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|
/*@@
@file GRHydro_Eigenproblem.F90
@date Sat Jan 26 01:25:44 2002
@author 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_Eigenproblem
implicit none
/*@@
@routine eigenvalues
@date Sat Jan 26 01:26:20 2002
@author 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 eigenvalues(handle,rho,velx,vely,velz,eps, &
w_lorentz,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 lam(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz
CCTK_REAL alp,beta,u
CCTK_REAL cs2,one,two
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
character*256 :: warnline
! 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)
if(cs2.lt.0.0d0) then
!$OMP CRITICAL
if (abs(cs2) .gt. 1.0d-4) then
write(warnline,'(a60,6g16.7)') 'abs(cs2), rho, dpdrho, press*dpdeps/rho**2, eps, press/rho: ', abs(cs2), rho, dpdrho, press * dpdeps / (rho**2), eps, press/rho
call CCTK_WARN(1,warnline)
call CCTK_WARN(1,"cs2 < 0! Check speed of sound calculation!")
cs2 = 0.0d0
else
cs2 = 0.0d0
endif
!$OMP END CRITICAL
endif
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 = w_lorentz
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
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
subroutine eigenvalues_hot(handle,keytemp,ii,jj,kk,rho,velx,vely,velz,eps, &
temp,ye,w_lorentz,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 lam(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz
CCTK_REAL alp,beta,u
CCTK_REAL temp,ye
CCTK_REAL cs2,one,two
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
! begin EOS Omni vars
integer :: n,keytemp,anyerr,keyerr(1)
real*8 :: xpress,xeps
n=1;anyerr=0;keyerr(1)=0
xpress=0.0d0;xeps=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
w = w_lorentz
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
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_hot
/*@@
@routine eigenproblem
@date Sat Jan 26 01:27:59 2002
@author Ian Hawke, Pedro Montero, Joachim Frieben
@desc
Despite the name this routine currently actually returns the
Roe flux given the input Roe average state.
@enddesc
@calls
@calledby
@history
Culled and altered from the routines in GR3D, author Mark Miller.
@endhistory
@@*/
subroutine eigenproblem(handle,rho,velx,vely,velz,eps,&
w_lorentz,gxx,gxy,gxz,gyy,gyz,gzz,u,&
alp,beta,qdiff1,qdiff2,qdiff3,qdiff4,qdiff5,&
roeflux1,roeflux2,roeflux3,roeflux4,roeflux5)
USE GRHydro_Scalars
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL rho,velx,vely,velz,eps,w_lorentz
CCTK_REAL lam(5),p(5,5),q(5,5),dw(5),rflux(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz,u
CCTK_REAL alp,beta,roeflux1,roeflux2,roeflux3,roeflux4,roeflux5
CCTK_REAL du(5),aa(5,5),qdiff1,qdiff2,qdiff3,qdiff4,qdiff5
integer i,j
CCTK_REAL paug(5,6),tmp1,tmp2,sump,summ,f_du(5)
integer ii,jj,kk
CCTK_REAL leivec1(5),leivec2(5),leivec3(5),leivecp(5),leivecm(5)
CCTK_REAL reivec1(5),reivec2(5),reivec3(5),reivecp(5),reivecm(5)
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
CCTK_REAL cs2,one,two
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL press,dpdrho,dpdeps,enthalpy,kappa
CCTK_REAL axp,axm,vxp,vxm,cxx,cxy,cxz,gam,xsi,dlt,vxa,vxb
CCTK_INT handle
!!$ Warning, warning. Nasty hack follows
! begin EOS Omni vars
integer :: n,keytemp,anyerr,keyerr(1)
real*8 :: xpress(1),xeps(1),xtemp(1),xye(1)
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_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)
! call EOS_Omni_cs2(handle,keytemp,GRHydro_eos_rf_prec,n,&
! rho,eps,xtemp,xye,cs2,keyerr,anyerr)
! if (cs2<0) cs2=0 ! this does not modify the roe crashing problem with shocktube
enthalpy = one + 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
w = w_lorentz
!!$Calculate eigenvalues and put them in conventional order
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
!!$ lam(1) = lamm
!!$ lam(2) = lam1
!!$ lam(3) = lam2
!!$ lam(4) = lam3
!!$ lam(5) = lamp
lam(1) = lamm
lam(5) = lam1
lam(3) = lam2
lam(4) = lam3
lam(2) = lamp
!!$Compute some auxiliary quantities
axp = (u - velx*velx)/(u - velx*lamp_nobeta)
axm = (u - velx*velx)/(u - velx*lamm_nobeta)
vxp = (velx - lamp_nobeta)/(u - velx * lamp_nobeta)
vxm = (velx - lamm_nobeta)/(u - velx * lamm_nobeta)
!!$Calculate associated right eigenvectors
kappa = dpdeps / (dpdeps - rho * cs2)
reivec1(1) = kappa / (enthalpy * w)
reivec1(2) = vlowx
reivec1(3) = vlowy
reivec1(4) = vlowz
reivec1(5) = one - reivec1(1)
reivec2(1) = w * vlowy
reivec2(2) = enthalpy * (gxy + two * w * w * vlowx * vlowy)
reivec2(3) = enthalpy * (gyy + two * w * w * vlowy * vlowy)
reivec2(4) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec2(5) = vlowy * w * (two * w * enthalpy - one)
reivec3(1) = w * vlowz
reivec3(2) = enthalpy * (gxz + two * w * w * vlowx * vlowz)
reivec3(3) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec3(4) = enthalpy * (gzz + two * w * w * vlowz * vlowz)
reivec3(5) = vlowz * w * (two * w * enthalpy - one)
reivecp(1) = one
reivecp(2) = enthalpy * w * (vlowx - vxp)
reivecp(3) = enthalpy * w * vlowy
reivecp(4) = enthalpy * w * vlowz
reivecp(5) = enthalpy * w * axp - one
reivecm(1) = one
reivecm(2) = enthalpy * w * (vlowx - vxm)
reivecm(3) = enthalpy * w * vlowy
reivecm(4) = enthalpy * w * vlowz
reivecm(5) = enthalpy * w * axm - one
!!$Calculate associated left eigenvectors if requested
if (ANALYTICAL) then
cxx = gyy * gzz - gyz * gyz
cxy = gxz * gyz - gxy * gzz
cxz = gxy * gyz - gxz * gyy
gam = gxx * cxx + gxy * cxy + gxz * cxz
xsi = cxx - gam * velx * velx
dlt = enthalpy**3 * w * (kappa - one) * (vxm - vxp) * xsi
tmp1 = w / (kappa - one)
leivec1(1) = tmp1 * (enthalpy - w)
leivec1(2) = tmp1 * w * velx
leivec1(3) = tmp1 * w * vely
leivec1(4) = tmp1 * w * velz
leivec1(5) =-tmp1 * w
tmp1 = one / (xsi * enthalpy)
leivec2(1) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec2(2) = (gzz * vlowy - gyz * vlowz) * tmp1 * velx
leivec2(3) = (gzz * (one - velx * vlowx) + gxz * vlowz * velx) * tmp1
leivec2(4) = (gyz * (velx * vlowx - one) - gxz * velx * vlowy) * tmp1
leivec2(5) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec3(1) = (gyz * vlowy - gyy * vlowz) * tmp1
leivec3(2) = (gyy * vlowz - gyz * vlowy) * tmp1 * velx
leivec3(3) = (gyz * (velx * vlowx - one) - gxy * velx * vlowz) * tmp1
leivec3(4) = (gyy * (one - velx * vlowx) + gxy * velx * vlowy) * tmp1
leivec3(5) = (gyz * vlowy - gyy * vlowz) * tmp1
tmp1 = enthalpy * enthalpy / dlt
tmp2 = w * w * xsi
leivecp(1) = - (enthalpy * w * vxm * xsi + (one - kappa) * (vxm * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxm) * tmp1
leivecp(2) = - (cxx * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecp(3) = - (cxy * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecp(4) = - (cxz * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecp(5) = - ((one - kappa) * (vxm * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxm) * tmp1
leivecm(1) = (enthalpy * w * vxp * xsi + (one - kappa) * (vxp * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxp) * tmp1
leivecm(2) = (cxx * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecm(3) = (cxy * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecm(4) = (cxz * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecm(5) = ((one - kappa) * (vxp * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxp) * tmp1
endif
du(1) = qdiff1
du(2) = qdiff2
du(3) = qdiff3
du(4) = qdiff4
du(5) = qdiff5
if (ANALYTICAL) then
if (FAST) then
sump = 0.0d0
summ = 0.0d0
do i=1,5
sump = sump + (abs(lamp) - abs(lam1)) * leivecp(i) * du(i)
summ = summ + (abs(lamm) - abs(lam1)) * leivecm(i) * du(i)
enddo
vxa = sump + summ
vxb =-(sump * vxp + summ * vxm)
rflux(1) = abs(lam1) * du(1) + vxa
rflux(2) = abs(lam1) * du(2) + enthalpy * w * (vlowx * vxa + vxb)
rflux(3) = abs(lam1) * du(3) + enthalpy * w * (vlowy * vxa)
rflux(4) = abs(lam1) * du(4) + enthalpy * w * (vlowz * vxa)
rflux(5) = abs(lam1) * du(5) + enthalpy * w * (velx * vxb + vxa) - vxa
else
!!$Form Jacobian matrix in characteristic form from right eigenvectors.
!!$Invert to get the characteristic jumps given the conserved variable
!!$jumps
!!$ p(:,1) = reivecm(:)
!!$ p(:,2) = reivec1(:)
!!$ p(:,3) = reivec2(:)
!!$ p(:,4) = reivec3(:)
!!$ p(:,5) = reivecp(:)
!!$
!!$ write(*,*) p
!!$ stop
p(:,1) = reivecm(:)
p(:,2) = reivecp(:)
p(:,3) = reivec2(:)
p(:,4) = reivec3(:)
p(:,5) = reivec1(:)
q(1,:) = leivecm(:)
q(2,:) = leivecp(:)
q(3,:) = leivec2(:)
q(4,:) = leivec3(:)
q(5,:) = leivec1(:)
do i=1,5
dw(i) = 0.0d0
do j=1,5
dw(i) = dw(i) + q(i,j) * du(j)
enddo
enddo
!!$Calculate the Roe flux from the standard formula
do i = 1, 5
rflux(i) = 0.d0
do j = 1, 5
rflux(i) = rflux(i) + p(i,j) * abs(lam(j)) * dw(j)
end do
end do
endif
else
p(:,1) = reivecm(:)
p(:,2) = reivecp(:)
p(:,3) = reivec2(:)
p(:,4) = reivec3(:)
p(:,5) = reivec1(:)
do i=1,5
dw(i) = du(i)
do j=1,5
aa(i,j) = p(i,j)
end do
enddo
do ii=1,5
paug(ii,1) = p(ii,1)
paug(ii,2) = p(ii,2)
paug(ii,3) = p(ii,3)
paug(ii,4) = p(ii,4)
paug(ii,5) = p(ii,5)
enddo
paug(1, 6) = du(1)
paug(2, 6) = du(2)
paug(3, 6) = du(3)
paug(4, 6) = du(4)
paug(5, 6) = du(5)
do ii=1,5
tmp1 = paug(ii,ii)
do jj=ii,6
paug(ii,jj) = paug(ii,jj)/tmp1
enddo
do jj=ii+1,5
tmp1 = - (paug(jj,ii))
do kk=ii,6
paug(jj,kk) = paug(jj,kk) + tmp1*paug(ii,kk)
enddo
enddo
enddo
f_du(5) = paug(5,6)
do ii=4,1,-1
f_du(ii) = paug(ii,6)
do jj=ii+1,5
f_du(ii) = f_du(ii) - paug(ii,jj)*f_du(jj)
enddo
enddo
dw(1) = f_du(1)
dw(2) = f_du(2)
dw(3) = f_du(3)
dw(4) = f_du(4)
dw(5) = f_du(5)
!!$ dw(1) = f_du(1)
!!$ dw(2) = f_du(5)
!!$ dw(3) = f_du(3)
!!$ dw(4) = f_du(4)
!!$ dw(5) = f_du(2)
!!$Calculate the Roe flux from the standard formula
do i = 1, 5
rflux(i) = 0.d0
do j = 1, 5
rflux(i) = rflux(i) + p(i,j) * abs(lam(j)) * dw(j)
end do
end do
endif
roeflux1 = rflux(1)
roeflux2 = rflux(2)
roeflux3 = rflux(3)
roeflux4 = rflux(4)
roeflux5 = rflux(5)
if(roeflux1.ne.roeflux1) then
call CCTK_WARN(0, "Found NaNs in roeflux1, aborting")
endif
end subroutine eigenproblem
/*@@
@routine eigenproblem_leftright
@date Sat Jan 26 01:27:59 2002
@author Ian Hawke, Pedro Montero, Joachim Frieben
@desc
Returns the left and right eigenvectors.
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
subroutine eigenproblem_leftright(handle,rho,velx,vely,velz,eps,&
w_lorentz,gxx,gxy,gxz,gyy,gyz,gzz,u,&
alp,beta,lambda,levec,revec)
USE GRHydro_Scalars
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL rho,velx,vely,velz,eps,w_lorentz
CCTK_REAL lambda(5),levec(5,5),revec(5,5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz,u
CCTK_REAL alp,beta
CCTK_REAL tmp1,tmp2
CCTK_REAL leivec1(5),leivec2(5),leivec3(5),leivecp(5),leivecm(5)
CCTK_REAL reivec1(5),reivec2(5),reivec3(5),reivecp(5),reivecm(5)
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
CCTK_REAL cs2,one,two
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL press,dpdrho,dpdeps,enthalpy,kappa
CCTK_REAL axp,axm,vxp,vxm,cxx,cxy,cxz,gam,xsi,dlt
CCTK_INT handle
! begin EOS Omni vars
integer :: n,keytemp,anyerr,keyerr(1)
real*8 :: xpress(1),xeps(1),xtemp(1),xye(1)
n = 1;keytemp = 0;anyerr = 0;keyerr(1) = 0
xpress = 0.0d0;xeps = 0.0d0;xtemp = 0.0d0;xye = 0.0d0
! end EOS Omni vars
one = 1.0d0
two = 2.0d0
!!$ Set required fluid quantities
call EOS_Omni_press(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,xtemp,xye,press,keyerr,anyerr)
call EOS_Omni_cs2(handle,keytemp,GRHydro_eos_rf_prec,n,&
rho,eps,xtemp,xye,cs2,keyerr,anyerr)
! if (cs2<0) cs2=0 ! this does not modify the roe crashing problem with shocktube
enthalpy = one + 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
w = w_lorentz
!!$Calculate eigenvalues and put them in conventional order
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
!!$ lam(1) = lamm
!!$ lam(2) = lam1
!!$ lam(3) = lam2
!!$ lam(4) = lam3
!!$ lam(5) = lamp
lambda(1) = lamm
lambda(2) = lam1
lambda(3) = lam2
lambda(4) = lam3
lambda(5) = lamp
!!$Compute some auxiliary quantities
axp = (u - velx*velx)/(u - velx*lamp_nobeta)
axm = (u - velx*velx)/(u - velx*lamm_nobeta)
vxp = (velx - lamp_nobeta)/(u - velx * lamp_nobeta)
vxm = (velx - lamm_nobeta)/(u - velx * lamm_nobeta)
!!$Calculate associated right eigenvectors
kappa = dpdeps / (dpdeps - rho * cs2)
reivec1(1) = kappa / (enthalpy * w)
reivec1(2) = vlowx
reivec1(3) = vlowy
reivec1(4) = vlowz
reivec1(5) = one - reivec1(1)
reivec2(1) = w * vlowy
reivec2(2) = enthalpy * (gxy + two * w * w * vlowx * vlowy)
reivec2(3) = enthalpy * (gyy + two * w * w * vlowy * vlowy)
reivec2(4) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec2(5) = vlowy * w * (two * w * enthalpy - one)
reivec3(1) = w * vlowz
reivec3(2) = enthalpy * (gxz + two * w * w * vlowx * vlowz)
reivec3(3) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec3(4) = enthalpy * (gzz + two * w * w * vlowz * vlowz)
reivec3(5) = vlowz * w * (two * w * enthalpy - one)
reivecp(1) = one
reivecp(2) = enthalpy * w * (vlowx - vxp)
reivecp(3) = enthalpy * w * vlowy
reivecp(4) = enthalpy * w * vlowz
reivecp(5) = enthalpy * w * axp - one
reivecm(1) = one
reivecm(2) = enthalpy * w * (vlowx - vxm)
reivecm(3) = enthalpy * w * vlowy
reivecm(4) = enthalpy * w * vlowz
reivecm(5) = enthalpy * w * axm - one
revec(1,:) = reivecm
revec(2,:) = reivec1
revec(3,:) = reivec2
revec(4,:) = reivec3
revec(5,:) = reivecp
!!$Calculate associated left eigenvectors if requested
cxx = gyy * gzz - gyz * gyz
cxy = gxz * gyz - gxy * gzz
cxz = gxy * gyz - gxz * gyy
gam = gxx * cxx + gxy * cxy + gxz * cxz
xsi = cxx - gam * velx * velx
dlt = enthalpy**3 * w * (kappa - one) * (vxm - vxp) * xsi
tmp1 = w / (kappa - one)
leivec1(1) = tmp1 * (enthalpy - w)
leivec1(2) = tmp1 * w * velx
leivec1(3) = tmp1 * w * vely
leivec1(4) = tmp1 * w * velz
leivec1(5) =-tmp1 * w
tmp1 = one / (xsi * enthalpy)
leivec2(1) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec2(2) = (gzz * vlowy - gyz * vlowz) * tmp1 * velx
leivec2(3) = (gzz * (one - velx * vlowx) + gxz * vlowz * velx) * tmp1
leivec2(4) = (gyz * (velx * vlowx - one) - gxz * velx * vlowy) * tmp1
leivec2(5) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec3(1) = (gyz * vlowy - gyy * vlowz) * tmp1
leivec3(2) = (gyy * vlowz - gyz * vlowy) * tmp1 * velx
leivec3(3) = (gyz * (velx * vlowx - one) - gxy * velx * vlowz) * tmp1
leivec3(4) = (gyy * (one - velx * vlowx) + gxy * velx * vlowy) * tmp1
leivec3(5) = (gyz * vlowy - gyy * vlowz) * tmp1
tmp1 = enthalpy * enthalpy / dlt
tmp2 = w * w * xsi
leivecp(1) = - (enthalpy * w * vxm * xsi + (one - kappa) * (vxm * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxm) * tmp1
leivecp(2) = - (cxx * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecp(3) = - (cxy * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecp(4) = - (cxz * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecp(5) = - ((one - kappa) * (vxm * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxm) * tmp1
leivecm(1) = (enthalpy * w * vxp * xsi + (one - kappa) * (vxp * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxp) * tmp1
leivecm(2) = (cxx * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecm(3) = (cxy * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecm(4) = (cxz * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecm(5) = ((one - kappa) * (vxp * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxp) * tmp1
levec(1,:) = leivecm
levec(2,:) = leivec1
levec(3,:) = leivec2
levec(4,:) = leivec3
levec(5,:) = leivecp
end subroutine eigenproblem_leftright
/*@@
@routine eigenvalues
@date Sat Jan 26 01:26:20 2002
@author 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_general(&
velx,vely,velz,cs2,&
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
CCTK_REAL cs2,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)
!!$ Calculate eigenvalues
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
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_general
/*@@
@routine eigenproblem_general
@date Sat Jan 26 01:27:59 2002
@author Ian Hawke, Pedro Montero, Joachim Frieben
@desc
Despite the name this routine currently actually returns the
Roe flux given the input Roe average state.
@enddesc
@calls
@calledby
@history
Culled and altered from the routines in GR3D, author Mark Miller.
@endhistory
@@*/
subroutine eigenproblem_general(&
rho,velx,vely,velz,eps,&
press,cs2,dpdeps,&
gxx,gxy,gxz,gyy,gyz,gzz,&
u,alp,beta,&
qdiff1,qdiff2,qdiff3,qdiff4,qdiff5,&
roeflux1,roeflux2,roeflux3,roeflux4,roeflux5)
USE GRHydro_Scalars
implicit none
DECLARE_CCTK_PARAMETERS
CCTK_REAL rho,velx,vely,velz,eps
CCTK_REAL lam(5),p(5,5),q(5,5),dw(5),rflux(5)
CCTK_REAL gxx,gxy,gxz,gyy,gyz,gzz,u
CCTK_REAL alp,beta,roeflux1,roeflux2,roeflux3,roeflux4,roeflux5
CCTK_REAL du(5),aa(5,5),qdiff1,qdiff2,qdiff3,qdiff4,qdiff5
integer i,j
CCTK_REAL paug(5,6),tmp1,tmp2,sump,summ,f_du(5)
integer ii,jj,kk
CCTK_REAL leivec1(5),leivec2(5),leivec3(5),leivecp(5),leivecm(5)
CCTK_REAL reivec1(5),reivec2(5),reivec3(5),reivecp(5),reivecm(5)
CCTK_REAL lam1,lam2,lam3,lamm,lamp,lamm_nobeta,lamp_nobeta
CCTK_REAL cs2,one,two
CCTK_REAL vlowx,vlowy,vlowz,v2,w
CCTK_REAL press,dpdeps,enthalpy,kappa
CCTK_REAL axp,axm,vxp,vxm,cxx,cxy,cxz,gam,xsi,dlt,vxa,vxb
one = 1.0d0
two = 2.0d0
!!$ Set required fluid quantities
enthalpy = one + 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
w = one / sqrt(one - v2)
!!$Calculate eigenvalues and put them in conventional order
lam1 = velx - beta/alp
lam2 = velx - beta/alp
lam3 = velx - beta/alp
lamp_nobeta = (velx*(one-cs2) + sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamm_nobeta = (velx*(one-cs2) - sqrt(cs2*(one-v2)*&
(u*(one-v2*cs2) - velx**2*(one-cs2))))/(one-v2*cs2)
lamp = lamp_nobeta - beta/alp
lamm = lamm_nobeta - beta/alp
!!$ lam(1) = lamm
!!$ lam(2) = lam1
!!$ lam(3) = lam2
!!$ lam(4) = lam3
!!$ lam(5) = lamp
lam(1) = lamm
lam(5) = lam1
lam(3) = lam2
lam(4) = lam3
lam(2) = lamp
!!$Compute some auxiliary quantities
axp = (u - velx*velx)/(u - velx*lamp_nobeta)
axm = (u - velx*velx)/(u - velx*lamm_nobeta)
vxp = (velx - lamp_nobeta)/(u - velx * lamp_nobeta)
vxm = (velx - lamm_nobeta)/(u - velx * lamm_nobeta)
!!$Calculate associated right eigenvectors
kappa = dpdeps / (dpdeps - rho * cs2)
reivec1(1) = kappa / (enthalpy * w)
reivec1(2) = vlowx
reivec1(3) = vlowy
reivec1(4) = vlowz
reivec1(5) = one - reivec1(1)
reivec2(1) = w * vlowy
reivec2(2) = enthalpy * (gxy + two * w * w * vlowx * vlowy)
reivec2(3) = enthalpy * (gyy + two * w * w * vlowy * vlowy)
reivec2(4) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec2(5) = vlowy * w * (two * w * enthalpy - one)
reivec3(1) = w * vlowz
reivec3(2) = enthalpy * (gxz + two * w * w * vlowx * vlowz)
reivec3(3) = enthalpy * (gyz + two * w * w * vlowy * vlowz)
reivec3(4) = enthalpy * (gzz + two * w * w * vlowz * vlowz)
reivec3(5) = vlowz * w * (two * w * enthalpy - one)
reivecp(1) = one
reivecp(2) = enthalpy * w * (vlowx - vxp)
reivecp(3) = enthalpy * w * vlowy
reivecp(4) = enthalpy * w * vlowz
reivecp(5) = enthalpy * w * axp - one
reivecm(1) = one
reivecm(2) = enthalpy * w * (vlowx - vxm)
reivecm(3) = enthalpy * w * vlowy
reivecm(4) = enthalpy * w * vlowz
reivecm(5) = enthalpy * w * axm - one
!!$Calculate associated left eigenvectors if requested
if (ANALYTICAL) then
cxx = gyy * gzz - gyz * gyz
cxy = gxz * gyz - gxy * gzz
cxz = gxy * gyz - gxz * gyy
gam = gxx * cxx + gxy * cxy + gxz * cxz
xsi = cxx - gam * velx * velx
dlt = enthalpy**3 * w * (kappa - one) * (vxm - vxp) * xsi
tmp1 = w / (kappa - one)
leivec1(1) = tmp1 * (enthalpy - w)
leivec1(2) = tmp1 * w * velx
leivec1(3) = tmp1 * w * vely
leivec1(4) = tmp1 * w * velz
leivec1(5) =-tmp1 * w
tmp1 = one / (xsi * enthalpy)
leivec2(1) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec2(2) = (gzz * vlowy - gyz * vlowz) * tmp1 * velx
leivec2(3) = (gzz * (one - velx * vlowx) + gxz * vlowz * velx) * tmp1
leivec2(4) = (gyz * (velx * vlowx - one) - gxz * velx * vlowy) * tmp1
leivec2(5) = (gyz * vlowz - gzz * vlowy) * tmp1
leivec3(1) = (gyz * vlowy - gyy * vlowz) * tmp1
leivec3(2) = (gyy * vlowz - gyz * vlowy) * tmp1 * velx
leivec3(3) = (gyz * (velx * vlowx - one) - gxy * velx * vlowz) * tmp1
leivec3(4) = (gyy * (one - velx * vlowx) + gxy * velx * vlowy) * tmp1
leivec3(5) = (gyz * vlowy - gyy * vlowz) * tmp1
tmp1 = enthalpy * enthalpy / dlt
tmp2 = w * w * xsi
leivecp(1) = - (enthalpy * w * vxm * xsi + (one - kappa) * (vxm * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxm) * tmp1
leivecp(2) = - (cxx * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecp(3) = - (cxy * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecp(4) = - (cxz * (one - kappa * axm) + (two * kappa - one) * vxm * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecp(5) = - ((one - kappa) * (vxm * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxm) * tmp1
leivecm(1) = (enthalpy * w * vxp * xsi + (one - kappa) * (vxp * &
(tmp2 - cxx) - gam * velx) - kappa * tmp2 * vxp) * tmp1
leivecm(2) = (cxx * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velx - cxx * velx)) * tmp1
leivecm(3) = (cxy * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * vely - cxy * velx)) * tmp1
leivecm(4) = (cxz * (one - kappa * axp) + (two * kappa - one) * vxp * &
(tmp2 * velz - cxz * velx)) * tmp1
leivecm(5) = ((one - kappa) * (vxp * (tmp2 - cxx) - gam * velx) - &
kappa * tmp2 * vxp) * tmp1
endif
du(1) = qdiff1
du(2) = qdiff2
du(3) = qdiff3
du(4) = qdiff4
du(5) = qdiff5
if (ANALYTICAL) then
if (FAST) then
sump = 0.0d0
summ = 0.0d0
do i=1,5
sump = sump + (abs(lamp) - abs(lam1)) * leivecp(i) * du(i)
summ = summ + (abs(lamm) - abs(lam1)) * leivecm(i) * du(i)
enddo
vxa = sump + summ
vxb =-(sump * vxp + summ * vxm)
rflux(1) = abs(lam1) * du(1) + vxa
rflux(2) = abs(lam1) * du(2) + enthalpy * w * (vlowx * vxa + vxb)
rflux(3) = abs(lam1) * du(3) + enthalpy * w * (vlowy * vxa)
rflux(4) = abs(lam1) * du(4) + enthalpy * w * (vlowz * vxa)
rflux(5) = abs(lam1) * du(5) + enthalpy * w * (velx * vxb + vxa) - vxa
else
!!$Form Jacobian matrix in characteristic form from right eigenvectors.
!!$Invert to get the characteristic jumps given the conserved variable
!!$jumps
!!$ p(:,1) = reivecm(:)
!!$ p(:,2) = reivec1(:)
!!$ p(:,3) = reivec2(:)
!!$ p(:,4) = reivec3(:)
!!$ p(:,5) = reivecp(:)
!!$
!!$ write(*,*) p
!!$ stop
p(:,1) = reivecm(:)
p(:,2) = reivecp(:)
p(:,3) = reivec2(:)
p(:,4) = reivec3(:)
p(:,5) = reivec1(:)
q(1,:) = leivecm(:)
q(2,:) = leivecp(:)
q(3,:) = leivec2(:)
q(4,:) = leivec3(:)
q(5,:) = leivec1(:)
do i=1,5
dw(i) = 0.0d0
do j=1,5
dw(i) = dw(i) + q(i,j) * du(j)
enddo
enddo
!!$Calculate the Roe flux from the standard formula
do i = 1, 5
rflux(i) = 0.d0
do j = 1, 5
rflux(i) = rflux(i) + p(i,j) * abs(lam(j)) * dw(j)
end do
end do
endif
else
p(:,1) = reivecm(:)
p(:,2) = reivecp(:)
p(:,3) = reivec2(:)
p(:,4) = reivec3(:)
p(:,5) = reivec1(:)
do i=1,5
dw(i) = du(i)
do j=1,5
aa(i,j) = p(i,j)
end do
enddo
do ii=1,5
paug(ii,1) = p(ii,1)
paug(ii,2) = p(ii,2)
paug(ii,3) = p(ii,3)
paug(ii,4) = p(ii,4)
paug(ii,5) = p(ii,5)
enddo
paug(1, 6) = du(1)
paug(2, 6) = du(2)
paug(3, 6) = du(3)
paug(4, 6) = du(4)
paug(5, 6) = du(5)
do ii=1,5
tmp1 = paug(ii,ii)
do jj=ii,6
paug(ii,jj) = paug(ii,jj)/tmp1
enddo
do jj=ii+1,5
tmp1 = - (paug(jj,ii))
do kk=ii,6
paug(jj,kk) = paug(jj,kk) + tmp1*paug(ii,kk)
enddo
enddo
enddo
f_du(5) = paug(5,6)
do ii=4,1,-1
f_du(ii) = paug(ii,6)
do jj=ii+1,5
f_du(ii) = f_du(ii) - paug(ii,jj)*f_du(jj)
enddo
enddo
dw(1) = f_du(1)
dw(2) = f_du(2)
dw(3) = f_du(3)
dw(4) = f_du(4)
dw(5) = f_du(5)
!!$
!!$ dw(1) = f_du(1)
!!$ dw(2) = f_du(5)
!!$ dw(3) = f_du(3)
!!$ dw(4) = f_du(4)
!!$ dw(5) = f_du(2)
!!$Calculate the Roe flux from the standard formula
do i = 1, 5
rflux(i) = 0.d0
do j = 1, 5
rflux(i) = rflux(i) + p(i,j) * abs(lam(j)) * dw(j)
end do
end do
endif
roeflux1 = rflux(1)
roeflux2 = rflux(2)
roeflux3 = rflux(3)
roeflux4 = rflux(4)
roeflux5 = rflux(5)
end subroutine eigenproblem_general
end module GRHydro_Eigenproblem
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