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  1. C CONJP4 SOURCE CB215821 16/04/21 21:15:59 8920
  2. c Subroutine appellé par konjp4.eso
  3. c cli153.eso
  4. c----------------------------------------------------------------------
  5. c GENERAL DESCRIPTION:
  6. c This subroutine provides the jacobians which are the derivatives
  7. c of the numerical flux function defined at the cell interface
  8. c with respect to the primitive variables of the left and right
  9. c cells (relative to the cell interface).
  10. c
  11. c EQUATIONS: 3D Euler equations of gas dynamics
  12. c
  13. c
  14. c REFERENCE: JCP, 129, 364-382 (1996)
  15. c " A Sequel to AUSM: AUSM+ ".
  16. c----------------------------------------------------------------------
  17. c INPUT:
  18. c
  19. c alpha -- parameter of the AUSM+ scheme in the Pressure function;
  20. c ( -3/4 <= alpha <= 3/16 ) (imposed as a parameter)
  21. c
  22. c beta -- parameter of the AUSM+ scheme in the Mach function;
  23. c ( -1/16 <= beta <= 1/2 ) (imposed as a parameter)
  24. c
  25. c wvec_l -- vector of the primitive variables (rho,ux,uy,uz,p) at the
  26. c left cell;
  27. c
  28. c wvec_r -- vector of the primitive variables (rho,ux,uy,uz,p) at the
  29. c right cell;
  30. c
  31. c nvect -- normal vector to the interface (3 components in 3D);
  32. c
  33. c tvec1 -- tangential vector to the interface;
  34. c
  35. c tvec2 -- tangential vector to the interface;
  36. c
  37. c ga -- ratio of the specific heats (assumed constant)
  38. c----------------------------------------------------------------------
  39. c
  40. c OUTPUT:
  41. c
  42. c jl -- jakobian matrix 5 by 5 - derivatives of the numerical
  43. c flux function with respect to the primitive variables
  44. c from the left cell;
  45. c
  46. c jr -- jakobian matrix 5 by 5 - derivatives of the numerical
  47. c flux function with respect to the primitive variables
  48. c from the right cell.
  49. c
  50. c N.B. The numerical flux is expressed in the global frame
  51. c (x,y,z); i.e.
  52. c
  53. c \rho un
  54. c \rho un ux + p (n.x)
  55. c \rho un uy + p (n.y)
  56. c \rho un uz + p (n.z)
  57. c \rho un ht
  58. c
  59. c----------------------------------------------------------------------
  60. SUBROUTINE CONJP4(JL,JR,WVEC_L,WVEC_R,NVECT,TVEC1,TVEC2,
  61. & ga)
  62. IMPLICIT INTEGER(I-N)
  63. real*8 wvec_l(5),wvec_r(5)
  64. real*8 nvect(3),tvec1(3),tvec2(3)
  65. real*8 jl(5,5),jr(5,5),f(5)
  66. real*8 alpha,beta
  67. real*8 ga, gm1,temph
  68. real*8 n_x,n_y,n_z,t1_x,t1_y,t1_z,t2_x,t2_y,t2_z
  69. real*8 un_l,un_r,ut1_l,ut1_r,ut2_l,ut2_r
  70. real*8 ml,mr,Mplus,Mmin,mmid
  71. real*8 mpl_m, mmin_m,am
  72. real*8 rold_l,uold_l,vold_l,wold_l,pold_l,eold_l
  73. real*8 rold_r,uold_r,vold_r,wold_r,pold_r,eold_r
  74. real*8 Pplus,Pmin,pmid
  75. real*8 hr_l,hr_r,det,c11,c12,c13,c21,c22,c23,c31,c32,c33
  76. real*8 br1,temp_l,temp_r,brac_l,brac_r
  77. real*8 aleft, arigh
  78. real*8 damr_l,damr_r,damu_l,damu_r
  79. real*8 damv_l,damv_r,damp_l,damp_r
  80. real*8 damw_l,damw_r
  81. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  82. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  83. real*8 dmlw_l,dmlw_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 dmrw_l,dmrw_r
  87. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  88. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_r
  89. real*8 dMpw_l,dMpw_r
  90. real*8 dMmr_l,dMmr_r,dMmu_l,dMmu_r
  91. real*8 dMmv_l,dMmv_r,dMmp_l,dMmp_r
  92. real*8 dMmw_l,dMmw_r
  93. real*8 dmir_l,dmir_r,dmiu_l,dmiu_r
  94. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  95. real*8 dmiw_l,dmiw_r
  96. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  97. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  98. real*8 d3mw_l,d3mw_r
  99. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  100. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  101. real*8 d2mw_l,d2mw_r
  102. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  103. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  104. real*8 dPpw_l,dPpw_r
  105. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  106. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  107. real*8 dPmw_l,dPmw_r
  108. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  109. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  110. real*8 dpiw_l,dpiw_r
  111. real*8 ff,fs,ft,dffr,dffu,dffv,dffw,dffp
  112. real*8 dfsr,dfsu,dfsv,dfsw,dfsp,dftr,dftu,dftv,dftw,dftp
  113. parameter(alpha = 0.1875D0, beta = 0.125D0)
  114. c-----------------------
  115. gm1=ga-1.0d0
  116. c-----------------------
  117. n_x=nvect(1)
  118. n_y=nvect(2)
  119. n_z=nvect(3)
  120. c-------------------
  121. t1_x=tvec1(1)
  122. t1_y=tvec1(2)
  123. t1_z=tvec1(3)
  124. c-------------------
  125. t2_x=tvec2(1)
  126. t2_y=tvec2(2)
  127. t2_z=tvec2(3)
  128. c-------------------------------------------
  129. c These are coefficients for the expressions
  130. c
  131. c un = (c11*ux + c12*uy + c13*uz)/det
  132. c ut1 = (c21*ux + c22*uy + c23*uz)/det
  133. c ut2 = (c31*ux + c32*uy + c33*uz)/det
  134. c-------------------------------------------
  135. c11=t1_y*t2_z - t1_z*t2_y
  136. c12=t1_z*t2_x - t1_x*t2_z
  137. c13=t1_x*t2_y - t1_y*t2_x
  138. det=n_x*c11 + n_y*c12 + n_z*c13
  139. c--------------------------------------
  140. c21=n_z*t2_y - n_y*t2_z
  141. c22=n_x*t2_z - n_z*t2_x
  142. c23=n_y*t2_x - n_x*t2_y
  143. c--------------------------------------
  144. c31=n_y*t1_z - n_z*t1_y
  145. c32=n_z*t1_x - n_x*t1_z
  146. c33=n_x*t1_y - n_y*t1_x
  147. c--------------------------------------
  148. rold_l=wvec_l(1)
  149. uold_l=wvec_l(2)
  150. vold_l=wvec_l(3)
  151. wold_l=wvec_l(4)
  152. pold_l=wvec_l(5)
  153. c-----------------------
  154. rold_r=wvec_r(1)
  155. uold_r=wvec_r(2)
  156. vold_r=wvec_r(3)
  157. wold_r=wvec_r(4)
  158. pold_r=wvec_r(5)
  159. c------------------------------------------------------------------
  160. c Computation of the specific total energy on the left and right.
  161. c------------------------------------------------------------------
  162. eold_l=(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0
  163. eold_l=eold_l+pold_l/(gm1*rold_l)
  164. eold_r=(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0
  165. eold_r=eold_r+pold_r/(gm1*rold_r)
  166. c-------------------------------------------------------------------
  167. c Computation of the speed of sound and its derivatives;
  168. c numerical speed of sound at the interface is taken as an average
  169. c of the speeds of sounds of the neighbouring cells
  170. c---------------------------------------------------------------------
  171. aleft=SQRT(ga*pold_l/rold_l)
  172. arigh=SQRT(ga*pold_r/rold_r)
  173. am=0.5d0*(aleft+arigh)
  174. c--------------------------------------------------------------------
  175. damr_r=-arigh/(4.0d0*rold_r)
  176. damu_r=0.0d0
  177. damv_r=0.0d0
  178. damw_r=0.0d0
  179. damp_r=ga/(4.0d0*arigh*rold_r)
  180. c-----------------------
  181. damr_l=-aleft/(4.0d0*rold_l)
  182. damu_l=0.0d0
  183. damv_l=0.0d0
  184. damw_l=0.0d0
  185. damp_l=ga/(4.0d0*aleft*rold_l)
  186. c-------------------------------------------------------------------
  187. c Computing numerical Mach number and its derivatives,
  188. c see p.370, under (A1).
  189. c-------------------------------------------------------------------
  190. un_l=uold_l*n_x+vold_l*n_y+wold_l*n_z
  191. un_r=uold_r*n_x+vold_r*n_y+wold_r*n_z
  192. c----------
  193. ut1_l=uold_l*t1_x+vold_l*t1_y+wold_l*t1_z
  194. ut1_r=uold_r*t1_x+vold_r*t1_y+wold_r*t1_z
  195. c----------
  196. ut2_l=uold_l*t2_x+vold_l*t2_y+wold_l*t2_z
  197. ut2_r=uold_r*t2_x+vold_r*t2_y+wold_r*t2_z
  198. c----------------------------------------
  199. ml=un_l/am
  200. mr=un_r/am
  201. c-------------------------------------------------------------------
  202. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  203. c see (19a) and (19b), p.367.
  204. c-------------------------------------------------------------------
  205. if(ABS(ml) .ge. 1.0d0) then
  206. Mplus=(ml+ABS(ml))/2.0d0
  207. else
  208. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  209. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  210. endif
  211. c-----------------
  212. if(ABS(mr) .ge. 1.0d0) then
  213. Mmin=(mr-ABS(mr))/2.0d0
  214. else
  215. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  216. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  217. endif
  218. c-------------------------------------------------------------------
  219. c Derivatives of ml and mr with respect to both sets of primitive
  220. c variables: left and right.
  221. c-------------------------------------------------------------------
  222. temp_l=-un_l/(am*am)
  223. temp_r=-un_r/(am*am)
  224. c--------
  225. dmlr_l=temp_l*damr_l
  226. dmlr_r=temp_l*damr_r
  227. dmrr_l=temp_r*damr_l
  228. dmrr_r=temp_r*damr_r
  229. c--------
  230. dmlu_l=n_x/am+temp_l*damu_l
  231. dmlu_r=temp_l*damu_r
  232. dmru_l=temp_r*damu_l
  233. dmru_r=n_x/am+temp_r*damu_r
  234. c--------
  235. dmlv_l=n_y/am+temp_l*damv_l
  236. dmlv_r=temp_l*damv_r
  237. dmrv_l=temp_r*damv_l
  238. dmrv_r=n_y/am+temp_r*damv_r
  239. c--------
  240. dmlw_l=n_z/am+temp_l*damw_l
  241. dmlw_r=temp_l*damw_r
  242. dmrw_l=temp_r*damw_l
  243. dmrw_r=n_z/am+temp_r*damw_r
  244. c--------
  245. dmlp_l=temp_l*damp_l
  246. dmlp_r=temp_l*damp_r
  247. dmrp_l=temp_r*damp_l
  248. dmrp_r=temp_r*damp_r
  249. c-----------------------------------------------------------
  250. c mmid is m_{1/2} (notation as in the paper)
  251. c----------------------------------------------------------
  252. mmid=Mplus+Mmin
  253. c-----------------------------------------------------------
  254. c Computing the derivatives of M+ and M-
  255. c-----------------------------------------------------------
  256. if(ml .ge. 1.0d0) then
  257. dMpr_l=dmlr_l
  258. dMpu_l=dmlu_l
  259. dMpv_l=dmlv_l
  260. dMpw_l=dmlw_l
  261. dMpp_l=dmlp_l
  262. c--------------------
  263. dMpr_r=dmlr_r
  264. dMpu_r=dmlu_r
  265. dMpv_r=dmlv_r
  266. dMpw_r=dmlw_r
  267. dMpp_r=dmlp_r
  268. else
  269. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  270. temph=(ml+1.0d0)/2.0d0
  271. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  272. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  273. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  274. dMpw_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_l
  275. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  276. c--------------------
  277. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  278. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  279. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  280. dMpw_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlw_r
  281. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  282. else
  283. dMpr_l=0.0d0
  284. dMpu_l=0.0d0
  285. dMpv_l=0.0d0
  286. dMpw_l=0.0d0
  287. dMpp_l=0.0d0
  288. c---------------------
  289. dMpr_r=0.0d0
  290. dMpu_r=0.0d0
  291. dMpv_r=0.0d0
  292. dMpw_r=0.0d0
  293. dMpp_r=0.0d0
  294. endif
  295. endif
  296. c-----------------------------------------------------------
  297. if(mr .ge. 1.0d0) then
  298. dMmr_l=0.0d0
  299. dMmu_l=0.0d0
  300. dMmv_l=0.0d0
  301. dMmw_l=0.0d0
  302. dMmp_l=0.0d0
  303. c---------------------
  304. dMmr_r=0.0d0
  305. dMmu_r=0.0d0
  306. dMmv_r=0.0d0
  307. dMmw_r=0.0d0
  308. dMmp_r=0.0d0
  309. else
  310. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  311. temph=(-mr+1.0d0)/2.0d0
  312. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  313. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  314. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  315. dMmw_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_l
  316. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  317. c--------------------
  318. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  319. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  320. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  321. dMmw_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrw_r
  322. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  323. else
  324. dMmr_l=dmrr_l
  325. dMmu_l=dmru_l
  326. dMmv_l=dmrv_l
  327. dMmw_l=dmrw_l
  328. dMmp_l=dmrp_l
  329. c--------------------
  330. dMmr_r=dmrr_r
  331. dMmu_r=dmru_r
  332. dMmv_r=dmrv_r
  333. dMmw_r=dmrw_r
  334. dMmp_r=dmrp_r
  335. endif
  336. endif
  337. c-----------------------------------------------------------------
  338. c computing the derivatives of m_{1/2} (notation as in the paper)
  339. c-----------------------------------------------------------------
  340. dmir_l=dMpr_l+dMmr_l
  341. dmir_r=dMpr_r+dMmr_r
  342. c-------------
  343. dmiu_l=dMpu_l+dMmu_l
  344. dmiu_r=dMpu_r+dMmu_r
  345. c-------------
  346. dmiv_l=dMpv_l+dMmv_l
  347. dmiv_r=dMpv_r+dMmv_r
  348. c-------------
  349. dmiw_l=dMpw_l+dMmw_l
  350. dmiw_r=dMpw_r+dMmw_r
  351. c-------------
  352. dmip_l=dMpp_l+dMmp_l
  353. dmip_r=dMpp_r+dMmp_r
  354. c-------------------------------------------------------------
  355. c computing the main convective variables and their derivatives
  356. c mpl_m is m^{+}_{1/2} (paper's notation) and
  357. c mmin_m is m^{-}_{1/2} (paper's notation)
  358. c-------------------------------------------------------------
  359. if(mmid .gt. 0.0d0) then
  360. mpl_m = mmid
  361. d2mr_l=dmir_l
  362. d2mu_l=dmiu_l
  363. d2mv_l=dmiv_l
  364. d2mw_l=dmiw_l
  365. d2mp_l=dmip_l
  366. c------------
  367. d2mr_r=dmir_r
  368. d2mu_r=dmiu_r
  369. d2mv_r=dmiv_r
  370. d2mw_r=dmiw_r
  371. d2mp_r=dmip_r
  372. c------------
  373. else
  374. mpl_m = 0.0d0
  375. d2mr_l=0.0d0
  376. d2mu_l=0.0d0
  377. d2mv_l=0.0d0
  378. d2mw_l=0.0d0
  379. d2mp_l=0.0d0
  380. c------------
  381. d2mr_r=0.0d0
  382. d2mu_r=0.0d0
  383. d2mv_r=0.0d0
  384. d2mw_r=0.0d0
  385. d2mp_r=0.0d0
  386. endif
  387. c---------------------------------------------
  388. if(mmid .lt. 0.0d0) then
  389. mmin_m = mmid
  390. d3mr_l=dmir_l
  391. d3mu_l=dmiu_l
  392. d3mv_l=dmiv_l
  393. d3mw_l=dmiw_l
  394. d3mp_l=dmip_l
  395. c------------
  396. d3mr_r=dmir_r
  397. d3mu_r=dmiu_r
  398. d3mv_r=dmiv_r
  399. d3mw_r=dmiw_r
  400. d3mp_r=dmip_r
  401. c------------
  402. else
  403. mmin_m = 0.0d0
  404. d3mr_l=0.0d0
  405. d3mu_l=0.0d0
  406. d3mv_l=0.0d0
  407. d3mw_l=0.0d0
  408. d3mp_l=0.0d0
  409. c------------
  410. d3mr_r=0.0d0
  411. d3mu_r=0.0d0
  412. d3mv_r=0.0d0
  413. d3mw_r=0.0d0
  414. d3mp_r=0.0d0
  415. endif
  416. c---------------------------------------------------------------
  417. c Computing the calligraphic P+ and P- with their derivatives
  418. c see (21a) & (21b) on p.368.
  419. c---------------------------------------------------------------
  420. if(ml .ge. 1.0d0) then
  421. Pplus = 1.0d0
  422. else
  423. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  424. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  425. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  426. else
  427. Pplus = 0.0d0
  428. endif
  429. endif
  430. c---------------------------------------------------------------
  431. if(mr .ge. 1.0d0) then
  432. Pmin = 0.0d0
  433. else
  434. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  435. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  436. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  437. else
  438. Pmin = 1.0d0
  439. endif
  440. endif
  441. c---------------------------------------------------------------
  442. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  443. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  444. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  445. c--------------
  446. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  447. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  448. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  449. c---------------------------------------------------------------
  450. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  451. dPpr_l=brac_l*dmlr_l
  452. dPpr_r=brac_l*dmlr_r
  453. c------------
  454. dPpu_l=brac_l*dmlu_l
  455. dPpu_r=brac_l*dmlu_r
  456. c------------
  457. dPpv_l=brac_l*dmlv_l
  458. dPpv_r=brac_l*dmlv_r
  459. c------------
  460. dPpw_l=brac_l*dmlw_l
  461. dPpw_r=brac_l*dmlw_r
  462. c------------
  463. dPpp_l=brac_l*dmlp_l
  464. dPpp_r=brac_l*dmlp_r
  465. c------------
  466. else
  467. dPpr_l=0.0d0
  468. dPpr_r=0.0d0
  469. c-----------
  470. dPpu_l=0.0d0
  471. dPpu_r=0.0d0
  472. c-----------
  473. dPpv_l=0.0d0
  474. dPpv_r=0.0d0
  475. c-----------
  476. dPpw_l=0.0d0
  477. dPpw_r=0.0d0
  478. c-----------
  479. dPpp_l=0.0d0
  480. dPpp_r=0.0d0
  481. c-----------
  482. endif
  483. c---------------------------------------------------------------
  484. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  485. dPmr_l=brac_r*dmrr_l
  486. dPmr_r=brac_r*dmrr_r
  487. c------------
  488. dPmu_l=brac_r*dmru_l
  489. dPmu_r=brac_r*dmru_r
  490. c------------
  491. dPmv_l=brac_r*dmrv_l
  492. dPmv_r=brac_r*dmrv_r
  493. c------------
  494. dPmw_l=brac_r*dmrw_l
  495. dPmw_r=brac_r*dmrw_r
  496. c------------
  497. dPmp_l=brac_r*dmrp_l
  498. dPmp_r=brac_r*dmrp_r
  499. c------------
  500. else
  501. dPmr_l=0.0d0
  502. dPmr_r=0.0d0
  503. c-----------
  504. dPmu_l=0.0d0
  505. dPmu_r=0.0d0
  506. c-----------
  507. dPmv_l=0.0d0
  508. dPmv_r=0.0d0
  509. c-----------
  510. dPmw_l=0.0d0
  511. dPmw_r=0.0d0
  512. c-----------
  513. dPmp_l=0.0d0
  514. dPmp_r=0.0d0
  515. c-----------
  516. endif
  517. c---------------------------------------------------------------------
  518. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  519. c---------------------------------------------------------------------
  520. pmid=Pplus*pold_l + Pmin*pold_r
  521. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  522. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  523. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  524. dpiw_l=dPpw_l*pold_l+dPmw_l*pold_r
  525. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  526. c----------------------------
  527. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  528. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  529. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  530. dpiw_r=dPpw_r*pold_l+dPmw_r*pold_r
  531. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  532. c---------------------------------------------------------------------
  533. c computing JACOBIAN as a derivative of the numerical flux function
  534. c with respect to the primitive variables.
  535. c Notation: jl(i,j) --- is the derivative of the i-component of the
  536. c flux function with respect to the j-component of the
  537. c vector of primitive variables of the left state.
  538. c jr(i,j) --- is the derivative of the i-component of the
  539. c flux function with respect to the j-component of the
  540. c vector of primitive variables of the right state.
  541. c---------------------------------------------------------------------
  542. f(1)=am*(mpl_m*rold_l+mmin_m*rold_r)
  543. c---------------------------------------------------------------------
  544. jl(1,1)=damr_l*f(1)/am+am*(d2mr_l*rold_l+mpl_m)
  545. jl(1,1)=jl(1,1)+am*d3mr_l*rold_r
  546. jl(1,2)=damu_l*f(1)/am+am*(d2mu_l*rold_l+d3mu_l*rold_r)
  547. jl(1,3)=damv_l*f(1)/am+am*(d2mv_l*rold_l+d3mv_l*rold_r)
  548. jl(1,4)=damw_l*f(1)/am+am*(d2mw_l*rold_l+d3mw_l*rold_r)
  549. jl(1,5)=damp_l*f(1)/am+am*(d2mp_l*rold_l+d3mp_l*rold_r)
  550. c------------------------------------
  551. jr(1,1)=damr_r*f(1)/am+am*(d2mr_r*rold_l+mmin_m)
  552. jr(1,1)=jr(1,1)+am*d3mr_r*rold_r
  553. jr(1,2)=damu_r*f(1)/am+am*(d2mu_r*rold_l+d3mu_r*rold_r)
  554. jr(1,3)=damv_r*f(1)/am+am*(d2mv_r*rold_l+d3mv_r*rold_r)
  555. jr(1,4)=damw_r*f(1)/am+am*(d2mw_r*rold_l+d3mw_r*rold_r)
  556. jr(1,5)=damp_r*f(1)/am+am*(d2mp_r*rold_l+d3mp_r*rold_r)
  557. c------------------------------------
  558. c------------------------------------
  559. ff=mpl_m*rold_l*un_l+mmin_m*rold_r*un_r
  560. dffr=d2mr_l*rold_l*un_l+mpl_m*un_l+d3mr_l*rold_r*un_r
  561. dffu=d2mu_l*rold_l*un_l+mpl_m*rold_l*c11/det
  562. dffu=dffu+d3mu_l*rold_r*un_r
  563. dffv=d2mv_l*rold_l*un_l+mpl_m*rold_l*c12/det
  564. dffv=dffv+d3mv_l*rold_r*un_r
  565. dffw=d2mw_l*rold_l*un_l+mpl_m*rold_l*c13/det
  566. dffw=dffw+d3mw_l*rold_r*un_r
  567. dffp=d2mp_l*rold_l*un_l+d3mp_l*rold_r*un_r
  568. c------------------------------------------------
  569. fs=mpl_m*rold_l*ut1_l+mmin_m*rold_r*ut1_r
  570. dfsr=d2mr_l*rold_l*ut1_l+mpl_m*ut1_l
  571. dfsr=dfsr+d3mr_l*rold_r*ut1_r
  572. dfsu=d2mu_l*rold_l*ut1_l+mpl_m*rold_l*c21/det
  573. dfsu=dfsu+d3mu_l*rold_r*ut1_r
  574. dfsv=d2mv_l*rold_l*ut1_l+mpl_m*rold_l*c22/det
  575. dfsv=dfsv+d3mv_l*rold_r*ut1_r
  576. dfsw=d2mw_l*rold_l*ut1_l+mpl_m*rold_l*c23/det
  577. dfsw=dfsw+d3mw_l*rold_r*ut1_r
  578. dfsp=d2mp_l*rold_l*ut1_l+d3mp_l*rold_r*ut1_r
  579. c-------------------------------------------------
  580. ft=mpl_m*rold_l*ut2_l+mmin_m*rold_r*ut2_r
  581. dftr=d2mr_l*rold_l*ut2_l+mpl_m*ut2_l
  582. dftr=dftr+d3mr_l*rold_r*ut2_r
  583. dftu=d2mu_l*rold_l*ut2_l+mpl_m*rold_l*c31/det
  584. dftu=dftu+d3mu_l*rold_r*ut2_r
  585. dftv=d2mv_l*rold_l*ut2_l+mpl_m*rold_l*c32/det
  586. dftv=dftv+d3mv_l*rold_r*ut2_r
  587. dftw=d2mw_l*rold_l*ut2_l+mpl_m*rold_l*c33/det
  588. dftw=dftw+d3mw_l*rold_r*ut2_r
  589. dftp=d2mp_l*rold_l*ut2_l+d3mp_l*rold_r*ut2_r
  590. c-------------------------------------------------
  591. f(2)=am*(ff*n_x+fs*t1_x+ft*t2_x)+pmid*n_x
  592. c-------------------------------------------------
  593. jl(2,1)=damr_l*(f(2)-pmid*n_x)/am+dpir_l*n_x
  594. jl(2,1)=jl(2,1)+am*(dffr*n_x+dfsr*t1_x+dftr*t2_x)
  595. jl(2,2)=damu_l*(f(2)-pmid*n_x)/am+dpiu_l*n_x
  596. jl(2,2)=jl(2,2)+am*(dffu*n_x+dfsu*t1_x+dftu*t2_x)
  597. jl(2,3)=damv_l*(f(2)-pmid*n_x)/am+dpiv_l*n_x
  598. jl(2,3)=jl(2,3)+am*(dffv*n_x+dfsv*t1_x+dftv*t2_x)
  599. jl(2,4)=damw_l*(f(2)-pmid*n_x)/am+dpiw_l*n_x
  600. jl(2,4)=jl(2,4)+am*(dffw*n_x+dfsw*t1_x+dftw*t2_x)
  601. jl(2,5)=damp_l*(f(2)-pmid*n_x)/am+dpip_l*n_x
  602. jl(2,5)=jl(2,5)+am*(dffp*n_x+dfsp*t1_x+dftp*t2_x)
  603. c-------------------------------------------------
  604. f(3)=am*(ff*n_y+fs*t1_y+ft*t2_y)+pmid*n_y
  605. c-------------------------------------------------
  606. jl(3,1)=damr_l*(f(3)-pmid*n_y)/am+dpir_l*n_y
  607. jl(3,1)=jl(3,1)+am*(dffr*n_y+dfsr*t1_y+dftr*t2_y)
  608. jl(3,2)=damu_l*(f(3)-pmid*n_y)/am+dpiu_l*n_y
  609. jl(3,2)=jl(3,2)+am*(dffu*n_y+dfsu*t1_y+dftu*t2_y)
  610. jl(3,3)=damv_l*(f(3)-pmid*n_y)/am+dpiv_l*n_y
  611. jl(3,3)=jl(3,3)+am*(dffv*n_y+dfsv*t1_y+dftv*t2_y)
  612. jl(3,4)=damw_l*(f(3)-pmid*n_y)/am+dpiw_l*n_y
  613. jl(3,4)=jl(3,4)+am*(dffw*n_y+dfsw*t1_y+dftw*t2_y)
  614. jl(3,5)=damp_l*(f(3)-pmid*n_y)/am+dpip_l*n_y
  615. jl(3,5)=jl(3,5)+am*(dffp*n_y+dfsp*t1_y+dftp*t2_y)
  616. c-------------------------------------------------
  617. f(4)=am*(ff*n_z+fs*t1_z+ft*t2_z)+pmid*n_z
  618. c-------------------------------------------------
  619. jl(4,1)=damr_l*(f(4)-pmid*n_z)/am+dpir_l*n_z
  620. jl(4,1)=jl(4,1)+am*(dffr*n_z+dfsr*t1_z+dftr*t2_z)
  621. jl(4,2)=damu_l*(f(4)-pmid*n_z)/am+dpiu_l*n_z
  622. jl(4,2)=jl(4,2)+am*(dffu*n_z+dfsu*t1_z+dftu*t2_z)
  623. jl(4,3)=damv_l*(f(4)-pmid*n_z)/am+dpiv_l*n_z
  624. jl(4,3)=jl(4,3)+am*(dffv*n_z+dfsv*t1_z+dftv*t2_z)
  625. jl(4,4)=damw_l*(f(4)-pmid*n_z)/am+dpiw_l*n_z
  626. jl(4,4)=jl(4,4)+am*(dffw*n_z+dfsw*t1_z+dftw*t2_z)
  627. jl(4,5)=damp_l*(f(4)-pmid*n_z)/am+dpip_l*n_z
  628. jl(4,5)=jl(4,5)+am*(dffp*n_z+dfsp*t1_z+dftp*t2_z)
  629. c-------------------------------------------------------
  630. c derivatives with respect to the right
  631. c set of primitive variables
  632. c-------------------------------------------------------
  633. dffr=d2mr_r*rold_l*un_l+mmin_m*un_r+d3mr_r*rold_r*un_r
  634. dffu=d2mu_r*rold_l*un_l+mmin_m*rold_r*c11/det
  635. dffu=dffu+d3mu_r*rold_r*un_r
  636. dffv=d2mv_r*rold_l*un_l+mmin_m*rold_r*c12/det
  637. dffv=dffv+d3mv_r*rold_r*un_r
  638. dffw=d2mw_r*rold_l*un_l+mmin_m*rold_r*c13/det
  639. dffw=dffw+d3mw_r*rold_r*un_r
  640. dffp=d2mp_r*rold_l*un_l+d3mp_r*rold_r*un_r
  641. c------------------------------------------------------
  642. dfsr=d2mr_r*rold_l*ut1_l+mmin_m*ut1_r
  643. dfsr=dfsr+d3mr_r*rold_r*ut1_r
  644. dfsu=d2mu_r*rold_l*ut1_l+mmin_m*rold_r*c21/det
  645. dfsu=dfsu+d3mu_r*rold_r*ut1_r
  646. dfsv=d2mv_r*rold_l*ut1_l+mmin_m*rold_r*c22/det
  647. dfsv=dfsv+d3mv_r*rold_r*ut1_r
  648. dfsw=d2mw_r*rold_l*ut1_l+mmin_m*rold_r*c23/det
  649. dfsw=dfsw+d3mw_r*rold_r*ut1_r
  650. dfsp=d2mp_r*rold_l*ut1_l+d3mp_r*rold_r*ut1_r
  651. c------------------------------------------------------
  652. dftr=d2mr_r*rold_l*ut2_l+mmin_m*ut2_r
  653. dftr=dftr+d3mr_r*rold_r*ut2_r
  654. dftu=d2mu_r*rold_l*ut2_l+mmin_m*rold_r*c31/det
  655. dftu=dftu+d3mu_r*rold_r*ut2_r
  656. dftv=d2mv_r*rold_l*ut2_l+mmin_m*rold_r*c32/det
  657. dftv=dftv+d3mv_r*rold_r*ut2_r
  658. dftw=d2mw_r*rold_l*ut2_l+mmin_m*rold_r*c33/det
  659. dftw=dftw+d3mw_r*rold_r*ut2_r
  660. dftp=d2mp_r*rold_l*ut2_l+d3mp_r*rold_r*ut2_r
  661. c-------------------------------------------------------
  662. jr(2,1)=damr_r*(f(2)-pmid*n_x)/am+dpir_r*n_x
  663. jr(2,1)=jr(2,1)+am*(dffr*n_x+dfsr*t1_x+dftr*t2_x)
  664. jr(2,2)=damu_r*(f(2)-pmid*n_x)/am+dpiu_r*n_x
  665. jr(2,2)=jr(2,2)+am*(dffu*n_x+dfsu*t1_x+dftu*t2_x)
  666. jr(2,3)=damv_r*(f(2)-pmid*n_x)/am+dpiv_r*n_x
  667. jr(2,3)=jr(2,3)+am*(dffv*n_x+dfsv*t1_x+dftv*t2_x)
  668. jr(2,4)=damw_r*(f(2)-pmid*n_x)/am+dpiw_r*n_x
  669. jr(2,4)=jr(2,4)+am*(dffw*n_x+dfsw*t1_x+dftw*t2_x)
  670. jr(2,5)=damp_r*(f(2)-pmid*n_x)/am+dpip_r*n_x
  671. jr(2,5)=jr(2,5)+am*(dffp*n_x+dfsp*t1_x+dftp*t2_x)
  672. c-------------------------------------------------------
  673. jr(3,1)=damr_r*(f(3)-pmid*n_y)/am+dpir_r*n_y
  674. jr(3,1)=jr(3,1)+am*(dffr*n_y+dfsr*t1_y+dftr*t2_y)
  675. jr(3,2)=damu_r*(f(3)-pmid*n_y)/am+dpiu_r*n_y
  676. jr(3,2)=jr(3,2)+am*(dffu*n_y+dfsu*t1_y+dftu*t2_y)
  677. jr(3,3)=damv_r*(f(3)-pmid*n_y)/am+dpiv_r*n_y
  678. jr(3,3)=jr(3,3)+am*(dffv*n_y+dfsv*t1_y+dftv*t2_y)
  679. jr(3,4)=damw_r*(f(3)-pmid*n_y)/am+dpiw_r*n_y
  680. jr(3,4)=jr(3,4)+am*(dffw*n_y+dfsw*t1_y+dftw*t2_y)
  681. jr(3,5)=damp_r*(f(3)-pmid*n_y)/am+dpip_r*n_y
  682. jr(3,5)=jr(3,5)+am*(dffp*n_y+dfsp*t1_y+dftp*t2_y)
  683. c--------------------------------------------------------
  684. jr(4,1)=damr_r*(f(4)-pmid*n_z)/am+dpir_r*n_z
  685. jr(4,1)=jr(4,1)+am*(dffr*n_z+dfsr*t1_z+dftr*t2_z)
  686. jr(4,2)=damu_r*(f(4)-pmid*n_z)/am+dpiu_r*n_z
  687. jr(4,2)=jr(4,2)+am*(dffu*n_z+dfsu*t1_z+dftu*t2_z)
  688. jr(4,3)=damv_r*(f(4)-pmid*n_z)/am+dpiv_r*n_z
  689. jr(4,3)=jr(4,3)+am*(dffv*n_z+dfsv*t1_z+dftv*t2_z)
  690. jr(4,4)=damw_r*(f(4)-pmid*n_z)/am+dpiw_r*n_z
  691. jr(4,4)=jr(4,4)+am*(dffw*n_z+dfsw*t1_z+dftw*t2_z)
  692. jr(4,5)=damp_r*(f(4)-pmid*n_z)/am+dpip_r*n_z
  693. jr(4,5)=jr(4,5)+am*(dffp*n_z+dfsp*t1_z+dftp*t2_z)
  694. c-------------------------------------------------------
  695. c-------------------------------------------------------
  696. c-------------------------------------------------------
  697. hr_l=(eold_l+pold_l/rold_l)*rold_l
  698. hr_r=(eold_r+pold_r/rold_r)*rold_r
  699. f(5)=am*(mpl_m*hr_l+mmin_m*hr_r)
  700. c-------------------------------------------------
  701. br1=d2mr_l*hr_l+d3mr_l*hr_r
  702. br1=br1+mpl_m*(uold_l*uold_l+vold_l*vold_l+wold_l*wold_l)/2.0d0
  703. jl(5,1)=damr_l*f(5)/am+am*br1
  704. c-------------------------------------------------
  705. br1=d2mu_l*hr_l+mpl_m*uold_l*rold_l
  706. br1=br1+d3mu_l*hr_r
  707. jl(5,2)=damu_l*f(5)/am+am*br1
  708. c-------------------------------------------------
  709. br1=d2mv_l*hr_l+mpl_m*vold_l*rold_l
  710. br1=br1+d3mv_l*hr_r
  711. jl(5,3)=damv_l*f(5)/am+am*br1
  712. c-------------------------------------------------
  713. br1=d2mw_l*hr_l+mpl_m*wold_l*rold_l
  714. br1=br1+d3mw_l*hr_r
  715. jl(5,4)=damw_l*f(5)/am+am*br1
  716. c-------------------------------------------------
  717. br1=d2mp_l*hr_l+mpl_m*ga/gm1
  718. br1=br1+d3mp_l*hr_r
  719. jl(5,5)=damp_l*f(5)/am+am*br1
  720. c-------------------------------------------------
  721. c-------------------------------------------------
  722. br1=d2mr_r*hr_l+d3mr_r*hr_r
  723. br1=br1+mmin_m*(uold_r*uold_r+vold_r*vold_r+wold_r*wold_r)/2.0d0
  724. jr(5,1)=damr_r*f(5)/am+am*br1
  725. c---------------------
  726. br1=d2mu_r*hr_l+mmin_m*uold_r*rold_r
  727. br1=br1+d3mu_r*hr_r
  728. jr(5,2)=damu_r*f(5)/am+am*br1
  729. c---------------------
  730. br1=d2mv_r*hr_l+mmin_m*vold_r*rold_r
  731. br1=br1+d3mv_r*hr_r
  732. jr(5,3)=damv_r*f(5)/am+am*br1
  733. c---------------------
  734. br1=d2mw_r*hr_l+mmin_m*wold_r*rold_r
  735. br1=br1+d3mw_r*hr_r
  736. jr(5,4)=damw_r*f(5)/am+am*br1
  737. c---------------------
  738. br1=d2mp_r*hr_l+mmin_m*ga/gm1
  739. br1=br1+d3mp_r*hr_r
  740. jr(5,5)=damp_r*f(5)/am+am*br1
  741. c-------------------------------------------------------------
  742. c-------------------------------------------------------------
  743. return
  744. end
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