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  1. C CONJAK SOURCE CB215821 16/04/21 21:15:57 8920
  2. SUBROUTINE CONJAK(JTL,JTR,WVEC_L,WVEC_R,NVECT,TVECT,
  3. & ga)
  4. C************************************************************************
  5. C
  6. C PROJET : CASTEM 2000
  7. C
  8. C NOM : CONJAK
  9. C
  10. C DESCRIPTION : Voir KONJA2
  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
  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 wvec_l -- vector of the primitive variables (rho,ux,uy,p) at the
  40. c left cell;
  41. c
  42. c wvec_r -- vector of the primitive variables (rho,ux,uy,p) at the
  43. c right cell;
  44. c
  45. c nvect -- normal vector to the interface (2 components in 2D);
  46. c
  47. c tvect -- tangential vector to the interface;
  48. c
  49. c ga -- ratio of the specific heats (assumed constant)
  50. c----------------------------------------------------------------------
  51. c
  52. c OUTPUT:
  53. c
  54. c jtl -- jakobian matrix 4 by 4 - derivatives of the numerical
  55. c flux function with respect to the conservative variables
  56. c from the left cell;
  57. c
  58. c jtr -- jakobian matrix 4 by 4 - derivatives of the numerical
  59. c flux function with respect to the conservative variables
  60. c from the right cell.
  61. c----------------------------------------------------------------------
  62. IMPLICIT INTEGER(I-N)
  63. real*8 wvec_l(4),wvec_r(4)
  64. real*8 nvect(2),tvect(2)
  65. real*8 jl(4,4),jr(4,4),f(4)
  66. real*8 wl(4,4),wr(4,4)
  67. real*8 jtl(4,4),jtr(4,4)
  68. real*8 alpha,beta
  69. real*8 ga, gm1,temph
  70. real*8 n_x,n_y,t_x,t_y
  71. real*8 un_l, un_r, ut_l, ut_r
  72. real*8 ml,mr,Mplus,Mmin,mmid
  73. real*8 mpl_m, mmin_m,am
  74. real*8 rold_l,uold_l,vold_l,pold_l,eold_l
  75. real*8 rold_r,uold_r,vold_r,pold_r,eold_r
  76. real*8 Pplus,Pmin,pmid
  77. real*8 hr_l,hr_r,det
  78. real*8 br1,br2,br3,br4,temp_l,temp_r,brac_l,brac_r
  79. real*8 aleft, arigh
  80. real*8 damr_l,damr_r,damu_l,damu_r
  81. real*8 damv_l,damv_r,damp_l,damp_r
  82. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  83. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  84. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  85. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  86. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  87. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r
  88. real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r
  89. real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r
  90. real*8 dmir_l,dmir_r,dmiu_l,dmiu_r
  91. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  92. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  93. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  94. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  95. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  96. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  97. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  98. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  99. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  100. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  101. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  102. integer i,j,k
  103. parameter(alpha = 0.1875D0, beta = 0.125D0)
  104. c-----------------------
  105. gm1=ga-1.0d0
  106. c-----------------------
  107. n_x=nvect(1)
  108. n_y=nvect(2)
  109. t_x=tvect(1)
  110. t_y=tvect(2)
  111. c----------------------------
  112. c----------------------------
  113. rold_l=wvec_l(1)
  114. uold_l=wvec_l(2)
  115. vold_l=wvec_l(3)
  116. pold_l=wvec_l(4)
  117. c-----------------------
  118. rold_r=wvec_r(1)
  119. uold_r=wvec_r(2)
  120. vold_r=wvec_r(3)
  121. pold_r=wvec_r(4)
  122. c------------------------------------------------------------------
  123. c Computation of the specific total energy on the left and right.
  124. c------------------------------------------------------------------
  125. eold_l=(uold_l*uold_l+vold_l*vold_l)/2.0d0
  126. eold_l=eold_l+pold_l/(gm1*rold_l)
  127. eold_r=(uold_r*uold_r+vold_r*vold_r)/2.0d0
  128. eold_r=eold_r+pold_r/(gm1*rold_r)
  129. c-------------------------------------------------------------------
  130. c Computation of the speed of sound and its derivatives;
  131. c numerical speed of sound at the interface is taken as an average
  132. c of the speeds of sounds of the neighbouring cells
  133. c-------------------------------------------------------------------
  134. aleft=SQRT(ga*pold_l/rold_l)
  135. arigh=SQRT(ga*pold_r/rold_r)
  136. am=0.5d0*(aleft+arigh)
  137. c-------------------------------------------------------------------
  138. damr_r=-arigh/(4.0d0*rold_r)
  139. damu_r=0.0d0
  140. damv_r=0.0d0
  141. damp_r=ga/(4.0d0*arigh*rold_r)
  142. c-----------------------
  143. damr_l=-aleft/(4.0d0*rold_l)
  144. damu_l=0.0d0
  145. damv_l=0.0d0
  146. damp_l=ga/(4.0d0*aleft*rold_l)
  147. c-------------------------------------------------------------------
  148. c Computing numerical Mach number and its derivatives,
  149. c see p.370, under (A1).
  150. c-------------------------------------------------------------------
  151. un_l=uold_l*n_x+vold_l*n_y
  152. un_r=uold_r*n_x+vold_r*n_y
  153. ut_l=uold_l*t_x+vold_l*t_y
  154. ut_r=uold_r*t_x+vold_r*t_y
  155. c-------------------------------------------------------------------
  156. ml=un_l/am
  157. mr=un_r/am
  158. c-------------------------------------------------------------------
  159. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  160. c see (19a) and (19b), p.367.
  161. c-------------------------------------------------------------------
  162. if(ABS(ml) .ge. 1.0d0) then
  163. Mplus=(ml+ABS(ml))/2.0d0
  164. else
  165. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  166. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  167. endif
  168. c-------------------------------------------------------------------
  169. if(ABS(mr) .ge. 1.0d0) then
  170. Mmin=(mr-ABS(mr))/2.0d0
  171. else
  172. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  173. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  174. endif
  175. c-------------------------------------------------------------------
  176. c Derivatives of ml and mr with respect to both sets of primitive
  177. c variables: left and right.
  178. c-------------------------------------------------------------------
  179. temp_l=-un_l/(am*am)
  180. temp_r=-un_r/(am*am)
  181. c--------
  182. dmlr_l=temp_l*damr_l
  183. dmlr_r=temp_l*damr_r
  184. dmrr_l=temp_r*damr_l
  185. dmrr_r=temp_r*damr_r
  186. c--------
  187. dmlu_l=n_x/am+temp_l*damu_l
  188. dmlu_r=temp_l*damu_r
  189. dmru_l=temp_r*damu_l
  190. dmru_r=n_x/am+temp_r*damu_r
  191. c--------
  192. dmlv_l=n_y/am+temp_l*damv_l
  193. dmlv_r=temp_l*damv_r
  194. dmrv_l=temp_r*damv_l
  195. dmrv_r=n_y/am+temp_r*damv_r
  196. c--------
  197. dmlp_l=temp_l*damp_l
  198. dmlp_r=temp_l*damp_r
  199. dmrp_l=temp_r*damp_l
  200. dmrp_r=temp_r*damp_r
  201. c-----------------------------------------------------------
  202. c mmid is m_{1/2} (notation as in the paper, see (13),p.366)
  203. c-----------------------------------------------------------
  204. mmid=Mplus+Mmin
  205. c-----------------------------------------------------------
  206. c Computing the derivatives of M+ and M-
  207. c-----------------------------------------------------------
  208. if(ml .ge. 1.0d0) then
  209. dMpr_l=dmlr_l
  210. dMpu_l=dmlu_l
  211. dMpv_l=dmlv_l
  212. dMpp_l=dmlp_l
  213. c--------------------
  214. dMpr_r=dmlr_r
  215. dMpu_r=dmlu_r
  216. dMpv_r=dmlv_r
  217. dMpp_r=dmlp_r
  218. else
  219. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  220. temph=(ml+1.0d0)/2.0d0
  221. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  222. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  223. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  224. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  225. c--------------------
  226. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  227. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  228. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  229. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  230. else
  231. dMpr_l=0.0d0
  232. dMpu_l=0.0d0
  233. dMpv_l=0.0d0
  234. dMpp_l=0.0d0
  235. c---------------------
  236. dMpr_r=0.0d0
  237. dMpu_r=0.0d0
  238. dMpv_r=0.0d0
  239. dMpp_r=0.0d0
  240. endif
  241. endif
  242. c-----------------------------------------------------------
  243. if(mr .ge. 1.0d0) then
  244. dMmr_l=0.0d0
  245. dMmu_l=0.0d0
  246. dMmv_l=0.0d0
  247. dMmp_l=0.0d0
  248. c---------------------
  249. dMmr_r=0.0d0
  250. dMmu_r=0.0d0
  251. dMmv_r=0.0d0
  252. dMmp_r=0.0d0
  253. else
  254. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  255. temph=(-mr+1.0d0)/2.0d0
  256. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  257. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  258. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  259. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  260. c--------------------
  261. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  262. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  263. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  264. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  265. else
  266. dMmr_l=dmrr_l
  267. dMmu_l=dmru_l
  268. dMmv_l=dmrv_l
  269. dMmp_l=dmrp_l
  270. c--------------------
  271. dMmr_r=dmrr_r
  272. dMmu_r=dmru_r
  273. dMmv_r=dmrv_r
  274. dMmp_r=dmrp_r
  275. endif
  276. endif
  277. c-----------------------------------------------------------------
  278. c computing the derivatives of m_{1/2} (notation as in the paper)
  279. c-----------------------------------------------------------------
  280. dmir_l=dMpr_l+dMmr_l
  281. dmir_r=dMpr_r+dMmr_r
  282. c-------------
  283. dmiu_l=dMpu_l+dMmu_l
  284. dmiu_r=dMpu_r+dMmu_r
  285. c-------------
  286. dmiv_l=dMpv_l+dMmv_l
  287. dmiv_r=dMpv_r+dMmv_r
  288. c-------------
  289. dmip_l=dMpp_l+dMmp_l
  290. dmip_r=dMpp_r+dMmp_r
  291. c----------------------------------------------------------------
  292. c computing the main convective variables and their derivatives
  293. c mpl_m is m^{+}_{1/2} (paper's notation) and
  294. c mmin_m is m^{-}_{1/2} (paper's notation), see (A2) on p.370.
  295. c----------------------------------------------------------------
  296. if(mmid .ge. 0.0d0) then
  297. mpl_m = mmid
  298. d2mr_l=dmir_l
  299. d2mu_l=dmiu_l
  300. d2mv_l=dmiv_l
  301. d2mp_l=dmip_l
  302. c------------
  303. d2mr_r=dmir_r
  304. d2mu_r=dmiu_r
  305. d2mv_r=dmiv_r
  306. d2mp_r=dmip_r
  307. c------------
  308. else
  309. mpl_m = 0.0d0
  310. d2mr_l=0.0d0
  311. d2mu_l=0.0d0
  312. d2mv_l=0.0d0
  313. d2mp_l=0.0d0
  314. c------------
  315. d2mr_r=0.0d0
  316. d2mu_r=0.0d0
  317. d2mv_r=0.0d0
  318. d2mp_r=0.0d0
  319. endif
  320. c---------------------------------------------
  321. if(mmid .le. 0.0d0) then
  322. mmin_m = mmid
  323. d3mr_l=dmir_l
  324. d3mu_l=dmiu_l
  325. d3mv_l=dmiv_l
  326. d3mp_l=dmip_l
  327. c------------
  328. d3mr_r=dmir_r
  329. d3mu_r=dmiu_r
  330. d3mv_r=dmiv_r
  331. d3mp_r=dmip_r
  332. c------------
  333. else
  334. mmin_m = 0.0d0
  335. d3mr_l=0.0d0
  336. d3mu_l=0.0d0
  337. d3mv_l=0.0d0
  338. d3mp_l=0.0d0
  339. c------------
  340. d3mr_r=0.0d0
  341. d3mu_r=0.0d0
  342. d3mv_r=0.0d0
  343. d3mp_r=0.0d0
  344. endif
  345. c---------------------------------------------------------------
  346. c Computing the calligraphic P+ and P- with their derivatives,
  347. c see (21a) & (21b) on p.368.
  348. c---------------------------------------------------------------
  349. if(ml .ge. 1.0d0) then
  350. Pplus = 1.0d0
  351. else
  352. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  353. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  354. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  355. else
  356. Pplus = 0.0d0
  357. endif
  358. endif
  359. c---------------------------------------------------------------
  360. if(mr .ge. 1.0d0) then
  361. Pmin = 0.0d0
  362. else
  363. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  364. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  365. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  366. else
  367. Pmin = 1.0d0
  368. endif
  369. endif
  370. c---------------------------------------------------------------
  371. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  372. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  373. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  374. c--------------
  375. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  376. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  377. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  378. c---------------------------------------------------------------
  379. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  380. dPpr_l=brac_l*dmlr_l
  381. dPpr_r=brac_l*dmlr_r
  382. c------------
  383. dPpu_l=brac_l*dmlu_l
  384. dPpu_r=brac_l*dmlu_r
  385. c------------
  386. dPpv_l=brac_l*dmlv_l
  387. dPpv_r=brac_l*dmlv_r
  388. c------------
  389. dPpp_l=brac_l*dmlp_l
  390. dPpp_r=brac_l*dmlp_r
  391. c------------
  392. else
  393. dPpr_l=0.0d0
  394. dPpr_r=0.0d0
  395. c-----------
  396. dPpu_l=0.0d0
  397. dPpu_r=0.0d0
  398. c-----------
  399. dPpv_l=0.0d0
  400. dPpv_r=0.0d0
  401. c-----------
  402. dPpp_l=0.0d0
  403. dPpp_r=0.0d0
  404. c-----------
  405. endif
  406. c---------------------------------------------------------------
  407. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  408. dPmr_l=brac_r*dmrr_l
  409. dPmr_r=brac_r*dmrr_r
  410. c------------
  411. dPmu_l=brac_r*dmru_l
  412. dPmu_r=brac_r*dmru_r
  413. c------------
  414. dPmv_l=brac_r*dmrv_l
  415. dPmv_r=brac_r*dmrv_r
  416. c------------
  417. dPmp_l=brac_r*dmrp_l
  418. dPmp_r=brac_r*dmrp_r
  419. c------------
  420. else
  421. dPmr_l=0.0d0
  422. dPmr_r=0.0d0
  423. c-----------
  424. dPmu_l=0.0d0
  425. dPmu_r=0.0d0
  426. c-----------
  427. dPmv_l=0.0d0
  428. dPmv_r=0.0d0
  429. c-----------
  430. dPmp_l=0.0d0
  431. dPmp_r=0.0d0
  432. c-----------
  433. endif
  434. c-------------------------------------------------------------------
  435. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  436. c-------------------------------------------------------------------
  437. pmid=Pplus*pold_l + Pmin*pold_r
  438. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  439. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  440. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  441. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  442. c----------------------------
  443. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  444. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  445. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  446. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  447. c---------------------------------------------------------------------
  448. c computing JACOBIAN as a derivative of the numerical flux function
  449. c with respect to the primitive variables.
  450. c Notation: jl(i,j) --- is the derivative of the i-component of the
  451. c flux function with respect to the j-component of the
  452. c vector of primitive variables of the left state.
  453. c jr(i,j) --- is the derivative of the i-component of the
  454. c flux function with respect to the j-component of the
  455. c vector of primitive variables of the right state.
  456. c---------------------------------------------------------------------
  457. f(1)=am*(mpl_m*rold_l+mmin_m*rold_r)
  458. c---------------------------------------------------------------------
  459. jl(1,1)=damr_l*f(1)/am+am*(d2mr_l*rold_l+mpl_m)
  460. jl(1,1)=jl(1,1)+am*d3mr_l*rold_r
  461. jl(1,2)=damu_l*f(1)/am+am*(d2mu_l*rold_l+d3mu_l*rold_r)
  462. jl(1,3)=damv_l*f(1)/am+am*(d2mv_l*rold_l+d3mv_l*rold_r)
  463. jl(1,4)=damp_l*f(1)/am+am*(d2mp_l*rold_l+d3mp_l*rold_r)
  464. c------------------------------------
  465. jr(1,1)=damr_r*f(1)/am+am*(d2mr_r*rold_l+mmin_m)
  466. jr(1,1)=jr(1,1)+am*d3mr_r*rold_r
  467. jr(1,2)=damu_r*f(1)/am+am*(d2mu_r*rold_l+d3mu_r*rold_r)
  468. jr(1,3)=damv_r*f(1)/am+am*(d2mv_r*rold_l+d3mv_r*rold_r)
  469. jr(1,4)=damp_r*f(1)/am+am*(d2mp_r*rold_l+d3mp_r*rold_r)
  470. c------------------------------------
  471. c------------------------------------
  472. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  473. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  474. f(2)=n_x*(am*br1+pmid)+am*t_x*br2
  475. c------------------
  476. det=n_x*t_y-n_y*t_x
  477. c---------------------------------------------------------
  478. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  479. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  480. jl(2,1)=n_x*(damr_l*br1+am*br3+dpir_l)
  481. jl(2,1)=jl(2,1)+t_x*damr_l*br2+am*t_x*br4
  482. c-------------------
  483. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  484. br3=br3+d3mu_l*rold_r*un_r
  485. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y)/det
  486. br4=br4+d3mu_l*rold_r*ut_r
  487. jl(2,2)=n_x*(damu_l*br1+am*br3+dpiu_l)
  488. jl(2,2)=jl(2,2)+t_x*damu_l*br2+am*t_x*br4
  489. c-------------------
  490. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x)/det
  491. br3=br3+d3mv_l*rold_r*un_r
  492. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  493. br4=br4+d3mv_l*rold_r*ut_r
  494. jl(2,3)=n_x*(damv_l*br1+am*br3+dpiv_l)
  495. jl(2,3)=jl(2,3)+t_x*damv_l*br2+am*t_x*br4
  496. c-------------------
  497. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  498. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  499. jl(2,4)=n_x*(damp_l*br1+am*br3+dpip_l)
  500. jl(2,4)=jl(2,4)+t_x*damp_l*br2+am*t_x*br4
  501. c-------------------------------------------------------------
  502. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  503. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  504. jr(2,1)=n_x*(damr_r*br1+am*br3+dpir_r)
  505. jr(2,1)=jr(2,1)+t_x*damr_r*br2+am*t_x*br4
  506. c-------------------
  507. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  508. br3=br3+d3mu_r*rold_r*un_r
  509. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  510. br4=br4+d3mu_r*rold_r*ut_r
  511. jr(2,2)=n_x*(damu_r*br1+am*br3+dpiu_r)
  512. jr(2,2)=jr(2,2)+t_x*damu_r*br2+am*t_x*br4
  513. c-------------------
  514. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  515. br3=br3+d3mv_r*rold_r*un_r
  516. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  517. br4=br4+d3mv_r*rold_r*ut_r
  518. jr(2,3)=n_x*(damv_r*br1+am*br3+dpiv_r)
  519. jr(2,3)=jr(2,3)+t_x*damv_r*br2+am*t_x*br4
  520. c-------------------
  521. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  522. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  523. jr(2,4)=n_x*(damp_r*br1+am*br3+dpip_r)
  524. jr(2,4)=jr(2,4)+t_x*damp_r*br2+am*t_x*br4
  525. c-------------------------------------------------------------
  526. c-------------------------------------------------------------
  527. br1=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  528. br2=mpl_m*rold_l*ut_l+mmin_m*rold_r*ut_r
  529. f(3)=n_y*(am*br1+pmid)+am*t_y*br2
  530. br3=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  531. br4=d2mr_l*rold_l*ut_l+mpl_m*ut_l+d3mr_l*rold_r*ut_r
  532. jl(3,1)=n_y*(damr_l*br1+am*br3+dpir_l)
  533. jl(3,1)=jl(3,1)+t_y*damr_l*br2+am*t_y*br4
  534. c-------------------
  535. br3=d2mu_l*rold_l*un_l+mpl_m*rold_l*t_y/det
  536. br3=br3+d3mu_l*rold_r*un_r
  537. br4=d2mu_l*rold_l*ut_l+mpl_m*rold_l*(-n_y/det)
  538. br4=br4+d3mu_l*rold_r*ut_r
  539. jl(3,2)=n_y*(damu_l*br1+am*br3+dpiu_l)
  540. jl(3,2)=jl(3,2)+t_y*damu_l*br2+am*t_y*br4
  541. c-------------------
  542. br3=d2mv_l*rold_l*un_l+mpl_m*rold_l*(-t_x/det)
  543. br3=br3+d3mv_l*rold_r*un_r
  544. br4=d2mv_l*rold_l*ut_l+mpl_m*rold_l*n_x/det
  545. br4=br4+d3mv_l*rold_r*ut_r
  546. jl(3,3)=n_y*(damv_l*br1+am*br3+dpiv_l)
  547. jl(3,3)=jl(3,3)+t_y*damv_l*br2+am*t_y*br4
  548. c-------------------
  549. br3=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  550. br4=d2mp_l*rold_l*ut_l+d3mp_l*rold_r*ut_r
  551. jl(3,4)=n_y*(damp_l*br1+am*br3+dpip_l)
  552. jl(3,4)=jl(3,4)+t_y*damp_l*br2+am*t_y*br4
  553. c-------------------------------------------------------------
  554. br3=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  555. br4=d2mr_r*rold_l*ut_l+mmin_m*ut_r+d3mr_r*rold_r*ut_r
  556. jr(3,1)=n_y*(damr_r*br1+am*br3+dpir_r)
  557. jr(3,1)=jr(3,1)+t_y*damr_r*br2+am*t_y*br4
  558. c-------------------
  559. br3=d2mu_r*rold_l*un_l+mmin_m*rold_r*t_y/det
  560. br3=br3+d3mu_r*rold_r*un_r
  561. br4=d2mu_r*rold_l*ut_l+mmin_m*rold_r*(-n_y/det)
  562. br4=br4+d3mu_r*rold_r*ut_r
  563. jr(3,2)=n_y*(damu_r*br1+am*br3+dpiu_r)
  564. jr(3,2)=jr(3,2)+t_y*damu_r*br2+am*t_y*br4
  565. c-------------------
  566. br3=d2mv_r*rold_l*un_l+mmin_m*rold_r*(-t_x/det)
  567. br3=br3+d3mv_r*rold_r*un_r
  568. br4=d2mv_r*rold_l*ut_l+mmin_m*rold_r*n_x/det
  569. br4=br4+d3mv_r*rold_r*ut_r
  570. jr(3,3)=n_y*(damv_r*br1+am*br3+dpiv_r)
  571. jr(3,3)=jr(3,3)+t_y*damv_r*br2+am*t_y*br4
  572. c-------------------
  573. br3=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  574. br4=d2mp_r*rold_l*ut_l+d3mp_r*rold_r*ut_r
  575. jr(3,4)=n_y*(damp_r*br1+am*br3+dpip_r)
  576. jr(3,4)=jr(3,4)+t_y*damp_r*br2+am*t_y*br4
  577. c-------------------------------------------------------------
  578. c ------ f44444444444444444444444444444 ---------
  579. c-------------------------------------------------------------
  580. hr_l=rold_l*(uold_l*uold_l+vold_l*vold_l)/2.0d0+ga*pold_l/gm1
  581. hr_r=rold_r*(uold_r*uold_r+vold_r*vold_r)/2.0d0+ga*pold_r/gm1
  582. f(4)=am*(mpl_m*hr_l+mmin_m*hr_r)
  583. c---------------------
  584. br1=d2mr_l*hr_l+mpl_m*(uold_l*uold_l+vold_l*vold_l)/2.0d0
  585. br1=br1+d3mr_l*hr_r
  586. jl(4,1)=damr_l*f(4)/am+am*br1
  587. c---------------------
  588. br1=d2mu_l*hr_l+mpl_m*uold_l*rold_l
  589. br1=br1+d3mu_l*hr_r
  590. jl(4,2)=damu_l*f(4)/am+am*br1
  591. c---------------------
  592. br1=d2mv_l*hr_l+mpl_m*vold_l*rold_l
  593. br1=br1+d3mv_l*hr_r
  594. jl(4,3)=damv_l*f(4)/am+am*br1
  595. c---------------------
  596. br1=d2mp_l*hr_l+mpl_m*ga/gm1
  597. br1=br1+d3mp_l*hr_r
  598. jl(4,4)=damp_l*f(4)/am+am*br1
  599. c----------------------------------------------------------
  600. c----------------------------------------------------------
  601. br1=d2mr_r*hr_l+mmin_m*(uold_r*uold_r+vold_r*vold_r)/2.0d0
  602. br1=br1+d3mr_r*hr_r
  603. jr(4,1)=damr_r*f(4)/am+am*br1
  604. c---------------------
  605. br1=d2mu_r*hr_l+mmin_m*uold_r*rold_r
  606. br1=br1+d3mu_r*hr_r
  607. jr(4,2)=damu_r*f(4)/am+am*br1
  608. c---------------------
  609. br1=d2mv_r*hr_l+mmin_m*vold_r*rold_r
  610. br1=br1+d3mv_r*hr_r
  611. jr(4,3)=damv_r*f(4)/am+am*br1
  612. c---------------------
  613. br1=d2mp_r*hr_l+mmin_m*ga/gm1
  614. br1=br1+d3mp_r*hr_r
  615. jr(4,4)=damp_r*f(4)/am+am*br1
  616. c-------------------------------------------------------------
  617. c matrix wl(i,j) represents the derivative of the i-component
  618. c of the vector of primitive variables of the left state with
  619. c respect to the j-component of the vector of the conservative
  620. c variables of the left state.
  621. c
  622. c Here: (rho, u, v, p) - vector of primitive variables;
  623. c (rho, rho u, rho v, rho e) -- conservative variables.
  624. c-------------------------------------------------------------
  625. wl(1,1)=1.0d0
  626. wl(1,2)=0.0d0
  627. wl(1,3)=0.0d0
  628. wl(1,4)=0.0d0
  629. c------------------------------
  630. wl(2,1)=-uold_l/rold_l
  631. wl(2,2)=1.0d0/rold_l
  632. wl(2,3)=0.0d0
  633. wl(2,4)=0.0d0
  634. c------------------------------
  635. wl(3,1)=-vold_l/rold_l
  636. wl(3,2)=0.0d0
  637. wl(3,3)=1.0d0/rold_l
  638. wl(3,4)=0.0d0
  639. c------------------------------
  640. wl(4,1)=gm1*(uold_l*uold_l+vold_l*vold_l)/2.0d0
  641. wl(4,2)=-uold_l*gm1
  642. wl(4,3)=-vold_l*gm1
  643. wl(4,4)=gm1
  644. c------------------------------
  645. c------------------------------
  646. wr(1,1)=1.0d0
  647. wr(1,2)=0.0d0
  648. wr(1,3)=0.0d0
  649. wr(1,4)=0.0d0
  650. c------------------------------
  651. wr(2,1)=-uold_r/rold_r
  652. wr(2,2)=1.0d0/rold_r
  653. wr(2,3)=0.0d0
  654. wr(2,4)=0.0d0
  655. c------------------------------
  656. wr(3,1)=-vold_r/rold_r
  657. wr(3,2)=0.0d0
  658. wr(3,3)=1.0d0/rold_r
  659. wr(3,4)=0.0d0
  660. c------------------------------
  661. wr(4,1)=gm1*(uold_r*uold_r+vold_r*vold_r)/2.0d0
  662. wr(4,2)=-uold_r*gm1
  663. wr(4,3)=-vold_r*gm1
  664. wr(4,4)=gm1
  665. c----------------------------------------------
  666. c----------------------------------------------
  667. do 1 i=1,4
  668. do 2 j=1,4
  669. jtl(i,j)=0.0d0
  670. jtr(i,j)=0.0d0
  671. do 3 k=1,4
  672. jtl(i,j)=jtl(i,j)+jl(i,k)*wl(k,j)
  673. jtr(i,j)=jtr(i,j)+jr(i,k)*wr(k,j)
  674. 3 continue
  675. 2 continue
  676. 1 continue
  677. c----------------------------------------------------------------------
  678. return
  679. end
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