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  1. C CONJP7 SOURCE CHAT 05/01/12 22:17:57 5004
  2. SUBROUTINE CONJP7(JL,WVEC_L,WVEC_R,NVECT,TVECT,
  3. & ga,v_inf)
  4. C************************************************************************
  5. C
  6. C PROJET : CASTEM 2000
  7. C
  8. C NOM : CONJP7
  9. C
  10. C DESCRIPTION : Voir KONJA5
  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 jacobian which is the derivatives
  21. c of the numerical flux function defined at the wall
  22. c with respect to the PRIMITIVE variables of the left
  23. c cell (relative to the wall).
  24. c The low-mach number corrections are made for the flux functions
  25. c
  26. c EQUATIONS: 2D Euler equations of gas dynamics
  27. c
  28. c
  29. c REFERENCE: 1) JCP, 129, 364-382 (1996)
  30. c " A Sequel to AUSM: AUSM+ ".
  31. c M.S.Liou
  32. c 2) AIAA Journal, Sept. 1998
  33. c " Low-Diffusion Flux-Splitting Methods for Flows at All Speeds"
  34. c J.R.Edwards and M.S.Liou
  35. c----------------------------------------------------------------------
  36. c INPUT:
  37. c
  38. c alpha -- parameter of the AUSM+ scheme in the Pressure function;
  39. c ( -3/4 <= alpha <= 3/16 ) (imposed as a parameter)
  40. c
  41. c beta -- parameter of the AUSM+ scheme in the Mach function;
  42. c ( -1/16 <= beta <= 1/2 ) (imposed as a parameter)
  43. c
  44. c wvec_l -- vector of the primitive variables (rho,ux,uy,p) at the
  45. c left cell;
  46. c
  47. c wvec_r -- vector of the primitive variables (rho,ux,uy,p) at the
  48. c right cell;
  49. c
  50. c nvect -- normal vector to the interface (2 components in 2D);
  51. c
  52. c tvect -- tangential vector to the interface;
  53. c
  54. c ga -- ratio of the specific heats (assumed constant)
  55. c
  56. c v_inf -- parameter for reference velocity, see Ref. 2).
  57. c----------------------------------------------------------------------
  58. c
  59. c OUTPUT:
  60. c
  61. c jl -- jakobian matrix 4 by 4 - derivatives of the numerical
  62. c flux function with respect to the PRIMITIVE variables
  63. c from the left cell;
  64. c
  65. c----------------------------------------------------------------------
  66. IMPLICIT INTEGER(I-N)
  67. real*8 wvec_l(4),wvec_r(4)
  68. real*8 nvect(2),tvect(2)
  69. real*8 jl(4,4),jr(4,4)
  70. real*8 alpha,beta
  71. real*8 ga,gm1,temph
  72. real*8 n_x,n_y,t_x,t_y
  73. real*8 un_l, un_r, ut_l, ut_r
  74. real*8 ml,mr,Mplus,Mmin,mmid
  75. real*8 mpl_m, mmin_m,am
  76. real*8 rold_l,uold_l,vold_l,pold_l,eold_l
  77. real*8 rold_r,uold_r,vold_r,pold_r,eold_r
  78. real*8 Pplus,Pmin
  79. real*8 top,bot,bots
  80. real*8 br3,br4,temp_l,temp_r,brac_l,brac_r
  81. real*8 aleft, arigh,tcoef,bcoef
  82. real*8 damr_l,damr_r,damu_l,damu_r
  83. real*8 damv_l,damv_r,damp_l,damp_r
  84. real*8 dmlr_l,dmlr_r,dmlu_l,dmlu_r
  85. real*8 dmlv_l,dmlv_r,dmlp_l,dmlp_r
  86. real*8 dmrr_l,dmrr_r,dmru_l,dmru_r
  87. real*8 dmrv_l,dmrv_r,dmrp_l,dmrp_r
  88. real*8 dMpr_l,dMpr_r,dMpu_l,dMpu_r
  89. real*8 dMpv_l,dMpv_r,dMpp_l,dMpp_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 dmir_l,dmir_r,dmiu_l,dmiu_r
  93. real*8 dmiv_l,dmiv_r,dmip_l,dmip_r
  94. real*8 d3mr_l,d3mr_r,d3mu_l,d3mu_r
  95. real*8 d3mv_l,d3mv_r,d3mp_l,d3mp_r
  96. real*8 d2mr_l,d2mr_r,d2mu_l,d2mu_r
  97. real*8 d2mv_l,d2mv_r,d2mp_l,d2mp_r
  98. real*8 dPpr_l,dPpr_r,dPpu_l,dPpu_r
  99. real*8 dPpv_l,dPpv_r,dPpp_l,dPpp_r
  100. real*8 dPmr_l,dPmr_r,dPmu_l,dPmu_r
  101. real*8 dPmv_l,dPmv_r,dPmp_l,dPmp_r
  102. real*8 dpir_l,dpir_r,dpiu_l,dpiu_r
  103. real*8 dpiv_l,dpiv_r,dpip_l,dpip_r
  104. real*8 epsil,qq,amw,Mmin1,Mplus1
  105. real*8 fmid,mlw,mrw,termp
  106. real*8 ur_r,ur_l,urm,mhalf,mhalfr
  107. real*8 durr_l,durr_r,duru_l,duru_r
  108. real*8 durv_l,durv_r,durp_l,durp_r
  109. real*8 dmhr_l,dmhr_r,dmhu_l,dmhu_r
  110. real*8 dmhv_l,dmhv_r,dmhp_l,dmhp_r
  111. real*8 dmfr_l,dmfr_r,dmfu_l,dmfu_r
  112. real*8 dmfv_l,dmfv_r,dmfp_l,dmfp_r
  113. real*8 dfm_mf,dfm_mh
  114. real*8 dfmr_l,dfmr_r,dfmu_l,dfmu_r
  115. real*8 dfmv_l,dfmv_r,dfmp_l,dfmp_r
  116. real*8 m1mr_l,m1mr_r,m1mu_l,m1mu_r
  117. real*8 m1mv_l,m1mv_r,m1mp_l,m1mp_r
  118. real*8 m1pr_l,m1pr_r,m1pu_l,m1pu_r
  119. real*8 m1pv_l,m1pv_r,m1pp_l,m1pp_r
  120. real*8 tmpr_l,tmpr_r,tmpu_l,tmpu_r
  121. real*8 tmpv_l,tmpv_r,tmpp_l,tmpp_r
  122. real*8 coef,canc,v_inf
  123. real*8 sr_l,sr_r,su_l,su_r,sv_l,sv_r,sp_l,sp_r
  124. real*8 rum,rumr_l,rumu_l,rumv_l,rump_l
  125. real*8 rumr_r,rumu_r,rumv_r,rump_r
  126. integer i
  127. parameter(alpha = 0.1875D0, beta = 0.125D0)
  128. parameter(epsil = 1.0d0)
  129. canc=1.0d0
  130. c-------------------------------------------------------------
  131. n_x=nvect(1)
  132. n_y=nvect(2)
  133. t_x=tvect(1)
  134. t_y=tvect(2)
  135. c----------------------------
  136. gm1=ga-1.0d0
  137. c----------------------------
  138. rold_l=wvec_l(1)
  139. uold_l=wvec_l(2)
  140. vold_l=wvec_l(3)
  141. pold_l=wvec_l(4)
  142. c-----------------------
  143. rold_r=wvec_r(1)
  144. uold_r=wvec_r(2)
  145. vold_r=wvec_r(3)
  146. pold_r=wvec_r(4)
  147. c------------------------------------------------------------------
  148. c Computation of the specific total energy on the left and right.
  149. c------------------------------------------------------------------
  150. eold_l=(uold_l*uold_l+vold_l*vold_l)/2.0d0
  151. eold_l=eold_l+pold_l/(gm1*rold_l)
  152. eold_r=(uold_r*uold_r+vold_r*vold_r)/2.0d0
  153. eold_r=eold_r+pold_r/(gm1*rold_r)
  154. c------------------------------------------------------------------
  155. c Computing reference velocity and its derivatives
  156. c------------------------------------------------------------------
  157. aleft=sqrt(ga*pold_l/rold_l)
  158. arigh=sqrt(ga*pold_r/rold_r)
  159. qq=sqrt(uold_l*uold_l+vold_l*vold_l)
  160. if(qq .lt. (epsil*v_inf)) then
  161. ur_l = epsil*v_inf
  162. durr_l=0.0d0
  163. duru_l=0.0d0
  164. durv_l=0.0d0
  165. durp_l=0.0d0
  166. else
  167. ur_l=qq
  168. durr_l=0.0d0
  169. duru_l=uold_l/qq
  170. durv_l=vold_l/qq
  171. durp_l=0.0d0
  172. endif
  173. c-----------------------
  174. if(ur_l .ge. aleft) then
  175. ur_l=aleft
  176. durr_l=-aleft/(2.0d0*rold_l)
  177. duru_l=0.0d0
  178. durv_l=0.0d0
  179. durp_l=ga/(2.0d0*aleft*rold_l)
  180. endif
  181. c------------------------------------------------------------------
  182. c-------------------------------------------------------------------
  183. qq=sqrt(uold_r*uold_r+vold_r*vold_r)
  184. if(qq .lt. (epsil*v_inf)) then
  185. ur_r = epsil*v_inf
  186. durr_r=0.0d0
  187. duru_r=0.0d0
  188. durv_r=0.0d0
  189. durp_r=0.0d0
  190. else
  191. ur_r=qq
  192. durr_r=0.0d0
  193. duru_r=uold_r/qq
  194. durv_r=vold_r/qq
  195. durp_r=0.0d0
  196. endif
  197. c----------------------------
  198. if(ur_r .ge. arigh) then
  199. ur_r=arigh
  200. durr_r=-arigh/(2.0d0*rold_r)
  201. duru_r=0.0d0
  202. durv_r=0.0d0
  203. durp_r=ga/(2.0d0*arigh*rold_r)
  204. endif
  205. c------------------------------------------------------------------
  206. c Reference velocity at the interface is taken as an average
  207. c of the reference velocities of the neighbouring cells
  208. c-------------------------------------------------------------------
  209. urm=0.5d0*(ur_l+ur_r)
  210. durr_l=0.5d0*durr_l
  211. duru_l=0.5d0*duru_l
  212. durv_l=0.5d0*durv_l
  213. durp_l=0.5d0*durp_l
  214. c-------------------------
  215. durr_r=0.5d0*durr_r
  216. duru_r=0.5d0*duru_r
  217. durv_r=0.5d0*durv_r
  218. durp_r=0.5d0*durp_r
  219. c-------------------------------------------------------------------
  220. c Computation of the speed of sound and its derivatives;
  221. c numerical speed of sound at the interface is taken as an average
  222. c of the speeds of sounds of the neighbouring cells
  223. c-------------------------------------------------------------------
  224. am=0.5d0*(aleft+arigh)
  225. c-------------------------------------------------------------------
  226. if(abs(urm/am-1.0d0).le.0.000001d0) then
  227. coef=0.0d0
  228. else
  229. coef=1.0d0
  230. endif
  231. c-------------------------------------------------------------------
  232. damr_r=-arigh/(4.0d0*rold_r)
  233. damu_r=0.0d0
  234. damv_r=0.0d0
  235. damp_r=ga/(4.0d0*arigh*rold_r)
  236. c-----------------------
  237. damr_l=-aleft/(4.0d0*rold_l)
  238. damu_l=0.0d0
  239. damv_l=0.0d0
  240. damp_l=ga/(4.0d0*aleft*rold_l)
  241. c-------------------------------------------------------------------
  242. c Computing numerical Mach number and its derivatives,
  243. c see p.370, under (A1).
  244. c-------------------------------------------------------------------
  245. un_l=uold_l*n_x+vold_l*n_y
  246. un_r=uold_r*n_x+vold_r*n_y
  247. ut_l=uold_l*t_x+vold_l*t_y
  248. ut_r=uold_r*t_x+vold_r*t_y
  249. c-------------------------------------------------------------------
  250. ml=un_l/am
  251. mr=un_r/am
  252. mhalf=0.5d0*(un_l+un_r)/am
  253. c---------------------
  254. top=0.5d0*(un_l+un_r)/(am*am)
  255. dmhr_l=-top*damr_l
  256. dmhu_l=n_x/2.0d0/am-top*damu_l
  257. dmhv_l=n_y/2.0d0/am-top*damv_l
  258. dmhp_l=-top*damp_l
  259. c---------------------
  260. dmhr_r=-top*damr_r
  261. dmhu_r=n_x/2.0d0/am-top*damu_r
  262. dmhv_r=n_y/2.0d0/am-top*damv_r
  263. dmhp_r=-top*damp_r
  264. c--------------------------------
  265. mhalfr=urm/am
  266. c---------------------
  267. top=urm/(am*am)
  268. dmfr_l=durr_l/am-top*damr_l
  269. dmfu_l=duru_l/am-top*damu_l
  270. dmfv_l=durv_l/am-top*damv_l
  271. dmfp_l=durp_l/am-top*damp_l
  272. c---------------------
  273. dmfr_r=durr_r/am-top*damr_r
  274. dmfu_r=duru_r/am-top*damu_r
  275. dmfv_r=durv_r/am-top*damv_r
  276. dmfp_r=durp_r/am-top*damp_r
  277. c-------------------------------------------------------------------
  278. c Scaling function for the speed of sound and its derivatives
  279. c-------------------------------------------------------------------
  280. top=(1.0d0-mhalfr*mhalfr)*(1.0d0-mhalfr*mhalfr)
  281. top=top*mhalf*mhalf+4.0d0*mhalfr*mhalfr
  282. bot=1.0d0+mhalfr*mhalfr
  283. if(abs(canc-0.0d0).lt.0.000001d0) then
  284. fmid=1.0d0
  285. else
  286. fmid=sqrt(top)/bot
  287. endif
  288. c--------------------------
  289. temph=-4.0d0*(1.0d0-mhalfr*mhalfr)*mhalfr
  290. temph=temph*mhalf*mhalf+8.0d0*mhalfr
  291. dfm_mf=temph/(sqrt(top)*2.0d0*bot)
  292. dfm_mf=dfm_mf-sqrt(top)*2.0d0*mhalfr/(bot*bot)
  293. c--------------------------
  294. temph=2.0d0*(1.0d0-mhalfr*mhalfr)*(1.0d0-mhalfr*mhalfr)*mhalf
  295. dfm_mh=temph/(2.0d0*bot*sqrt(top))
  296. c--------------------------
  297. dfmr_l=dfm_mf*dmfr_l+dfm_mh*dmhr_l
  298. dfmu_l=dfm_mf*dmfu_l+dfm_mh*dmhu_l
  299. dfmv_l=dfm_mf*dmfv_l+dfm_mh*dmhv_l
  300. dfmp_l=dfm_mf*dmfp_l+dfm_mh*dmhp_l
  301. c--------------------------
  302. dfmr_r=dfm_mf*dmfr_r+dfm_mh*dmhr_r
  303. dfmu_r=dfm_mf*dmfu_r+dfm_mh*dmhu_r
  304. dfmv_r=dfm_mf*dmfv_r+dfm_mh*dmhv_r
  305. dfmp_r=dfm_mf*dmfp_r+dfm_mh*dmhp_r
  306. c--------------------------
  307. amw=fmid*am
  308. mlw=un_l/amw
  309. mrw=un_r/amw
  310. c--------------------------
  311. damr_l=canc*coef*dfmr_l*am+fmid*damr_l
  312. damu_l=canc*coef*dfmu_l*am+fmid*damu_l
  313. damv_l=canc*coef*dfmv_l*am+fmid*damv_l
  314. damp_l=canc*coef*dfmp_l*am+fmid*damp_l
  315. c--------------------------
  316. damr_r=canc*coef*dfmr_r*am+fmid*damr_r
  317. damu_r=canc*coef*dfmu_r*am+fmid*damu_r
  318. damv_r=canc*coef*dfmv_r*am+fmid*damv_r
  319. damp_r=canc*coef*dfmp_r*am+fmid*damp_r
  320. c-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/
  321. am=amw
  322. c-------------------------------------------------------------------
  323. c Redefinition of the numerical mach numbers
  324. c-------------------------------------------------------------------
  325. if(abs(canc-0.0d0).lt.0.000001d0) then
  326. top=2.0d0
  327. bot=0.0d0
  328. else
  329. top=1.0d0+mhalfr*mhalfr
  330. bot=1.0d0-mhalfr*mhalfr
  331. endif
  332. ml=0.5d0*(top*mlw+bot*mrw)
  333. mr=0.5d0*(top*mrw+bot*mlw)
  334. c-------------------------------------------------------------------
  335. c Mplus and Mmin are calligraphic lettes M+ and M- from the paper,
  336. c see (19a) and (19b), p.367.
  337. c-------------------------------------------------------------------
  338. if(abs(ml) .ge. 1.0d0) then
  339. Mplus=(ml+abs(ml))/2.0d0
  340. else
  341. Mplus=(ml+1.0d0)*(ml+1.0d0)/4.0d0
  342. Mplus=Mplus+beta*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  343. endif
  344. Mplus1=(ml+abs(ml))/2.0d0
  345. c-------------------------------------------------------------------
  346. if(abs(mr) .ge. 1.0d0) then
  347. Mmin=(mr-abs(mr))/2.0d0
  348. else
  349. Mmin=-(mr-1.0d0)*(mr-1.0d0)/4.0d0
  350. Mmin=Mmin-beta*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  351. endif
  352. Mmin1=(mr-abs(mr))/2.0d0
  353. c-------------------------------------------------------------------
  354. c Derivatives of ml and mr with respect to both sets of primitive
  355. c variables: left and right.
  356. c-------------------------------------------------------------------
  357. temp_l=-un_l/(am*am)
  358. temp_r=-un_r/(am*am)
  359. c--------
  360. dmlr_l=temp_l*damr_l
  361. dmlr_r=temp_l*damr_r
  362. dmrr_l=temp_r*damr_l
  363. dmrr_r=temp_r*damr_r
  364. c--------
  365. dmlu_l=n_x/am+temp_l*damu_l
  366. dmlu_r=temp_l*damu_r
  367. dmru_l=temp_r*damu_l
  368. dmru_r=n_x/am+temp_r*damu_r
  369. c--------
  370. dmlv_l=n_y/am+temp_l*damv_l
  371. dmlv_r=temp_l*damv_r
  372. dmrv_l=temp_r*damv_l
  373. dmrv_r=n_y/am+temp_r*damv_r
  374. c--------
  375. dmlp_l=temp_l*damp_l
  376. dmlp_r=temp_l*damp_r
  377. dmrp_l=temp_r*damp_l
  378. dmrp_r=temp_r*damp_r
  379. c-----------------------------
  380. sr_l=dmlr_l
  381. sr_r=dmlr_r
  382. su_l=dmlu_l
  383. su_r=dmlu_r
  384. sv_l=dmlv_l
  385. sv_r=dmlv_r
  386. sp_l=dmlp_l
  387. sp_r=dmlp_r
  388. c-----------------------------------------------------------------
  389. c Redefinition of the derivatives of the ml & mr
  390. c-----------------------------------------------------------------
  391. temp_l=(mlw-mrw)*mhalfr
  392. temp_r=-temp_l
  393. c--------
  394. dmlr_l=0.5d0*(top*dmlr_l+bot*dmrr_l)+canc*coef*temp_l*dmfr_l
  395. dmlu_l=0.5d0*(top*dmlu_l+bot*dmru_l)+canc*coef*temp_l*dmfu_l
  396. dmlv_l=0.5d0*(top*dmlv_l+bot*dmrv_l)+canc*coef*temp_l*dmfv_l
  397. dmlp_l=0.5d0*(top*dmlp_l+bot*dmrp_l)+canc*coef*temp_l*dmfp_l
  398. c--------
  399. dmlr_r=0.5d0*(top*dmlr_r+bot*dmrr_r)+canc*coef*temp_l*dmfr_r
  400. dmlu_r=0.5d0*(top*dmlu_r+bot*dmru_r)+canc*coef*temp_l*dmfu_r
  401. dmlv_r=0.5d0*(top*dmlv_r+bot*dmrv_r)+canc*coef*temp_l*dmfv_r
  402. dmlp_r=0.5d0*(top*dmlp_r+bot*dmrp_r)+canc*coef*temp_l*dmfp_r
  403. c--------
  404. dmrr_l=0.5d0*(top*dmrr_l+bot*sr_l)+canc*coef*temp_r*dmfr_l
  405. dmru_l=0.5d0*(top*dmru_l+bot*su_l)+canc*coef*temp_r*dmfu_l
  406. dmrv_l=0.5d0*(top*dmrv_l+bot*sv_l)+canc*coef*temp_r*dmfv_l
  407. dmrp_l=0.5d0*(top*dmrp_l+bot*sp_l)+canc*coef*temp_r*dmfp_l
  408. c--------
  409. dmrr_r=0.5d0*(top*dmrr_r+bot*sr_r)+canc*coef*temp_r*dmfr_r
  410. dmru_r=0.5d0*(top*dmru_r+bot*su_r)+canc*coef*temp_r*dmfu_r
  411. dmrv_r=0.5d0*(top*dmrv_r+bot*sv_r)+canc*coef*temp_r*dmfv_r
  412. dmrp_r=0.5d0*(top*dmrp_r+bot*sp_r)+canc*coef*temp_r*dmfp_r
  413. c-----------------------------------------------------------
  414. c mmid is m_{1/2} (notation as in the paper, see (13),p.366)
  415. c-----------------------------------------------------------
  416. mmid=Mplus+Mmin
  417. c-----------------------------------------------------------
  418. c Computing the derivatives of M+ and M-
  419. c-----------------------------------------------------------
  420. if(ml .ge. 1.0d0) then
  421. dMpr_l=dmlr_l
  422. dMpu_l=dmlu_l
  423. dMpv_l=dmlv_l
  424. dMpp_l=dmlp_l
  425. c--------------------
  426. dMpr_r=dmlr_r
  427. dMpu_r=dmlu_r
  428. dMpv_r=dmlv_r
  429. dMpp_r=dmlp_r
  430. else
  431. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  432. temph=(ml+1.0d0)/2.0d0
  433. dMpr_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_l
  434. dMpu_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_l
  435. dMpv_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_l
  436. dMpp_l=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_l
  437. c--------------------
  438. dMpr_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlr_r
  439. dMpu_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlu_r
  440. dMpv_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlv_r
  441. dMpp_r=(temph+4.0d0*beta*ml*(ml*ml-1.0d0))*dmlp_r
  442. else
  443. dMpr_l=0.0d0
  444. dMpu_l=0.0d0
  445. dMpv_l=0.0d0
  446. dMpp_l=0.0d0
  447. c---------------------
  448. dMpr_r=0.0d0
  449. dMpu_r=0.0d0
  450. dMpv_r=0.0d0
  451. dMpp_r=0.0d0
  452. endif
  453. endif
  454. c-----------------------------------------------------------
  455. c addition of low Mach number
  456. c-----------------------------------------------------------
  457. if(ml .ge. 0.0d0) then
  458. m1pr_l=dmlr_l
  459. m1pu_l=dmlu_l
  460. m1pv_l=dmlv_l
  461. m1pp_l=dmlp_l
  462. c---------------------
  463. m1pr_r=dmlr_r
  464. m1pu_r=dmlu_r
  465. m1pv_r=dmlv_r
  466. m1pp_r=dmlp_r
  467. else
  468. m1pr_l=0.0d0
  469. m1pu_l=0.0d0
  470. m1pv_l=0.0d0
  471. m1pp_l=0.0d0
  472. c--------------------
  473. m1pr_r=0.0d0
  474. m1pu_r=0.0d0
  475. m1pv_r=0.0d0
  476. m1pp_r=0.0d0
  477. endif
  478. c-----------------------------------------------------------
  479. if(mr .ge. 1.0d0) then
  480. dMmr_l=0.0d0
  481. dMmu_l=0.0d0
  482. dMmv_l=0.0d0
  483. dMmp_l=0.0d0
  484. c---------------------
  485. dMmr_r=0.0d0
  486. dMmu_r=0.0d0
  487. dMmv_r=0.0d0
  488. dMmp_r=0.0d0
  489. else
  490. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  491. temph=(-mr+1.0d0)/2.0d0
  492. dMmr_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_l
  493. dMmu_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_l
  494. dMmv_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_l
  495. dMmp_l=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_l
  496. c--------------------
  497. dMmr_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrr_r
  498. dMmu_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmru_r
  499. dMmv_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrv_r
  500. dMmp_r=(temph-4.0d0*beta*mr*(mr*mr-1.0d0))*dmrp_r
  501. else
  502. dMmr_l=dmrr_l
  503. dMmu_l=dmru_l
  504. dMmv_l=dmrv_l
  505. dMmp_l=dmrp_l
  506. c--------------------
  507. dMmr_r=dmrr_r
  508. dMmu_r=dmru_r
  509. dMmv_r=dmrv_r
  510. dMmp_r=dmrp_r
  511. endif
  512. endif
  513. c-----------------------------------------------------------
  514. c addition of low Mach number
  515. c-----------------------------------------------------------
  516. if(mr .le. 0.0d0) then
  517. m1mr_l=dmrr_l
  518. m1mu_l=dmru_l
  519. m1mv_l=dmrv_l
  520. m1mp_l=dmrp_l
  521. c---------------------
  522. m1mr_r=dmrr_r
  523. m1mu_r=dmru_r
  524. m1mv_r=dmrv_r
  525. m1mp_r=dmrp_r
  526. else
  527. m1mr_l=0.0d0
  528. m1mu_l=0.0d0
  529. m1mv_l=0.0d0
  530. m1mp_l=0.0d0
  531. c--------------------
  532. m1mr_r=0.0d0
  533. m1mu_r=0.0d0
  534. m1mv_r=0.0d0
  535. m1mp_r=0.0d0
  536. endif
  537. c-----------------------------------------------------------------
  538. c computing the derivatives of m_{1/2} (notation as in the paper)
  539. c-----------------------------------------------------------------
  540. dmir_l=dMpr_l+dMmr_l
  541. dmir_r=dMpr_r+dMmr_r
  542. c-------------
  543. dmiu_l=dMpu_l+dMmu_l
  544. dmiu_r=dMpu_r+dMmu_r
  545. c-------------
  546. dmiv_l=dMpv_l+dMmv_l
  547. dmiv_r=dMpv_r+dMmv_r
  548. c-------------
  549. dmip_l=dMpp_l+dMmp_l
  550. dmip_r=dMpp_r+dMmp_r
  551. c----------------------------------------------------------------
  552. c computing the main convective variables and their derivatives
  553. c mpl_m is m^{+}_{1/2} (paper's notation) and
  554. c mmin_m is m^{-}_{1/2} (paper's notation), see (A2) on p.370.
  555. c----------------------------------------------------------------
  556. termp=(Mmin1-Mmin+Mplus-Mplus1)*(1.0d0/(mhalfr*mhalfr)-1.0d0)
  557. termp=termp*(pold_l-pold_r)/(pold_l/rold_l+pold_r/rold_r)
  558. c-------------------------------------------------------------
  559. c derivatives of the termp
  560. c-------------------------------------------------------------
  561. top=(Mmin1-Mmin+Mplus-Mplus1)
  562. bots=1.0d0/(pold_l/rold_l+pold_r/rold_r)
  563. bot=(pold_l-pold_r)*bots
  564. temph=1.0d0/(mhalfr*mhalfr)-1.0d0
  565. c---------------------------
  566. tmpr_l=(m1mr_l-dMmr_l+dMpr_l-m1pr_l)*bot*temph
  567. tmpr_l=tmpr_l-2.0d0*bot*top*dmfr_l/(mhalfr*mhalfr*mhalfr)
  568. tmpr_l=tmpr_l+temph*top*bot*bots*(pold_l/rold_l/rold_l)
  569. c---------------------------
  570. tmpu_l=(m1mu_l-dMmu_l+dMpu_l-m1pu_l)*bot*temph
  571. tmpu_l=tmpu_l-2.0d0*bot*top*dmfu_l/(mhalfr*mhalfr*mhalfr)
  572. c---------------------------
  573. tmpv_l=(m1mv_l-dMmv_l+dMpv_l-m1pv_l)*bot*temph
  574. tmpv_l=tmpv_l-2.0d0*bot*top*dmfv_l/(mhalfr*mhalfr*mhalfr)
  575. c---------------------------
  576. tmpp_l=(m1mp_l-dMmp_l+dMpp_l-m1pp_l)*bot*temph
  577. tmpp_l=tmpp_l-2.0d0*bot*top*dmfp_l/(mhalfr*mhalfr*mhalfr)
  578. tmpp_l=tmpp_l+temph*top*bots*(1.0d0-bot/rold_l)
  579. c------------rrrrrrrr-------
  580. c------------rrrrrrrr-------
  581. tmpr_r=(m1mr_r-dMmr_r+dMpr_r-m1pr_r)*bot*temph
  582. tmpr_r=tmpr_r-2.0d0*bot*top*dmfr_r/(mhalfr*mhalfr*mhalfr)
  583. tmpr_r=tmpr_r+temph*top*bot*bots*(pold_r/rold_r/rold_r)
  584. c---------------------------
  585. tmpu_r=(m1mu_r-dMmu_r+dMpu_r-m1pu_r)*bot*temph
  586. tmpu_r=tmpu_r-2.0d0*bot*top*dmfu_r/(mhalfr*mhalfr*mhalfr)
  587. c---------------------------
  588. tmpv_r=(m1mv_r-dMmv_r+dMpv_r-m1pv_r)*bot*temph
  589. tmpv_r=tmpv_r-2.0d0*bot*top*dmfv_r/(mhalfr*mhalfr*mhalfr)
  590. c---------------------------
  591. tmpp_r=(m1mp_r-dMmp_r+dMpp_r-m1pp_r)*bot*temph
  592. tmpp_r=tmpp_r-2.0d0*bot*top*dmfp_r/(mhalfr*mhalfr*mhalfr)
  593. tmpp_r=tmpp_r-temph*top*bots*(1.0d0+bot/rold_r)
  594. c-------------------------------------------------------------
  595. if(mmid .ge. 0.0d0) then
  596. mpl_m = mmid
  597. d2mr_l=dmir_l
  598. d2mu_l=dmiu_l
  599. d2mv_l=dmiv_l
  600. d2mp_l=dmip_l
  601. c------------
  602. d2mr_r=dmir_r
  603. d2mu_r=dmiu_r
  604. d2mv_r=dmiv_r
  605. d2mp_r=dmip_r
  606. c------------
  607. else
  608. mpl_m = 0.0d0
  609. d2mr_l=0.0d0
  610. d2mu_l=0.0d0
  611. d2mv_l=0.0d0
  612. d2mp_l=0.0d0
  613. c------------
  614. d2mr_r=0.0d0
  615. d2mu_r=0.0d0
  616. d2mv_r=0.0d0
  617. d2mp_r=0.0d0
  618. endif
  619. c---------------------------------------------
  620. cc derivatives for the term termm
  621. cc------------------------------------------------------------------
  622. if(mmid .le. 0.0d0) then
  623. mmin_m = mmid
  624. d3mr_l=dmir_l
  625. d3mu_l=dmiu_l
  626. d3mv_l=dmiv_l
  627. d3mp_l=dmip_l
  628. c------------
  629. d3mr_r=dmir_r
  630. d3mu_r=dmiu_r
  631. d3mv_r=dmiv_r
  632. d3mp_r=dmip_r
  633. c------------
  634. else
  635. mmin_m = 0.0d0
  636. d3mr_l=0.0d0
  637. d3mu_l=0.0d0
  638. d3mv_l=0.0d0
  639. d3mp_l=0.0d0
  640. c------------
  641. d3mr_r=0.0d0
  642. d3mu_r=0.0d0
  643. d3mv_r=0.0d0
  644. d3mp_r=0.0d0
  645. endif
  646. c---------------------------------------------------------------
  647. c Computing the calligraphic P+ and P- with their derivatives,
  648. c see (21a) & (21b) on p.368.
  649. c---------------------------------------------------------------
  650. if(ml .ge. 1.0d0) then
  651. Pplus = 1.0d0
  652. else
  653. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  654. Pplus=(ml+1.0d0)*(ml+1.0d0)*(2.0d0-ml)/4.0d0
  655. Pplus=Pplus+alpha*ml*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  656. else
  657. Pplus = 0.0d0
  658. endif
  659. endif
  660. c---------------------------------------------------------------
  661. if(mr .ge. 1.0d0) then
  662. Pmin = 0.0d0
  663. else
  664. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  665. Pmin=(mr-1.0d0)*(mr-1.0d0)*(2.0d0+mr)/4.0d0
  666. Pmin=Pmin-alpha*mr*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  667. else
  668. Pmin = 1.0d0
  669. endif
  670. endif
  671. c---------------------------------------------------------------
  672. brac_l=(ml+1.0d0)*(2.0d0-ml)/2.0d0-(ml+1.0d0)*(ml+1.0d0)/4.0d0
  673. brac_l=brac_l+alpha*(ml*ml-1.0d0)*(ml*ml-1.0d0)
  674. brac_l=brac_l+4.0d0*alpha*ml*ml*(ml*ml-1.0d0)
  675. c--------------
  676. brac_r=(mr-1.0d0)*(2.0d0+mr)/2.0d0+(mr-1.0d0)*(mr-1.0d0)/4.0d0
  677. brac_r=brac_r-alpha*(mr*mr-1.0d0)*(mr*mr-1.0d0)
  678. brac_r=brac_r-4.0d0*alpha*mr*mr*(mr*mr-1.0d0)
  679. c---------------------------------------------------------------
  680. if((ml .gt. -1.0d0) .and. (ml .lt. 1.0d0)) then
  681. dPpr_l=brac_l*dmlr_l
  682. dPpr_r=brac_l*dmlr_r
  683. c------------
  684. dPpu_l=brac_l*dmlu_l
  685. dPpu_r=brac_l*dmlu_r
  686. c------------
  687. dPpv_l=brac_l*dmlv_l
  688. dPpv_r=brac_l*dmlv_r
  689. c------------
  690. dPpp_l=brac_l*dmlp_l
  691. dPpp_r=brac_l*dmlp_r
  692. c------------
  693. else
  694. dPpr_l=0.0d0
  695. dPpr_r=0.0d0
  696. c-----------
  697. dPpu_l=0.0d0
  698. dPpu_r=0.0d0
  699. c-----------
  700. dPpv_l=0.0d0
  701. dPpv_r=0.0d0
  702. c-----------
  703. dPpp_l=0.0d0
  704. dPpp_r=0.0d0
  705. c-----------
  706. endif
  707. c---------------------------------------------------------------
  708. if((mr .gt. -1.0d0) .and. (mr .lt. 1.0d0)) then
  709. dPmr_l=brac_r*dmrr_l
  710. dPmr_r=brac_r*dmrr_r
  711. c------------
  712. dPmu_l=brac_r*dmru_l
  713. dPmu_r=brac_r*dmru_r
  714. c------------
  715. dPmv_l=brac_r*dmrv_l
  716. dPmv_r=brac_r*dmrv_r
  717. c------------
  718. dPmp_l=brac_r*dmrp_l
  719. dPmp_r=brac_r*dmrp_r
  720. c------------
  721. else
  722. dPmr_l=0.0d0
  723. dPmr_r=0.0d0
  724. c-----------
  725. dPmu_l=0.0d0
  726. dPmu_r=0.0d0
  727. c-----------
  728. dPmv_l=0.0d0
  729. dPmv_r=0.0d0
  730. c-----------
  731. dPmp_l=0.0d0
  732. dPmp_r=0.0d0
  733. c-----------
  734. endif
  735. c-------------------------------------------------------------------
  736. c computing pmid -- p_{1/2} and its derivatives, see (20b), p.367.
  737. c-------------------------------------------------------------------
  738. dpir_l=dPpr_l*pold_l+dPmr_l*pold_r
  739. dpiu_l=dPpu_l*pold_l+dPmu_l*pold_r
  740. dpiv_l=dPpv_l*pold_l+dPmv_l*pold_r
  741. dpip_l=dPpp_l*pold_l+Pplus+dPmp_l*pold_r
  742. c----------------------------
  743. dpir_r=dPpr_r*pold_l+dPmr_r*pold_r
  744. dpiu_r=dPpu_r*pold_l+dPmu_r*pold_r
  745. dpiv_r=dPpv_r*pold_l+dPmv_r*pold_r
  746. dpip_r=dPpp_r*pold_l+Pmin+dPmp_r*pold_r
  747. c---------------------------------------------------------------------
  748. c Computation of the mass flux (rho * u)_1/2
  749. c---------------------------------------------------------------
  750. rum=am*(mpl_m*rold_l+mmin_m*rold_r)+canc*am*termp
  751. c-------------------------------------------------------
  752. rumr_l=damr_l*(mpl_m*rold_l+mmin_m*rold_r)+
  753. & am*(d2mr_l*rold_l+mpl_m+d3mr_l*rold_r)
  754. rumr_l=rumr_l+canc*coef*(damr_l*termp+am*tmpr_l)
  755. rumu_l=damu_l*(mpl_m*rold_l+mmin_m*rold_r)+
  756. & am*(d2mu_l*rold_l+d3mu_l*rold_r)
  757. rumu_l=rumu_l+canc*coef*(damu_l*termp+am*tmpu_l)
  758. rumv_l=damv_l*(mpl_m*rold_l+mmin_m*rold_r)+
  759. & am*(d2mv_l*rold_l+d3mv_l*rold_r)
  760. rumv_l=rumv_l+canc*coef*(damv_l*termp+am*tmpv_l)
  761. rump_l=damp_l*(mpl_m*rold_l+mmin_m*rold_r)+
  762. & am*(d2mp_l*rold_l+d3mp_l*rold_r)
  763. rump_l=rump_l+canc*coef*(damp_l*termp+am*tmpp_l)
  764. c-------------------------------------------------
  765. rumr_r=damr_r*(mpl_m*rold_l+mmin_m*rold_r)+
  766. & am*(d2mr_r*rold_l+mmin_m+d3mr_r*rold_r)
  767. rumr_r=rumr_r+canc*coef*(damr_r*termp+am*tmpr_r)
  768. rumu_r=damu_r*(mpl_m*rold_l+mmin_m*rold_r)+
  769. & am*(d2mu_r*rold_l+d3mu_r*rold_r)
  770. rumu_r=rumu_r+canc*coef*(damu_r*termp+am*tmpu_r)
  771. rumv_r=damv_r*(mpl_m*rold_l+mmin_m*rold_r)+
  772. & am*(d2mv_r*rold_l+d3mv_r*rold_r)
  773. rumv_r=rumv_r+canc*coef*(damv_r*termp+am*tmpv_r)
  774. rump_r=damp_r*(mpl_m*rold_l+mmin_m*rold_r)+
  775. & am*(d2mp_r*rold_l+d3mp_r*rold_r)
  776. rump_r=rump_r+canc*coef*(damp_r*termp+am*tmpp_r)
  777. c---------------------------------------------------------------------
  778. c computing JACOBIAN as a derivative of the numerical flux function
  779. c with respect to the primitive variables.
  780. c Notation: jl(i,j) --- is the derivative of the i-component of the
  781. c flux function with respect to the j-component of the
  782. c vector of primitive variables of the left state.
  783. c jr(i,j) --- is the derivative of the i-component of the
  784. c flux function with respect to the j-component of the
  785. c vector of primitive variables of the right state.
  786. c---------------------------------------------------------------------
  787. jl(1,1)=0.0d0
  788. jl(1,2)=0.0d0
  789. jl(1,3)=0.0d0
  790. jl(1,4)=0.0d0
  791. c------------------------------------
  792. jr(1,1)=0.0d0
  793. jr(1,2)=0.0d0
  794. jr(1,3)=0.0d0
  795. jr(1,4)=0.0d0
  796. c------------------------------------
  797. c---------------------------------------------------------
  798. if(rum .ge. 0.0d0) then
  799. br3=rumr_l*un_l
  800. br4=rumr_l*ut_l
  801. else
  802. br3=rumr_l*un_r
  803. br4=rumr_l*ut_r
  804. endif
  805. jl(2,1)=n_x*(br3+dpir_l)+br4*t_x
  806. jl(3,1)=n_y*(br3+dpir_l)+br4*t_y
  807. c-------------------
  808. if(rum .ge. 0.0d0) then
  809. br3=rumu_l*un_l+rum*n_x
  810. br4=rumu_l*ut_l+rum*t_x
  811. else
  812. br3=rumu_l*un_r
  813. br4=rumu_l*ut_r
  814. endif
  815. jl(2,2)=n_x*(br3+dpiu_l)+br4*t_x
  816. jl(3,2)=n_y*(br3+dpiu_l)+br4*t_y
  817. c-------------------
  818. if(rum .ge. 0.0d0) then
  819. br3=rumv_l*un_l+rum*n_y
  820. br4=rumv_l*ut_l+rum*t_y
  821. else
  822. br3=rumv_l*un_r
  823. br4=rumv_l*ut_r
  824. endif
  825. jl(2,3)=n_x*(br3+dpiv_l)+br4*t_x
  826. jl(3,3)=n_y*(br3+dpiv_l)+br4*t_y
  827. c-------------------
  828. if(rum .ge. 0.0d0) then
  829. br3=rump_l*un_l
  830. br4=rump_l*ut_l
  831. else
  832. br3=rump_l*un_r
  833. br4=rump_l*ut_r
  834. endif
  835. jl(2,4)=n_x*(br3+dpip_l)+br4*t_x
  836. jl(3,4)=n_y*(br3+dpip_l)+br4*t_y
  837. c-------------------------------------------------------------
  838. c-------------------------------------------------------------
  839. if(rum .ge. 0.0d0) then
  840. br3=rumr_r*un_l
  841. br4=rumr_r*ut_l
  842. else
  843. br3=rumr_r*un_r
  844. br4=rumr_r*ut_r
  845. endif
  846. jr(2,1)=n_x*(br3+dpir_r)+br4*t_x
  847. jr(3,1)=n_y*(br3+dpir_r)+br4*t_y
  848. c-------------------
  849. if(rum .ge. 0.0d0) then
  850. br3=rumu_r*un_l
  851. br4=rumu_r*ut_l
  852. else
  853. br3=rumu_r*un_r+rum*n_x
  854. br4=rumu_r*ut_r+rum*t_x
  855. endif
  856. jr(2,2)=n_x*(br3+dpiu_r)+br4*t_x
  857. jr(3,2)=n_y*(br3+dpiu_r)+br4*t_y
  858. c-------------------
  859. if(rum .ge. 0.0d0) then
  860. br3=rumv_r*un_l
  861. br4=rumv_r*ut_l
  862. else
  863. br3=rumv_r*un_r+rum*n_y
  864. br4=rumv_r*ut_r+rum*t_y
  865. endif
  866. jr(2,3)=n_x*(br3+dpiv_r)+br4*t_x
  867. jr(3,3)=n_y*(br3+dpiv_r)+br4*t_y
  868. c-------------------
  869. if(rum .ge. 0.0d0) then
  870. br3=rump_r*un_l
  871. br4=rump_r*ut_l
  872. else
  873. br3=rump_r*un_r
  874. br4=rump_r*ut_r
  875. endif
  876. jr(2,4)=n_x*(br3+dpip_r)+br4*t_x
  877. jr(3,4)=n_y*(br3+dpip_r)+br4*t_y
  878. c-------------------------------------------------------------
  879. c ------ f44444444444444444444444444444 ---------
  880. c-------------------------------------------------------------
  881. jl(4,1)=0.0d0
  882. jl(4,2)=0.0d0
  883. jl(4,3)=0.0d0
  884. jl(4,4)=0.0d0
  885. c----------------------------------------------------------
  886. jr(4,1)=0.0d0
  887. jr(4,2)=0.0d0
  888. jr(4,3)=0.0d0
  889. jr(4,4)=0.0d0
  890. c-------------------------------------------------------------
  891. c---------------------------------------------------------------------
  892. tcoef=nvect(1)*tvect(2)+tvect(1)*nvect(2)
  893. bcoef=nvect(1)*tvect(2)-tvect(1)*nvect(2)
  894. c----------------------------------------------------------------------
  895. do 11 i=1,4
  896. jl(i,1)=jl(i,1)+jr(i,1)
  897. jl(i,2)=jl(i,2)+jr(i,2)*(-tcoef/bcoef)+
  898. & jr(i,3)*2.0d0*nvect(1)*tvect(1)/bcoef
  899. jl(i,3)=jl(i,3)+jr(i,2)*(-2.0d0*nvect(2)*tvect(2)/bcoef)+
  900. & jr(i,3)*tcoef/bcoef
  901. jl(i,4)=jl(i,4)+jr(i,4)
  902. 11 continue
  903. c----------------------------------------------------------------------
  904. return
  905. end
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