_r*rold_r
  899. br1=br1+d3mu_r*hr_r
  900. jr.jac(4,2)=damu_r*f.fu(4)/am+am*br1
  901. c---------------------
  902. br1=d2mv_r*hr_l+mmin_m*vold_r*rold_r
  903. br1=br1+d3mv_r*hr_r
  904. jr.jac(4,3)=damv_r*f.fu(4)/am+am*br1
  905. c---------------------
  906. br1=d2mp_r*hr_l+mmin_m*gar/gm1r
  907. br1=br1+d3mp_r*hr_r
  908. jr.jac(4,4)=damp_r*f.fu(4)/am+am*br1
  909. c---------------------
  910. do 79 i=1,(nsp-1)
  911. br1=d2my_r.vv(i)*hr_l+mmin_m*
  912. & (-pold_r)*dgdyr.vv(i)/(gm1r*gm1r)
  913. br1=br1+d3my_r.vv(i)*hr_r
  914. jr.jac(4,4+i)=damg_r*dgdyr.vv(i)*f.fu(4)/am+am*br1
  915. 79 continue
  916. c-------------------------------------------------------------
  917. c ------------------ f5++ ------------------------------------
  918. c-------------------------------------------------------------
  919. do 80 i=1,(nsp-1)
  920. f.fu(4+i)=am*(mpl_m*rold_l*yl.yet(i)+mmin_m*rold_r*yr.yet(i))
  921. c---------------------
  922. jl.jac(4+i,1)=damr_l*f.fu(4+i)/am+
  923. & am*(d2mr_l*rold_l*yl.yet(i)+mpl_m*yl.yet(i))
  924. jl.jac(4+i,1)=jl.jac(4+i,1)+am*d3mr_l*rold_r*yr.yet(i)
  925. jl.jac(4+i,2)=damu_l*f.fu(4+i)/am+am*(d2mu_l*rold_l*yl.yet(i)+
  926. & d3mu_l*rold_r*yr.yet(i))
  927. jl.jac(4+i,3)=damv_l*f.fu(4+i)/am+am*(d2mv_l*rold_l*yl.yet(i)+
  928. & d3mv_l*rold_r*yr.yet(i))
  929. jl.jac(4+i,4)=damp_l*f.fu(4+i)/am+am*(d2mp_l*rold_l*yl.yet(i)+
  930. & d3mp_l*rold_r*yr.yet(i))
  931. do 81 j=5,(4+nsp-1)
  932. if((4+i).eq.j) then
  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)+mpl_m*rold_l+
  935. & d3my_l.vv(j-4)*rold_r*yr.yet(i))
  936. else
  937. jl.jac(4+i,j)=damg_l*dgdyl.vv(j-4)*f.fu(4+i)/am+
  938. & am*(d2my_l.vv(j-4)*rold_l*yl.yet(i)+
  939. & d3my_l.vv(j-4)*rold_r*yr.yet(i))
  940. endif
  941. 81 continue
  942. c------------------------------------
  943. jr.jac(4+i,1)=damr_r*f.fu(4+i)/am+
  944. & am*(d2mr_r*rold_l*yl.yet(i)+mmin_m*yr.yet(i))
  945. jr.jac(4+i,1)=jr.jac(4+i,1)+am*d3mr_r*rold_r*yr.yet(i)
  946. jr.jac(4+i,2)=damu_r*f.fu(4+i)/am+am*(d2mu_r*rold_l*yl.yet(i)+
  947. & d3mu_r*rold_r*yr.yet(i))
  948. jr.jac(4+i,3)=damv_r*f.fu(4+i)/am+am*(d2mv_r*rold_l*yl.yet(i)+
  949. & d3mv_r*rold_r*yr.yet(i))
  950. jr.jac(4+i,4)=damp_r*f.fu(4+i)/am+am*(d2mp_r*rold_l*yl.yet(i)+
  951. & d3mp_r*rold_r*yr.yet(i))
  952. do 82 j=1,(nsp-1)
  953. if(i.eq.j) then
  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)+mmin_m*rold_r+
  956. & d3my_r.vv(j)*rold_r*yr.yet(i))
  957. else
  958. jr.jac(4+i,4+j)=damg_r*dgdyr.vv(j)*f.fu(4+i)/am+
  959. & am*(d2my_r.vv(j)*rold_l*yl.yet(i)+
  960. & d3my_r.vv(j)*rold_r*yr.yet(i))
  961. endif
  962. 82 continue
  963. 80 continue
  964. C-------------------------------------------------------------
  965. C This operation is made for the outlet boundary conditions
  966. C when the pressure at the outlet is given.
  967. C To find the flux it was assumed that rho_l = rho_r,
  968. C velocity_l=velocity_r and yl = yr
  969. C therefore we hace to modify the jacobian
  970. C-------------------------------------------------------------
  971. DO 105 I=1,(3+NSP)
  972. DO 106 J=1,(3+NSP)
  973. IF(J .EQ. 4) THEN
  974. JL.JAC(I,J) = JL.JAC(I,J)
  975. ELSE
  976. JL.JAC(I,J)=JL.JAC(I,J)+JR.JAC(I,J)
  977. ENDIF
  978. 106 CONTINUE
  979. 105 CONTINUE
  980. c-------------------------------------------------------------
  981. c matrix wl(i,j) represents the derivative of the i-component
  982. c of the vector of primitive variables of the left state with
  983. c respect to the j-component of the vector of the conservative
  984. c variables of the left state.
  985. c
  986. c Here: (rho, ux, uy, p, Y_1,...,Y_(nsp-1)) -
  987. c vector of primitive variables;
  988. c (rho, rho ux, rho uy, rho e, rho Y_1,..., rho Y_(nsp-1)) -
  989. c vector of conservative variables.
  990. c-------------------------------------------------------------
  991. wl.jac(1,1)=1.0d0
  992. wl.jac(1,2)=0.0d0
  993. wl.jac(1,3)=0.0d0
  994. wl.jac(1,4)=0.0d0
  995. do 83 i=1,(nsp-1)
  996. wl.jac(1,4+i)=0.0d0
  997. 83 continue
  998. c------------------------------
  999. wl.jac(2,1)=-uold_l/rold_l
  1000. wl.jac(2,2)=1.0d0/rold_l
  1001. wl.jac(2,3)=0.0d0
  1002. wl.jac(2,4)=0.0d0
  1003. do 84 i=1,(nsp-1)
  1004. wl.jac(2,4+i)=0.0d0
  1005. 84 continue
  1006. c------------------------------
  1007. wl.jac(3,1)=-vold_l/rold_l
  1008. wl.jac(3,2)=0.0d0
  1009. wl.jac(3,3)=1.0d0/rold_l
  1010. wl.jac(3,4)=0.0d0
  1011. do 85 i=1,(nsp-1)
  1012. wl.jac(3,4+i)=0.0d0
  1013. 85 continue
  1014. c------------------------------
  1015. br1=0.0d0
  1016. do 86 i=1,(nsp-1)
  1017. br1=br1+dgdyl.vv(i)*yl.yet(i)
  1018. 86 continue
  1019. br1=br1*pold_l/(rold_l*gm1l)
  1020. wl.jac(4,1)=gm1l*(uold_l*uold_l+vold_l*vold_l)/2.0d0-br1
  1021. wl.jac(4,2)=-uold_l*gm1l
  1022. wl.jac(4,3)=-vold_l*gm1l
  1023. wl.jac(4,4)=gm1l
  1024. do 87 i=1,(nsp-1)
  1025. wl.jac(4,4+i)=dgdyl.vv(i)*pold_l/(rold_l*gm1l)
  1026. 87 continue
  1027. c------------------------------
  1028. do 88 i=1,(nsp-1)
  1029. do 89 j=1,4
  1030. wl.jac(4+i,j)=0.0d0
  1031. if(j.eq.1) wl.jac(4+i,j)=-yl.yet(i)/rold_l
  1032. 89 continue
  1033. c------------
  1034. do 890 j=5,(4+nsp-1)
  1035. wl.jac(4+i,j)=0.0d0
  1036. if(4+i.eq.j) then
  1037. wl.jac(4+i,j)=1.0d0/rold_l
  1038. endif
  1039. 890 continue
  1040. 88 continue
  1041. c------------------------------
  1042. c----------------------------------------------
  1043. do 1 i=1,(3+nsp)
  1044. do 2 j=1,(3+nsp)
  1045. jtl.jac(i,j)=0.0d0
  1046. do 3 k=1,(3+nsp)
  1047. jtl.jac(i,j)=jtl.jac(i,j)+jl.jac(i,k)*wl.jac(k,j)
  1048. 3 continue
  1049. 2 continue
  1050. 1 continue
  1051. c----------------------------------------------------------------------
  1052. SEGSUP DMLY_L, DMLY_R,
  1053. & dmry_l, dmry_r,
  1054. & dMpy_l, dMpy_r,
  1055. & dMmy_l, dMmy_r,
  1056. & dmiy_l, dmiy_r,
  1057. & d3my_l, d3my_r,
  1058. & d2my_l, d2my_r,
  1059. & dPpy_l, dPpy_r,
  1060. & dPmy_l, dPmy_r,
  1061. & dpiy_l, dpiy_r,
  1062. & dgdyl, dgdyr
  1063. C--------------------------------------------
  1064. SEGSUP f
  1065. C--------------------------------------------
  1066. jpl = jl
  1067. SEGDES JL
  1068. SEGDES JR
  1069. SEGSUP WL
  1070. C--------------------------------------------
  1071. jll=jtl
  1072. SEGDES JTL
  1073. SEGDES YL
  1074. SEGDES YR
  1075. SEGDES CP
  1076. SEGDES CV
  1077. SEGDES MLRECP, MLRECV
  1078. C--------------------------------------------
  1079. return
  1080. end
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