1 |
C ------------
|
2 |
CN NAME: R I E M A N N
|
3 |
C ------------
|
4 |
|
5 |
CP PURPOSE:
|
6 |
CP THIS PROGRAM COMPUTES THE SOLUTION OF A 1D
|
7 |
CP RELATIVISTIC RIEMANN PROBLEM (FOR CONSTANT-GAMMA IDEAL GASES) WITH
|
8 |
CP INITIAL DATA UL IF X<0.5 AND UR IF X>0.5
|
9 |
CP IN THE WHOLE SPATIAL DOMAIN [0, 1]
|
10 |
C
|
11 |
|
12 |
CC COMMENTS:
|
13 |
CC SEE MARTI AND MUELLER, JFM, 1994
|
14 |
CC
|
15 |
CC WRITTEN BY: Jose-Maria Marti
|
16 |
CC Departamento de Astronomia y Astrofisica
|
17 |
CC Universidad de Valencia
|
18 |
CC 46100 Burjassot (Valencia), Spain
|
19 |
CC jose-maria.marti@uv.es
|
20 |
CC AND
|
21 |
CC Ewald Mueller
|
22 |
CC Max-Planck-Institut fuer Astrophysik
|
23 |
CC Karl-Schwarzschild-Str. 1
|
24 |
CC 85741 Garching, Germany
|
25 |
CC emueller@mpa-garching.mpg.de
|
26 |
C
|
27 |
|
28 |
PROGRAM RIEMANN
|
29 |
|
30 |
IMPLICIT NONE
|
31 |
|
32 |
C -------
|
33 |
C COMMON BLOCKS
|
34 |
C -------
|
35 |
|
36 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
37 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
38 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
39 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
40 |
|
41 |
DOUBLE PRECISION RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
42 |
COMMON /LS/ RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL
|
43 |
|
44 |
DOUBLE PRECISION RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
45 |
COMMON /RS/ RHORS, URS, HRS, CSRS, VELRS, VSHOCKR
|
46 |
|
47 |
DOUBLE PRECISION GAMMA
|
48 |
COMMON /ADIND/ GAMMA
|
49 |
|
50 |
C ---------
|
51 |
C INTERNAL VARIABLES
|
52 |
C ---------
|
53 |
|
54 |
INTEGER MN, N, I, ILOOP
|
55 |
PARAMETER (MN = 400)
|
56 |
|
57 |
DOUBLE PRECISION TOL, PMIN, PMAX, DVEL1, DVEL2, CHECK
|
58 |
|
59 |
DOUBLE PRECISION PS, VELS
|
60 |
|
61 |
DOUBLE PRECISION RHOA(MN), PA(MN), VELA(MN), UA(MN)
|
62 |
|
63 |
DOUBLE PRECISION XI
|
64 |
|
65 |
DOUBLE PRECISION RAD(MN), X1, X2, X3, X4, X5, T
|
66 |
|
67 |
C -------
|
68 |
C INITIAL STATES
|
69 |
C -------
|
70 |
|
71 |
WRITE(*,*) ' ADIABATIC INDEX OF THE GAS: '
|
72 |
READ (*,*) GAMMA
|
73 |
|
74 |
WRITE(*,*) ' TIME FOR THE SOLUTION: '
|
75 |
READ (*,*) T
|
76 |
|
77 |
C -----
|
78 |
C LEFT STATE
|
79 |
C -----
|
80 |
|
81 |
WRITE(*,*) ' -- LEFT STATE -- '
|
82 |
WRITE(*,*) ' PRESSURE : '
|
83 |
READ (*,*) PL
|
84 |
WRITE(*,*) ' DENSITY : '
|
85 |
READ (*,*) RHOL
|
86 |
WRITE(*,*) ' FLOW VELOCITY: '
|
87 |
READ (*,*) VELL
|
88 |
|
89 |
C ------
|
90 |
C RIGHT STATE
|
91 |
C ------
|
92 |
|
93 |
WRITE(*,*) ' -- RIGHT STATE -- '
|
94 |
WRITE(*,*) ' PRESSURE : '
|
95 |
READ (*,*) PR
|
96 |
WRITE(*,*) ' DENSITY : '
|
97 |
READ (*,*) RHOR
|
98 |
WRITE(*,*) ' FLOW VELOCITY: '
|
99 |
READ (*,*) VELR
|
100 |
|
101 |
C ------------------------------
|
102 |
C SPECIFIC INTERNAL ENERGY, SPECIFIC ENTHALPY, SOUND SPEED AND
|
103 |
C FLOW LORENTZ FACTORS IN THE INITIAL STATES
|
104 |
C ------------------------------
|
105 |
|
106 |
UL = PL/(GAMMA-1.D0)/RHOL
|
107 |
UR = PR/(GAMMA-1.D0)/RHOR
|
108 |
|
109 |
HL = 1.D0+UL+PL/RHOL
|
110 |
HR = 1.D0+UR+PR/RHOR
|
111 |
|
112 |
CSL = DSQRT(GAMMA*PL/RHOL/HL)
|
113 |
CSR = DSQRT(GAMMA*PR/RHOR/HR)
|
114 |
|
115 |
WL = 1.D0/DSQRT(1.D0-VELL**2)
|
116 |
WR = 1.D0/DSQRT(1.D0-VELR**2)
|
117 |
|
118 |
C --------
|
119 |
C NUMBER OF POINTS
|
120 |
C --------
|
121 |
|
122 |
N = 400
|
123 |
|
124 |
C -------------
|
125 |
C TOLERANCE FOR THE SOLUTION
|
126 |
C -------------
|
127 |
|
128 |
TOL = 0.D0
|
129 |
|
130 |
C
|
131 |
|
132 |
ILOOP = 0
|
133 |
|
134 |
PMIN = (PL + PR)/2.D0
|
135 |
PMAX = PMIN
|
136 |
|
137 |
5 ILOOP = ILOOP + 1
|
138 |
|
139 |
PMIN = 0.5D0*MAX(PMIN,0.D0)
|
140 |
PMAX = 2.D0*PMAX
|
141 |
|
142 |
CALL GETDVEL(PMIN, DVEL1)
|
143 |
|
144 |
CALL GETDVEL(PMAX, DVEL2)
|
145 |
|
146 |
CHECK = DVEL1*DVEL2
|
147 |
IF (CHECK.GT.0.D0) GOTO 5
|
148 |
|
149 |
C ---------------------------
|
150 |
C PRESSURE AND FLOW VELOCITY IN THE INTERMEDIATE STATES
|
151 |
C ---------------------------
|
152 |
|
153 |
CALL GETP(PMIN, PMAX, TOL, PS)
|
154 |
|
155 |
VELS = 0.5D0*(VELLS + VELRS)
|
156 |
|
157 |
C ---------------
|
158 |
C SOLUTION ON THE NUMERICAL MESH
|
159 |
C ---------------
|
160 |
|
161 |
C -----------
|
162 |
C POSITIONS OF THE WAVES
|
163 |
C -----------
|
164 |
|
165 |
IF (PL.GE.PS) THEN
|
166 |
|
167 |
X1 = 0.5D0 + (VELL - CSL)/(1.D0 - VELL*CSL)*T
|
168 |
X2 = 0.5D0 + (VELS - CSLS)/(1.D0 - VELS*CSLS)*T
|
169 |
|
170 |
ELSE
|
171 |
|
172 |
X1 = 0.5D0 + VSHOCKL*T
|
173 |
X2 = X1
|
174 |
|
175 |
END IF
|
176 |
|
177 |
X3 = 0.5D0 + VELS*T
|
178 |
|
179 |
IF (PR.GE.PS) THEN
|
180 |
|
181 |
X4 = 0.5D0 + (VELS + CSRS)/(1.D0 + VELS*CSRS)*T
|
182 |
X5 = 0.5D0 + (VELR + CSR)/(1.D0 + VELR*CSR)*T
|
183 |
|
184 |
ELSE
|
185 |
|
186 |
X4 = 0.5D0 + VSHOCKR*T
|
187 |
X5 = X4
|
188 |
|
189 |
END IF
|
190 |
|
191 |
C ----------
|
192 |
C SOLUTION ON THE MESH
|
193 |
C ----------
|
194 |
|
195 |
DO 100 I=1,N
|
196 |
|
197 |
RAD(I) = DFLOAT(I)/DFLOAT(N)
|
198 |
|
199 |
100 CONTINUE
|
200 |
|
201 |
DO 120 I=1,N
|
202 |
|
203 |
IF (RAD(I).LE.X1) THEN
|
204 |
|
205 |
PA(I) = PL
|
206 |
RHOA(I) = RHOL
|
207 |
VELA(I) = VELL
|
208 |
UA(I) = UL
|
209 |
|
210 |
ELSE IF (RAD(I).LE.X2) THEN
|
211 |
|
212 |
XI = (RAD(I) - 0.5D0)/T
|
213 |
|
214 |
CALL RAREF(XI, RHOL, PL, UL, CSL, VELL, 'L',
|
215 |
& RHOA(I), PA(I), UA(I), VELA(I))
|
216 |
|
217 |
ELSE IF (RAD(I).LE.X3) THEN
|
218 |
|
219 |
PA(I) = PS
|
220 |
RHOA(I) = RHOLS
|
221 |
VELA(I) = VELS
|
222 |
UA(I) = ULS
|
223 |
|
224 |
ELSE IF (RAD(I).LE.X4) THEN
|
225 |
|
226 |
PA(I) = PS
|
227 |
RHOA(I) = RHORS
|
228 |
VELA(I) = VELS
|
229 |
UA(I) = URS
|
230 |
|
231 |
ELSE IF (RAD(I).LE.X5) THEN
|
232 |
|
233 |
XI = (RAD(I) - 0.5D0)/T
|
234 |
|
235 |
CALL RAREF(XI, RHOR, PR, UR, CSR, VELR, 'R',
|
236 |
& RHOA(I), PA(I), UA(I), VELA(I))
|
237 |
|
238 |
ELSE
|
239 |
|
240 |
PA(I) = PR
|
241 |
RHOA(I) = RHOR
|
242 |
VELA(I) = VELR
|
243 |
UA(I) = UR
|
244 |
|
245 |
END IF
|
246 |
|
247 |
120 CONTINUE
|
248 |
|
249 |
OPEN (3,FILE='solution.dat',FORM='FORMATTED',STATUS='NEW')
|
250 |
|
251 |
WRITE(3,150) N, T
|
252 |
150 FORMAT(I5,1X,F10.5)
|
253 |
|
254 |
DO 60 I=1,N
|
255 |
WRITE(3,200) RAD(I),PA(I),RHOA(I),VELA(I),UA(I)
|
256 |
60 CONTINUE
|
257 |
|
258 |
200 FORMAT(5(E15.8,1X))
|
259 |
|
260 |
CLOSE(3)
|
261 |
|
262 |
STOP
|
263 |
END
|
264 |
|
265 |
C ----------
|
266 |
CN NAME: G E T D V E L
|
267 |
C ----------
|
268 |
|
269 |
CP PURPOSE:
|
270 |
CP COMPUTE THE DIFFERENCE IN FLOW SPEED BETWEEN LEFT AND RIGHT INTERMEDIATE
|
271 |
CP STATES FOR GIVEN LEFT AND RIGHT STATES AND PRESSURE
|
272 |
C
|
273 |
|
274 |
CC COMMENTS
|
275 |
CC NONE
|
276 |
|
277 |
SUBROUTINE GETDVEL( P, DVEL)
|
278 |
|
279 |
IMPLICIT NONE
|
280 |
|
281 |
C -----
|
282 |
C ARGUMENTS
|
283 |
C -----
|
284 |
|
285 |
DOUBLEPRECISION P, DVEL
|
286 |
|
287 |
C -------
|
288 |
C COMMON BLOCKS
|
289 |
C -------
|
290 |
|
291 |
DOUBLE PRECISION RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
292 |
COMMON /LS/ RHOLS,ULS,HLS,CSLS,VELLS,VSHOCKL
|
293 |
|
294 |
DOUBLE PRECISION RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
295 |
COMMON /RS/ RHORS,URS,HRS,CSRS,VELRS,VSHOCKR
|
296 |
|
297 |
DOUBLE PRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
298 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
299 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
300 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
301 |
|
302 |
DOUBLE PRECISION GAMMA
|
303 |
COMMON /ADIND/ GAMMA
|
304 |
|
305 |
C -----
|
306 |
C LEFT WAVE
|
307 |
C -----
|
308 |
|
309 |
CALL GETVEL(P, RHOL, PL, UL, HL, CSL, VELL, WL, 'L',
|
310 |
& RHOLS, ULS, HLS, CSLS, VELLS, VSHOCKL)
|
311 |
|
312 |
C -----
|
313 |
C RIGHT WAVE
|
314 |
C -----
|
315 |
|
316 |
CALL GETVEL(P, RHOR, PR, UR, HR, CSR, VELR, WR, 'R',
|
317 |
& RHORS, URS, HRS, CSRS, VELRS, VSHOCKR)
|
318 |
|
319 |
DVEL = VELLS - VELRS
|
320 |
|
321 |
RETURN
|
322 |
END
|
323 |
|
324 |
C -------
|
325 |
CN NAME: G E T P
|
326 |
C -------
|
327 |
|
328 |
CP PURPOSE:
|
329 |
CP FIND THE PRESSURE IN THE INTERMEDIATE STATE OF A RIEMANN PROBLEM IN
|
330 |
CP RELATIVISTIC HYDRODYNAMICS
|
331 |
C
|
332 |
|
333 |
CC COMMENTS:
|
334 |
CC THIS ROUTINE USES A COMBINATION OF INTERVAL BISECTION AND INVERSE
|
335 |
CC QUADRATIC INTERPOLATION TO FIND THE ROOT IN A SPECIFIED INTERVAL.
|
336 |
CC IT IS ASSUMED THAT DVEL(PMIN) AND DVEL(PMAX) HAVE OPPOSITE SIGNS WITHOUT
|
337 |
CC A CHECK.
|
338 |
CC ADAPTED FROM "COMPUTER METHODS FOR MATHEMATICAL COMPUTATION",
|
339 |
CC BY G. E. FORSYTHE, M. A. MALCOLM, AND C. B. MOLER,
|
340 |
CC PRENTICE-HALL, ENGLEWOOD CLIFFS N.J.
|
341 |
C
|
342 |
SUBROUTINE GETP( PMIN, PMAX, TOL, PS)
|
343 |
|
344 |
IMPLICIT NONE
|
345 |
|
346 |
C -----
|
347 |
C ARGUMENTS
|
348 |
C -----
|
349 |
|
350 |
DOUBLEPRECISION PMIN, PMAX, TOL, PS
|
351 |
|
352 |
C -------
|
353 |
C COMMON BLOCKS
|
354 |
C -------
|
355 |
|
356 |
DOUBLEPRECISION GAMMA
|
357 |
COMMON /ADIND/ GAMMA
|
358 |
|
359 |
DOUBLEPRECISION RHOL, PL, UL, HL, CSL, VELL, WL,
|
360 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
361 |
COMMON /STATES/ RHOL, PL, UL, HL, CSL, VELL, WL,
|
362 |
& RHOR, PR, UR, HR, CSR, VELR, WR
|
363 |
|
364 |
C ---------
|
365 |
C INTERNAL VARIABLES
|
366 |
C ---------
|
367 |
|
368 |
DOUBLEPRECISION A, B, C, D, E, EPS, FA, FB, FC, TOL1,
|
369 |
& XM, P, Q, R, S
|
370 |
|
371 |
C -------------
|
372 |
C COMPUTE MACHINE PRECISION
|
373 |
C -------------
|
374 |
|
375 |
EPS = 1.D0
|
376 |
10 EPS = EPS/2.D0
|
377 |
TOL1 = 1.D0 + EPS
|
378 |
IF( TOL1 .GT. 1.D0) GO TO 10
|
379 |
|
380 |
C -------
|
381 |
C INITIALIZATION
|
382 |
C -------
|
383 |
|
384 |
A = PMIN
|
385 |
B = PMAX
|
386 |
CALL GETDVEL(A,FA)
|
387 |
CALL GETDVEL(B,FB)
|
388 |
|
389 |
C -----
|
390 |
C BEGIN STEP
|
391 |
C -----
|
392 |
|
393 |
20 C = A
|
394 |
FC = FA
|
395 |
D = B - A
|
396 |
E = D
|
397 |
30 IF( DABS(FC) .GE. DABS(FB))GO TO 40
|
398 |
A = B
|
399 |
B = C
|
400 |
C = A
|
401 |
FA = FB
|
402 |
FB = FC
|
403 |
FC = FA
|
404 |
|
405 |
C --------
|
406 |
C CONVERGENCE TEST
|
407 |
C --------
|
408 |
|
409 |
40 TOL1 = 2.D0*EPS*DABS(B) + 0.5D0*TOL
|
410 |
XM = 0.5D0*(C - B)
|
411 |
IF( DABS(XM) .LE. TOL1) GO TO 90
|
412 |
IF( FB .EQ. 0.D0) GO TO 90
|
413 |
|
414 |
C ------------
|
415 |
C IS BISECTION NECESSARY?
|
416 |
C ------------
|
417 |
|
418 |
IF( DABS(E) .LT. TOL1) GO TO 70
|
419 |
IF( DABS(FA) .LE. DABS(FB)) GO TO 70
|
420 |
|
421 |
C ------------------
|
422 |
C IS QUADRATIC INTERPOLATION POSSIBLE?
|
423 |
C ------------------
|
424 |
|
425 |
IF( A .NE. C) GO TO 50
|
426 |
|
427 |
C ----------
|
428 |
C LINEAR INTERPOLATION
|
429 |
C ----------
|
430 |
|
431 |
S = FB/FA
|
432 |
P = 2.D0*XM*S
|
433 |
Q = 1.D0 - S
|
434 |
GO TO 60
|
435 |
|
436 |
C ----------------
|
437 |
C INVERSE QUADRATIC INTERPOLATION
|
438 |
C ----------------
|
439 |
|
440 |
50 Q = FA/FC
|
441 |
R = FB/FC
|
442 |
S = FB/FA
|
443 |
P = S*(2.D0*XM*Q*(Q - R) - (B - A)*(R - 1.D0))
|
444 |
Q = (Q - 1.D0)*(R - 1.D0)*(S - 1.D0)
|
445 |
|
446 |
C ------
|
447 |
C ADJUST SIGNS
|
448 |
C ------
|
449 |
|
450 |
60 IF( P .GT. 0.D0) Q = -Q
|
451 |
P = DABS(P)
|
452 |
|
453 |
C --------------
|
454 |
C IS INTERPOLATION ACCEPTABLE?
|
455 |
C --------------
|
456 |
|
457 |
IF( (2.D0*P) .GE. (3.D0*XM*Q-DABS(TOL1*Q))) GO TO 70
|
458 |
IF( P .GE. DABS(0.5D0*E*Q)) GO TO 70
|
459 |
E = D
|
460 |
D = P/Q
|
461 |
GO TO 80
|
462 |
|
463 |
C -----
|
464 |
C BISECTION
|
465 |
C -----
|
466 |
|
467 |
70 D = XM
|
468 |
E = D
|
469 |
|
470 |
C -------
|
471 |
C COMPLETE STEP
|
472 |
C -------
|
473 |
|
474 |
80 A = B
|
475 |
FA = FB
|
476 |
IF( DABS(D) .GT. TOL1) B = B+D
|
477 |
IF( DABS(D) .LE. TOL1) B = B+DSIGN(TOL1,XM)
|
478 |
CALL GETDVEL(B,FB)
|
479 |
IF( (FB*(FC/DABS(FC))) .GT. 0.D0) GO TO 20
|
480 |
GO TO 30
|
481 |
|
482 |
C --
|
483 |
C DONE
|
484 |
C --
|
485 |
|
486 |
90 PS = B
|
487 |
|
488 |
RETURN
|
489 |
END
|
490 |
|
491 |
C ---------
|
492 |
CN NAME: G E T V E L
|
493 |
C ---------
|
494 |
|
495 |
CP PURPOSE:
|
496 |
CP COMPUTE THE FLOW VELOCITY BEHIND A RAREFACTION OR SHOCK IN TERMS OF THE
|
497 |
CP POST-WAVE PRESSURE FOR A GIVEN STATE AHEAD THE WAVE IN A RELATIVISTIC
|
498 |
CP FLOW
|
499 |
C
|
500 |
|
501 |
CC COMMENTS:
|
502 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER,
|
503 |
CC J. FLUID MECH., (1994)
|
504 |
|
505 |
SUBROUTINE GETVEL( P, RHOA, PA, UA, HA, CSA, VELA, WA, S,
|
506 |
& RHO, U, H, CS, VEL, VSHOCK)
|
507 |
|
508 |
IMPLICIT NONE
|
509 |
|
510 |
C -----
|
511 |
C ARGUMENTS
|
512 |
C -----
|
513 |
|
514 |
DOUBLE PRECISION P, RHOA, PA, UA, HA, CSA, VELA, WA
|
515 |
CHARACTER*1 S
|
516 |
DOUBLE PRECISION RHO, U, H, CS, VEL, VSHOCK
|
517 |
|
518 |
C -------
|
519 |
C COMMON BLOCKS
|
520 |
C -------
|
521 |
|
522 |
DOUBLE PRECISION GAMMA
|
523 |
COMMON /ADIND/ GAMMA
|
524 |
|
525 |
C ---------
|
526 |
C INTERNAL VARIABLES
|
527 |
C ---------
|
528 |
|
529 |
DOUBLE PRECISION A, B, C, SIGN
|
530 |
DOUBLE PRECISION J, WSHOCK
|
531 |
DOUBLE PRECISION K, SQGL1
|
532 |
|
533 |
C ---------------
|
534 |
C LEFT OR RIGHT PROPAGATING WAVE
|
535 |
C ---------------
|
536 |
|
537 |
IF (S.EQ.'L') SIGN = -1.D0
|
538 |
|
539 |
IF (S.EQ.'R') SIGN = 1.D0
|
540 |
|
541 |
C
|
542 |
|
543 |
IF (P.GT.PA) THEN
|
544 |
|
545 |
C ---
|
546 |
C SHOCK
|
547 |
C ---
|
548 |
|
549 |
A = 1.D0+(GAMMA-1.D0)*(PA-P)/GAMMA/P
|
550 |
B = 1.D0-A
|
551 |
C = HA*(PA-P)/RHOA-HA**2
|
552 |
|
553 |
C ----------------
|
554 |
C CHECK FOR UNPHYSICAL ENTHALPIES
|
555 |
C ----------------
|
556 |
|
557 |
IF (C.GT.(B**2/4.D0/A)) STOP
|
558 |
& 'GETVEL: UNPHYSICAL SPECIFIC ENTHALPY IN INTERMEDIATE STATE'
|
559 |
|
560 |
C -----------------------------
|
561 |
C SPECIFIC ENTHALPY IN THE POST-WAVE STATE
|
562 |
C (FROM THE EQUATION OF STATE AND THE TAUB ADIABAT,
|
563 |
C EQ.(74), MM94)
|
564 |
C -----------------------------
|
565 |
|
566 |
H = (-B+DSQRT(B**2-4.D0*A*C))/2.D0/A
|
567 |
|
568 |
C ---------------
|
569 |
C DENSITY IN THE POST-WAVE STATE
|
570 |
C (FROM EQ.(73), MM94)
|
571 |
C ---------------
|
572 |
|
573 |
RHO = GAMMA*P/(GAMMA-1.D0)/(H-1.D0)
|
574 |
|
575 |
C ------------------------
|
576 |
C SPECIFIC INTERNAL ENERGY IN THE POST-WAVE STATE
|
577 |
C (FROM THE EQUATION OF STATE)
|
578 |
C ------------------------
|
579 |
|
580 |
U = P/(GAMMA-1.D0)/RHO
|
581 |
|
582 |
C --------------------------
|
583 |
C MASS FLUX ACROSS THE WAVE
|
584 |
C (FROM THE RANKINE-HUGONIOT RELATIONS, EQ.(71), MM94)
|
585 |
C --------------------------
|
586 |
|
587 |
J = SIGN*DSQRT((P-PA)/(HA/RHOA-H/RHO))
|
588 |
|
589 |
C ----------
|
590 |
C SHOCK VELOCITY
|
591 |
C (FROM EQ.(86), MM94
|
592 |
C ----------
|
593 |
|
594 |
A = J**2+(RHOA*WA)**2
|
595 |
B = -VELA*RHOA**2*WA**2
|
596 |
VSHOCK = (-B+SIGN*J**2*DSQRT(1.D0+RHOA**2/J**2))/A
|
597 |
WSHOCK = 1.D0/DSQRT(1.D0-VSHOCK**2)
|
598 |
|
599 |
C -------------------
|
600 |
C FLOW VELOCITY IN THE POST-SHOCK STATE
|
601 |
C (FROM EQ.(67), MM94)
|
602 |
C -------------------
|
603 |
|
604 |
A = WSHOCK*(P-PA)/J+HA*WA*VELA
|
605 |
B = HA*WA+(P-PA)*(WSHOCK*VELA/J+1.D0/RHOA/WA)
|
606 |
|
607 |
VEL = A/B
|
608 |
|
609 |
C ---------------------
|
610 |
C LOCAL SOUND SPEED IN THE POST-SHOCK STATE
|
611 |
C (FROM THE EQUATION OF STATE)
|
612 |
C ---------------------
|
613 |
|
614 |
CS = DSQRT(GAMMA*P/RHO/H)
|
615 |
|
616 |
ELSE
|
617 |
|
618 |
C ------
|
619 |
C RAREFACTION
|
620 |
C ------
|
621 |
|
622 |
C ---------------------------
|
623 |
C POLITROPIC CONSTANT OF THE GAS ACROSS THE RAREFACTION
|
624 |
C ---------------------------
|
625 |
|
626 |
K = PA/RHOA**GAMMA
|
627 |
|
628 |
C ---------------
|
629 |
C DENSITY BEHIND THE RAREFACTION
|
630 |
C ---------------
|
631 |
|
632 |
RHO = (P/K)**(1.D0/GAMMA)
|
633 |
|
634 |
C ------------------------
|
635 |
C SPECIFIC INTERNAL ENERGY BEHIND THE RAREFACTION
|
636 |
C (FROM THE EQUATION OF STATE)
|
637 |
C ------------------------
|
638 |
|
639 |
U = P/(GAMMA-1.D0)/RHO
|
640 |
|
641 |
C --------------------
|
642 |
C LOCAL SOUND SPEED BEHIND THE RAREFACTION
|
643 |
C (FROM THE EQUATION OF STATE)
|
644 |
C --------------------
|
645 |
|
646 |
CS = DSQRT(GAMMA*P/(RHO+GAMMA*P/(GAMMA-1.D0)))
|
647 |
|
648 |
C ------------------
|
649 |
C FLOW VELOCITY BEHIND THE RAREFACTION
|
650 |
C ------------------
|
651 |
|
652 |
SQGL1 = DSQRT(GAMMA-1.D0)
|
653 |
A = (1.D0+VELA)/(1.D0-VELA)*
|
654 |
& ((SQGL1+CSA)/(SQGL1-CSA)*
|
655 |
& (SQGL1-CS)/(SQGL1+CS))**(-SIGN*2.D0/SQGL1)
|
656 |
|
657 |
VEL = (A-1.D0)/(A+1.D0)
|
658 |
|
659 |
END IF
|
660 |
|
661 |
END
|
662 |
|
663 |
C --------
|
664 |
CN NAME: R A R E F
|
665 |
C --------
|
666 |
|
667 |
CP PURPOSE:
|
668 |
CP COMPUTE THE FLOW STATE IN A RAREFACTION FOR GIVEN PRE-WAVE STATE
|
669 |
C
|
670 |
|
671 |
CC COMMENTS:
|
672 |
CC THIS ROUTINE CLOSELY FOLLOWS THE EXPRESSIONS IN MARTI AND MUELLER,
|
673 |
CC J. FLUID MECH., (1994)
|
674 |
|
675 |
SUBROUTINE RAREF( XI, RHOA, PA, UA, CSA, VELA, S, RHO, P, U, VEL)
|
676 |
|
677 |
IMPLICIT NONE
|
678 |
|
679 |
C -----
|
680 |
C ARGUMENTS
|
681 |
C -----
|
682 |
|
683 |
DOUBLE PRECISION XI
|
684 |
|
685 |
DOUBLE PRECISION RHOA, PA, UA, CSA, VELA
|
686 |
|
687 |
CHARACTER S
|
688 |
|
689 |
DOUBLE PRECISION RHO, P, U, VEL
|
690 |
|
691 |
C -------
|
692 |
C COMMON BLOCKS
|
693 |
C -------
|
694 |
|
695 |
DOUBLE PRECISION GAMMA
|
696 |
COMMON /ADIND/ GAMMA
|
697 |
|
698 |
C ---------
|
699 |
C INTERNAL VARIABLES
|
700 |
C ---------
|
701 |
|
702 |
DOUBLE PRECISION B, C, D, K, L, V, OCS2, FCS2, DFDCS2, CS2, SIGN
|
703 |
|
704 |
C ---------------
|
705 |
C LEFT OR RIGHT PROPAGATING WAVE
|
706 |
C ---------------
|
707 |
|
708 |
IF (S.EQ.'L') SIGN = 1.D0
|
709 |
|
710 |
IF (S.EQ.'R') SIGN = -1.D0
|
711 |
|
712 |
B = DSQRT(GAMMA - 1.D0)
|
713 |
C = (B + CSA)/(B - CSA)
|
714 |
D = -SIGN*B/2.D0
|
715 |
K = (1.D0 + XI)/(1.D0 - XI)
|
716 |
L = C*K**D
|
717 |
V = ((1.D0 - VELA)/(1.D0 + VELA))**D
|
718 |
|
719 |
OCS2 = CSA
|
720 |
|
721 |
25 FCS2 = L*V*(1.D0 + SIGN*OCS2)**D*(OCS2 - B) +
|
722 |
& (1.D0 - SIGN*OCS2)**D*(OCS2 + B)
|
723 |
|
724 |
DFDCS2 = L*V*(1.D0 + SIGN*OCS2)**D*
|
725 |
& (1.D0 + SIGN*D*(OCS2 - B)/(1.D0 + SIGN*OCS2)) +
|
726 |
& (1.D0 - SIGN*OCS2)**D*
|
727 |
& (1.D0 - SIGN*D*(OCS2 + B)/(1.D0 - SIGN*OCS2))
|
728 |
|
729 |
CS2 = OCS2 - FCS2/DFDCS2
|
730 |
|
731 |
IF (ABS(CS2 - OCS2)/OCS2.GT.5.E-7)THEN
|
732 |
OCS2 = CS2
|
733 |
GOTO 25
|
734 |
END IF
|
735 |
|
736 |
VEL = (XI + SIGN*CS2)/(1.D0 + SIGN*XI*CS2)
|
737 |
|
738 |
RHO = RHOA*((CS2**2*(GAMMA - 1.D0 - CSA**2))/
|
739 |
& (CSA**2*(GAMMA - 1.D0 - CS2**2)))
|
740 |
& **(1.D0/(GAMMA - 1.D0))
|
741 |
|
742 |
P = CS2**2*(GAMMA - 1.D0)*RHO/(GAMMA - 1.D0 - CS2**2)/GAMMA
|
743 |
|
744 |
U = P/(GAMMA - 1.D0)/RHO
|
745 |
|
746 |
RETURN
|
747 |
END
|