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/*@@
@file GRHydro_EigenproblemM.F90
@date August 30, 2010
@author Joshua Faber, Scott Noble, Bruno Mundim, Ian Hawke, Pedro Montero, Joachim Frieben
@desc
Computes the spectral decomposition of a given state.
Implements the analytical scheme devised by J. M. Ibanez
et al., "Godunov Methods: Theory and Applications", New
York, 2001, 485-503. The optimized method for computing
the Roe flux in the special relativistic case is due to
M. A. Aloy et al., Comput. Phys. Commun. 120 (1999)
115-121, and has been extended to the general relativistic
case as employed in this subroutine by J. Frieben, J. M.
Ibanez, and J. Pons (in preparation).
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
module GRHydro_EigenproblemM
implicit none
/*@@
@routine eigenvaluesM
@date Aug 30, 2010
@author Joshua Faber, Scott Noble, Bruno Mundim, Ian Hawke
@desc
Computes the eigenvalues of the Jacobian matrix evaluated
at the given state.
@enddesc
@calls
@calledby
@history
Culled from the routines in GR3D, author Mark Miller.
@endhistory
@@*/
CONTAINS
subroutine eigenvaluesM(handle,rho,velx,vely,velz,eps,w_lorentz,&
Bvcx,Bvcy,Bvcz,lam,gxx,gxy,gxz,gyy,gyz,gzz,u,alp,beta)
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL rho,velx,vely,velz,eps,w_lorentz
CCTK_REAL Bvcx,Bvcy,Bvcz
CCTK_REAL lam(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz
CCTK_REAL alp,beta,u
CCTK_REAL cs2,one,two,U2
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
CCTK_INT handle
CCTK_REAL dpdrho,dpdeps,press
CCTK_REAL Bvcxlow,Bvcylow,Bvczlow,Bvc2,rhohstar,va2
CCTK_REAL Bdotv,b2
! begin EOS Omni vars
integer :: n,keytemp,anyerr,keyerr(1)
real*8 :: xpress,xeps,xtemp,xye
n=1;keytemp=0;anyerr=0;keyerr(1)=0
xpress=0.0d0;xeps=0.0d0;xtemp=0.0d0;xye=0.0d0
! end EOS Omni vars
one = 1.0d0
two = 2.0d0
!!$ Set required fluid quantities
! call EOS_Omni_cs2(handle,keytemp,GRHydro_eos_rf_prec,n,&
! rho,eps,xtemp,xye,cs2,keyerr,anyerr)
call EOS_Omni_press(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,xtemp,xye,press,keyerr,anyerr)
call EOS_Omni_DPressByDEps(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,xtemp,xye,dpdeps,keyerr,anyerr)
call EOS_Omni_DPressByDRho(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,xtemp,xye,dpdrho,keyerr,anyerr)
cs2 = (dpdrho + press * dpdeps / (rho**2))/ &
(1.0d0 + eps + press/rho)
vlowx = gxx*velx + gxy*vely + gxz*velz
vlowy = gxy*velx + gyy*vely + gyz*velz
vlowz = gxz*velx + gyz*vely + gzz*velz
v2 = vlowx*velx + vlowy*vely + vlowz*velz
!!$ Lower the B-field, and square of the magnitude
Bvcxlow = gxx*Bvcx + gxy*Bvcy + gxz*Bvcz
Bvcylow = gxy*Bvcx + gyy*Bvcy + gyz*Bvcz
Bvczlow = gxz*Bvcx + gyz*Bvcy + gzz*Bvcz
Bvc2 = Bvcxlow*Bvcx + Bvcylow*Bvcy + Bvczlow*Bvcz
Bdotv = Bvcxlow*velx + Bvcylow*vely + Bvczlow*velz
w = w_lorentz
b2=Bvc2/w**2+Bdotv**2
!!$ rhohstar is the term that appears in Tmunu as well = rho*enth + b^2
rhohstar = rho*(1.0+eps)+press+b2
!!$ Alfven velocity squared
va2 = b2/(rhohstar)
!!$ The following combination always comes up in the wavespeed calculation:
!!$ U2 = v_a^2 + c_s^2(1-v_a^2)
!!$ In the unmagnetized case, it reduces to cs2
U2 = va2+cs2*(1.d0-va2)
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-U2) + sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamm_nobeta = (velx*(one-U2) - sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
lam(1) = lamm
lam(2) = lam1
lam(3) = lam2
lam(4) = lam3
lam(5) = lamp
end subroutine eigenvaluesM
subroutine eigenvaluesM_hot(handle,ii,jj,kk,rho,velx,vely,velz,eps,w_lorentz,&
Bvcx,Bvcy,Bvcz,temp,ye,lam,gxx,gxy,gxz,gyy,gyz,gzz,u,alp,beta)
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL rho,velx,vely,velz,eps,w_lorentz
CCTK_REAL Bvcx,Bvcy,Bvcz
CCTK_REAL lam(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz
CCTK_REAL alp,beta,u
CCTK_REAL temp,ye
CCTK_REAL cs2,one,two,U2
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
CCTK_INT handle, ii,jj,kk
CCTK_REAL dpdrho,dpdeps,press
CCTK_REAL Bvcxlow,Bvcylow,Bvczlow,Bvc2,rhohstar,va2
CCTK_REAL Bdotv,b2
! begin EOS Omni vars
integer :: n,keytemp,anyerr,keyerr(1)
real*8 :: xpress,xeps,xtemp,xye
n=1;keytemp=0;anyerr=0;keyerr(1)=0
xpress=0.0d0;xeps=0.0d0;xtemp=0.0d0;xye=0.0d0
! end EOS Omni vars
one = 1.0d0
two = 2.0d0
!!$ Set required fluid quantities
call EOS_Omni_cs2(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,temp,ye,cs2,keyerr,anyerr)
vlowx = gxx*velx + gxy*vely + gxz*velz
vlowy = gxy*velx + gyy*vely + gyz*velz
vlowz = gxz*velx + gyz*vely + gzz*velz
v2 = vlowx*velx + vlowy*vely + vlowz*velz
!!$ Lower the B-field, and square of the magnitude
Bvcxlow = gxx*Bvcx + gxy*Bvcy + gxz*Bvcz
Bvcylow = gxy*Bvcx + gyy*Bvcy + gyz*Bvcz
Bvczlow = gxz*Bvcx + gyz*Bvcy + gzz*Bvcz
Bvc2 = Bvcxlow*Bvcx + Bvcylow*Bvcy + Bvczlow*Bvcz
Bdotv = Bvcxlow*velx + Bvcylow*vely + Bvczlow*velz
w = w_lorentz
b2=Bvc2/w**2+Bdotv**2
!!$ rhohstar is the term that appears in Tmunu as well = rho*enth + b^2
rhohstar = rho*(1.0+eps)+press+b2
!!$ Alfven velocity squared
va2 = b2/(rhohstar)
!!$ The following combination always comes up in the wavespeed calculation:
!!$ U2 = v_a^2 + c_s^2(1-v_a^2)
!!$ In the unmagnetized case, it reduces to cs2
U2 = va2+cs2*(1.d0-va2)
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-U2) + sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamm_nobeta = (velx*(one-U2) - sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
lam(1) = lamm
lam(2) = lam1
lam(3) = lam2
lam(4) = lam3
lam(5) = lamp
end subroutine eigenvaluesM_hot
!!$ WE need to implement eigenproblem and eigenproblem_leftright!!!!
/*@@
@routine eigenvalues_generalM
@date Aug 30, 2010
@author Joshua Faber, Scott Noble, Bruno Mundim, Ian Hawke
@desc
Computes the eigenvalues of the Jacobian matrix evaluated
at the given state.
@enddesc
@calls
@calledby
@history
Culled from the routines in GR3D, author Mark Miller.
@endhistory
@@*/
subroutine eigenvalues_generalM(&
velx,vely,velz,cs2,va2,&
lam,&
gxx,gxy,gxz,gyy,gyz,gzz,&
u,alp,beta)
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL velx,vely,velz
CCTK_REAL lam(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz
CCTK_REAL alp,beta,u,U2
CCTK_REAL cs2,va2,one,two
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
one = 1.0d0
two = 2.0d0
!!$ Set required fluid quantities
vlowx = gxx*velx + gxy*vely + gxz*velz
vlowy = gxy*velx + gyy*vely + gyz*velz
vlowz = gxz*velx + gyz*vely + gzz*velz
v2 = vlowx*velx + vlowy*vely + vlowz*velz
w = one / sqrt(one - v2)
U2 = va2+cs2*(1-va2)
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-U2) + sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamm_nobeta = (velx*(one-U2) - sqrt(U2*(one-v2)*&
(u*(one-v2*U2) - velx**2*(one-U2))))/(one-v2*U2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
lam(1) = lamm
lam(2) = lam1
lam(3) = lam2
lam(4) = lam3
lam(5) = lamp
end subroutine eigenvalues_generalM
!!$ We'll need to implement eigenproblem_general
end module GRHydro_EigenproblemM
|
