| 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
|