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  1. C CONJ3W SOURCE CB215821 16/04/21 21:15:56 8920
  2. c----------------------------------------------------------------------
  3. c GENERAL DESCRIPTION:
  4. c This subroutine provides the jacobians which are the derivatives
  5. c of the numerical flux function defined at the cell interface
  6. c with respect to the conservative variables of the left and right
  7. c cells (relative to the cell interface).
  8. c
  9. c EQUATIONS: 3D Euler equations of gas dynamics
  10. c
  11. c
  12. c REFERENCE: JCP, 129, 364-382 (1996)
  13. c " A Sequel to AUSM: AUSM+ ".
  14. c----------------------------------------------------------------------
  15. c INPUT:
  16. c
  17. c alpha -- parameter of the AUSM+ scheme in the Pressure function;
  18. c ( -3/4 <= alpha <= 3/16 ) (imposed as a parameter)
  19. c
  20. c beta -- parameter of the AUSM+ scheme in the Mach function;
  21. c ( -1/16 <= beta <= 1/2 ) (imposed as a parameter)
  22. c
  23. c wvec_l -- vector of the primitive variables (rho,ux,uy,uz,p) at the
  24. c left cell;
  25. c
  26. c wvec_r -- vector of the primitive variables (rho,ux,uy,uz,p) at the
  27. c right cell;
  28. c
  29. c nvect -- normal vector to the interface (3 components in 3D);
  30. c
  31. c tvec1 -- tangential vector to the interface;
  32. c
  33. c tvec2 -- tangential vector to the interface;
  34. c
  35. c ga -- ratio of the specific heats (assumed constant)
  36. c----------------------------------------------------------------------
  37. c
  38. c OUTPUT:
  39. c
  40. c jtl -- jakobian matrix 5 by 5 - derivatives of the numerical
  41. c flux function with respect to the conservative variables
  42. c from the left cell;
  43. c
  44. c jtr -- jakobian matrix 5 by 5 - derivatives of the numerical
  45. c flux function with respect to the conservative variables
  46. c from the right cell.
  47. c----------------------------------------------------------------------
  48. SUBROUTINE CONJ3W(JTL,JTR,WVEC_L,WVEC_R,NVECT,TVECT1,TVECT2,
  49. & ga)
  50. IMPLICIT INTEGER(I-N)
  51. real*8 wvec_l(5),wvec_r(5)
  52. real*8 nvect(3),tvect1(3),tvect2(3)
  53. real*8 jl(5,5),jr(5,5)
  54. real*8 wl(5,5),wr(5,5)
  55. real*8 jtl(5,5),jtr(5,5)
  56. real*8 alpha,beta
  57. real*8 ga, gm1
  58. real*8 n_x,n_y,n_z,t1_x,t1_y,t1_z,t2_x,t2_y,t2_z
  59. real*8 un_l,un_r
  60. real*8 ml,mr,Mplus,Mmin
  61. real*8 am
  62. real*8 rold_l,uold_l,vold_l,wold_l,pold_l,eold_l
  63. real*8 rold_r,uold_r,vold_r,wold_r,pold_r,eold_r
  64. real*8 Pplus,Pmin
  65. real*8 temp_l,temp_r,brac_l,brac_r
  66. real*8 aleft, arigh
  67. real*8 damr_l,damr_r,damu_l,damu_r
  68. real*8 damv_l,damv_r,damp_l,damp_r
  69. real*8 damw_l,damw_r
  70. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  71. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  72. real*8 dmlw_l,dmlw_r
  73. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  74. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  75. real*8 dmrw_l,dmrw_r
  76. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  77. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  78. real*8 dPpw_l,dPpw_r
  79. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  80. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  81. real*8 dPmw_l,dPmw_r
  82. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  83. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  84. real*8 dpiw_l,dpiw_r
  85. real*8 c11,c12,c13,c21,c22,c23,c31,c32,c33,det
  86. real*8 zc11,zc12,zc13,zc21,zc22,zc23,zc31,zc32,zc33
  87. integer i,j,k
  88. parameter(alpha = 0.1875D0, beta = 0.125D0)
  89. c-----------------------
  90. gm1=ga-1.0d0
  91. c-----------------------
  92. n_x=nvect(1)
  93. n_y=nvect(2)
  94. n_z=nvect(3)
  95. c-----------------------
  96. t1_x=tvect1(1)
  97. t1_y=tvect1(2)
  98. t1_z=tvect1(3)
  99. c-----------------------
  100. t2_x=tvect2(1)
  101. t2_y=tvect2(2)
  102. t2_z=tvect2(3)
  103. c--------------------------------------
  104. rold_l=wvec_l(1)
  105. uold_l=wvec_l(2)
  106. vold_l=wvec_l(3)
  107. wold_l=wvec_l(4)
  108. pold_l=wvec_l(5)
  109. c-----------------------
  110. rold_r=wvec_r(1)
  111. uold_r=wvec_r(2)
  112. vold_r=wvec_r(3)
  113. wold_r=wvec_r(4)
  114. pold_r=wvec_r(5)
  115. c------------------------------------------------------------------
  116. c Computation of the specific total energy on the left and right.
  117. c------------------------------------------------------------------
  118. eold_l=(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0
  119. eold_l=eold_l+pold_l/(gm1*rold_l)
  120. eold_r=(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0
  121. eold_r=eold_r+pold_r/(gm1*rold_r)
  122. c-------------------------------------------------------------------
  123. c Computation of the speed of sound and its derivatives;
  124. c numerical speed of sound at the interface is taken as an average
  125. c of the speeds of sounds of the neighbouring cells
  126. c---------------------------------------------------------------------
  127. aleft=SQRT(ga*pold_l/rold_l)
  128. arigh=SQRT(ga*pold_r/rold_r)
  129. am=0.5d0*(aleft+arigh)
  130. c--------------------------------------------------------------------
  131. damr_r=-arigh/(4.0d0*rold_r)
  132. damu_r=0.0d0
  133. damv_r=0.0d0
  134. damw_r=0.0d0
  135. damp_r=ga/(4.0d0*arigh*rold_r)
  136. c-----------------------
  137. damr_l=-aleft/(4.0d0*rold_l)
  138. damu_l=0.0d0
  139. damv_l=0.0d0
  140. damw_l=0.0d0
  141. damp_l=ga/(4.0d0*aleft*rold_l)
  142. c-------------------------------------------------------------------
  143. c Computing numerical Mach number and its derivatives,
  144. c see p.370, under (A1).
  145. c-------------------------------------------------------------------
  146. un_l=uold_l*n_x+vold_l*n_y+wold_l*n_z
  147. un_r=uold_r*n_x+vold_r*n_y+wold_r*n_z
  148. c----------------------------------------
  149. ml=un_l/am
  150. mr=un_r/am
  151. c-------------------------------------------------------------------
  152. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  153. c see (19a) and (19b), p.367.
  154. c-------------------------------------------------------------------
  155. if(ABS(ml) .ge. 1.0d0) then
  156. Mplus=(ml+ABS(ml))/2.0d0
  157. else
  158. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  159. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  160. endif
  161. c-----------------
  162. if(ABS(mr) .ge. 1.0d0) then
  163. Mmin=(mr-ABS(mr))/2.0d0
  164. else
  165. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  166. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  167. endif
  168. c-------------------------------------------------------------------
  169. c Derivatives of ml and mr with respect to both sets of primitive
  170. c variables: left and right.
  171. c-------------------------------------------------------------------
  172. temp_l=-un_l/(am*am)
  173. temp_r=-un_r/(am*am)
  174. c--------
  175. dmlr_l=temp_l*damr_l
  176. dmlr_r=temp_l*damr_r
  177. dmrr_l=temp_r*damr_l
  178. dmrr_r=temp_r*damr_r
  179. c--------
  180. dmlu_l=n_x/am+temp_l*damu_l
  181. dmlu_r=temp_l*damu_r
  182. dmru_l=temp_r*damu_l
  183. dmru_r=n_x/am+temp_r*damu_r
  184. c--------
  185. dmlv_l=n_y/am+temp_l*damv_l
  186. dmlv_r=temp_l*damv_r
  187. dmrv_l=temp_r*damv_l
  188. dmrv_r=n_y/am+temp_r*damv_r
  189. c--------
  190. dmlw_l=n_z/am+temp_l*damw_l
  191. dmlw_r=temp_l*damw_r
  192. dmrw_l=temp_r*damw_l
  193. dmrw_r=n_z/am+temp_r*damw_r
  194. c--------
  195. dmlp_l=temp_l*damp_l
  196. dmlp_r=temp_l*damp_r
  197. dmrp_l=temp_r*damp_l
  198. dmrp_r=temp_r*damp_r
  199. c---------------------------------------------------------------
  200. c Computing the calligraphic P+ and P- with their derivatives
  201. c see (21a) & (21b) on p.368.
  202. c---------------------------------------------------------------
  203. if(ml .ge. 1.0d0) then
  204. Pplus = 1.0d0
  205. else
  206. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  207. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  208. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  209. else
  210. Pplus = 0.0d0
  211. endif
  212. endif
  213. c---------------------------------------------------------------
  214. if(mr .ge. 1.0d0) then
  215. Pmin = 0.0d0
  216. else
  217. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  218. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  219. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  220. else
  221. Pmin = 1.0d0
  222. endif
  223. endif
  224. c---------------------------------------------------------------
  225. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  226. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  227. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  228. c--------------
  229. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  230. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  231. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  232. c---------------------------------------------------------------
  233. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  234. dPpr_l=brac_l*dmlr_l
  235. dPpr_r=brac_l*dmlr_r
  236. c------------
  237. dPpu_l=brac_l*dmlu_l
  238. dPpu_r=brac_l*dmlu_r
  239. c------------
  240. dPpv_l=brac_l*dmlv_l
  241. dPpv_r=brac_l*dmlv_r
  242. c------------
  243. dPpw_l=brac_l*dmlw_l
  244. dPpw_r=brac_l*dmlw_r
  245. c------------
  246. dPpp_l=brac_l*dmlp_l
  247. dPpp_r=brac_l*dmlp_r
  248. c------------
  249. else
  250. dPpr_l=0.0d0
  251. dPpr_r=0.0d0
  252. c-----------
  253. dPpu_l=0.0d0
  254. dPpu_r=0.0d0
  255. c-----------
  256. dPpv_l=0.0d0
  257. dPpv_r=0.0d0
  258. c-----------
  259. dPpw_l=0.0d0
  260. dPpw_r=0.0d0
  261. c-----------
  262. dPpp_l=0.0d0
  263. dPpp_r=0.0d0
  264. c-----------
  265. endif
  266. c---------------------------------------------------------------
  267. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  268. dPmr_l=brac_r*dmrr_l
  269. dPmr_r=brac_r*dmrr_r
  270. c------------
  271. dPmu_l=brac_r*dmru_l
  272. dPmu_r=brac_r*dmru_r
  273. c------------
  274. dPmv_l=brac_r*dmrv_l
  275. dPmv_r=brac_r*dmrv_r
  276. c------------
  277. dPmw_l=brac_r*dmrw_l
  278. dPmw_r=brac_r*dmrw_r
  279. c------------
  280. dPmp_l=brac_r*dmrp_l
  281. dPmp_r=brac_r*dmrp_r
  282. c------------
  283. else
  284. dPmr_l=0.0d0
  285. dPmr_r=0.0d0
  286. c-----------
  287. dPmu_l=0.0d0
  288. dPmu_r=0.0d0
  289. c-----------
  290. dPmv_l=0.0d0
  291. dPmv_r=0.0d0
  292. c-----------
  293. dPmw_l=0.0d0
  294. dPmw_r=0.0d0
  295. c-----------
  296. dPmp_l=0.0d0
  297. dPmp_r=0.0d0
  298. c-----------
  299. endif
  300. c---------------------------------------------------------------------
  301. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  302. c---------------------------------------------------------------------
  303. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  304. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  305. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  306. dpiw_l=dPpw_l*pold_l+dPmw_l*pold_r
  307. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  308. c----------------------------
  309. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  310. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  311. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  312. dpiw_r=dPpw_r*pold_l+dPmw_r*pold_r
  313. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  314. c---------------------------------------------------------------------
  315. c computing JACOBIAN as a derivative of the numerical flux function
  316. c with respect to the primitive variables.
  317. c Notation: jl(i,j) --- is the derivative of the i-component of the
  318. c flux function with respect to the j-component of the
  319. c vector of primitive variables of the left state.
  320. c jr(i,j) --- is the derivative of the i-component of the
  321. c flux function with respect to the j-component of the
  322. c vector of primitive variables of the right state.
  323. c---------------------------------------------------------------------
  324. jl(1,1)=0.0D0
  325. jl(1,2)=0.0D0
  326. jl(1,3)=0.0D0
  327. jl(1,4)=0.0D0
  328. jl(1,5)=0.0D0
  329. c------------------------------------
  330. jr(1,1)=0.0D0
  331. jr(1,2)=0.0D0
  332. jr(1,3)=0.0D0
  333. jr(1,4)=0.0D0
  334. jr(1,5)=0.0D0
  335. c------------------------------------
  336. c------------------------------------
  337. jl(2,1)=dpir_l*n_x
  338. c------------------------
  339. jl(2,2)=dpiu_l*n_x
  340. c------------------------
  341. jl(2,3)=dpiv_l*n_x
  342. c------------------------
  343. jl(2,4)=dpiw_l*n_x
  344. c------------------------
  345. jl(2,5)=dpip_l*n_x
  346. c-------------------------------------------------
  347. c-------------------------------------------------
  348. jl(3,1)=dpir_l*n_y
  349. c------------------------
  350. jl(3,2)=dpiu_l*n_y
  351. c------------------------
  352. jl(3,3)=dpiv_l*n_y
  353. c------------------------
  354. jl(3,4)=dpiw_l*n_y
  355. c------------------------
  356. jl(3,5)=dpip_l*n_y
  357. c-------------------------------------------------
  358. c-------------------------------------------------
  359. jl(4,1)=dpir_l*n_z
  360. c------------------------
  361. jl(4,2)=dpiu_l*n_z
  362. c------------------------
  363. jl(4,3)=dpiv_l*n_z
  364. c------------------------
  365. jl(4,4)=dpiw_l*n_z
  366. c------------------------
  367. jl(4,5)=dpip_l*n_z
  368. c-------------------------------------------------------
  369. c derivatives with respect to the right
  370. c set of primitive variables
  371. c-------------------------------------------------------
  372. jr(2,1)=dpir_r*n_x
  373. c------------------------
  374. jr(2,2)=dpiu_r*n_x
  375. c------------------------
  376. jr(2,3)=dpiv_r*n_x
  377. c------------------------
  378. jr(2,4)=dpiw_r*n_x
  379. c------------------------
  380. jr(2,5)=dpip_r*n_x
  381. c-------------------------------------------------------
  382. jr(3,1)=dpir_r*n_y
  383. c------------------------
  384. jr(3,2)=dpiu_r*n_y
  385. c------------------------
  386. jr(3,3)=dpiv_r*n_y
  387. c------------------------
  388. jr(3,4)=dpiw_r*n_y
  389. c------------------------
  390. jr(3,5)=dpip_r*n_y
  391. c--------------------------------------------------------
  392. jr(4,1)=dpir_r*n_z
  393. c------------------------
  394. jr(4,2)=dpiu_r*n_z
  395. c------------------------
  396. jr(4,3)=dpiv_r*n_z
  397. c------------------------
  398. jr(4,4)=dpiw_r*n_z
  399. c------------------------
  400. jr(4,5)=dpip_r*n_z
  401. c-------------------------------------------------------
  402. c-------------------------------------------------------
  403. jl(5,1)=0.0D0
  404. jl(5,2)=0.0D0
  405. jl(5,3)=0.0D0
  406. jl(5,4)=0.0D0
  407. jl(5,5)=0.0D0
  408. c-------------------------------------------------
  409. c-------------------------------------------------
  410. jr(5,1)=0.0D0
  411. jr(5,2)=0.0D0
  412. jr(5,3)=0.0D0
  413. jr(5,4)=0.0D0
  414. jr(5,5)=0.0D0
  415. c-------------------------------------------------------------
  416. c matrix wl(i,j) represents the derivative of the i-component
  417. c of the vector of primitive variables of the left state with
  418. c respect to the j-component of the vector of the conservative
  419. c variables of the left state.
  420. c
  421. c Here: (rho, u, v, w, p) - vector of primitive variables;
  422. c (rho, rho u, rh o v, rho w, rho e) - conservative variables.
  423. c-------------------------------------------------------------
  424. wl(1,1)=1.0d0
  425. wl(1,2)=0.0d0
  426. wl(1,3)=0.0d0
  427. wl(1,4)=0.0d0
  428. wl(1,5)=0.0d0
  429. c------------------------------
  430. wl(2,1)=-uold_l/rold_l
  431. wl(2,2)=1.0d0/rold_l
  432. wl(2,3)=0.0d0
  433. wl(2,4)=0.0d0
  434. wl(2,5)=0.0d0
  435. c------------------------------
  436. wl(3,1)=-vold_l/rold_l
  437. wl(3,2)=0.0d0
  438. wl(3,3)=1.0d0/rold_l
  439. wl(3,4)=0.0d0
  440. wl(3,5)=0.0d0
  441. c------------------------------
  442. wl(4,1)=-wold_l/rold_l
  443. wl(4,2)=0.0d0
  444. wl(4,3)=0.0d0
  445. wl(4,4)=1.0d0/rold_l
  446. wl(4,5)=0.0d0
  447. c------------------------------
  448. wl(5,1)=gm1*(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0
  449. wl(5,2)=-uold_l*gm1
  450. wl(5,3)=-vold_l*gm1
  451. wl(5,4)=-wold_l*gm1
  452. wl(5,5)=gm1
  453. c------------------------------
  454. c------------------------------
  455. wr(1,1)=1.0d0
  456. wr(1,2)=0.0d0
  457. wr(1,3)=0.0d0
  458. wr(1,4)=0.0d0
  459. wr(1,5)=0.0d0
  460. c------------------------------
  461. wr(2,1)=-uold_r/rold_r
  462. wr(2,2)=1.0d0/rold_r
  463. wr(2,3)=0.0d0
  464. wr(2,4)=0.0d0
  465. wr(2,5)=0.0d0
  466. c------------------------------
  467. wr(3,1)=-vold_r/rold_r
  468. wr(3,2)=0.0d0
  469. wr(3,3)=1.0d0/rold_r
  470. wr(3,4)=0.0d0
  471. wr(3,5)=0.0d0
  472. c------------------------------
  473. wr(4,1)=-wold_r/rold_r
  474. wr(4,2)=0.0d0
  475. wr(4,3)=0.0d0
  476. wr(4,4)=1.0d0/rold_r
  477. wr(4,5)=0.0d0
  478. c------------------------------
  479. wr(5,1)=gm1*(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0
  480. wr(5,2)=-uold_r*gm1
  481. wr(5,3)=-vold_r*gm1
  482. wr(5,4)=-wold_r*gm1
  483. wr(5,5)=gm1
  484. c----------------------------------------------
  485. c----------------------------------------------
  486. do 1 i=1,5
  487. do 2 j=1,5
  488. jtl(i,j)=0.0d0
  489. jtr(i,j)=0.0d0
  490. do 3 k=1,5
  491. jtl(i,j)=jtl(i,j)+jl(i,k)*wl(k,j)
  492. jtr(i,j)=jtr(i,j)+jr(i,k)*wr(k,j)
  493. 3 continue
  494. 2 continue
  495. 1 continue
  496. c-----------------------------------------------
  497. c Taking in account the dependancy of variables
  498. c-----------------------------------------------
  499. c11=t1_y*t2_z - t1_z*t2_y
  500. c12=n_y*t2_z - n_z*t2_y
  501. c13=n_y*t1_z - n_z*t1_y
  502. c-------------------------------------
  503. c21=t1_x*t2_z - t1_z*t2_x
  504. c22=n_x*t2_z - n_z*t2_x
  505. c23=n_x*t1_z - n_z*t1_x
  506. c-------------------------------------
  507. c31=t1_x*t2_y - t1_y*t2_x
  508. c32=n_x*t2_y - n_y*t2_x
  509. c33=n_x*t1_y - n_y*t1_x
  510. det=n_x*c11 - n_y*c21 + n_z*c31
  511. c----------------------------------------------------------------------
  512. ZC11=-NVECT(1)*C11-TVECT1(1)*C12+TVECT2(1)*C13
  513. ZC12=-NVECT(2)*C11-TVECT1(2)*C12+TVECT2(2)*C13
  514. ZC13=-NVECT(3)*C11-TVECT1(3)*C12+TVECT2(3)*C13
  515. C---------------------------------
  516. ZC21=NVECT(1)*C21+TVECT1(1)*C22-TVECT2(1)*C23
  517. ZC22=NVECT(2)*C21+TVECT1(2)*C22-TVECT2(2)*C23
  518. ZC23=NVECT(3)*C21+TVECT1(3)*C22-TVECT2(3)*C23
  519. C---------------------------------
  520. ZC31=-NVECT(1)*C31-TVECT1(1)*C32+TVECT2(1)*C33
  521. ZC32=-NVECT(2)*C31-TVECT1(2)*C32+TVECT2(2)*C33
  522. ZC33=-NVECT(3)*C31-TVECT1(3)*C32+TVECT2(3)*C33
  523. c---------------------------------------------------------------------
  524. do 11 i=1,5
  525. jtl(i,1)=jtl(i,1)+jtr(i,1)
  526. jtl(i,2)=jtl(i,2)+jtr(i,2)*zc11/det+jtr(i,3)*zc21/det+
  527. & jtr(i,4)*zc31/det
  528. jtl(i,3)=jtl(i,3)+jtr(i,2)*zc12/det+jtr(i,3)*zc22/det+
  529. & jtr(i,4)*zc32/det
  530. jtl(i,4)=jtl(i,4)+jtr(i,2)*zc13/det+jtr(i,3)*zc23/det+
  531. & jtr(i,4)*zc33/det
  532. jtl(i,5)=jtl(i,5)+jtr(i,5)
  533. 11 continue
  534. c----------------------------------------------------------------------
  535. return
  536. end
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