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/*@@
@file GRHydro_AdvectedLoopM.F90
@date Aug 15, 2011
@author Scott Noble, Joshua Faber, Bruno Mundim
@desc
Advected loop test as implemented by Beckwith and Stone Astrophys.J.Suppl.
193 (2011) 6, arXiv:1101.3573.
Other relevant references: Devore JCP 92, 142 (1991),
Toth and Odstrcil JCP 128,82 (1996),
Gardiner and Stone JCP 227, 4123 (2008);
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "GRHydro_Macros.h"
#define velx(i,j,k) vel(i,j,k,1)
#define vely(i,j,k) vel(i,j,k,2)
#define velz(i,j,k) vel(i,j,k,3)
#define sx(i,j,k) scon(i,j,k,1)
#define sy(i,j,k) scon(i,j,k,2)
#define sz(i,j,k) scon(i,j,k,3)
#define Bvecx(i,j,k) Bvec(i,j,k,1)
#define Bvecy(i,j,k) Bvec(i,j,k,2)
#define Bvecz(i,j,k) Bvec(i,j,k,3)
#define Bconsx(i,j,k) Bcons(i,j,k,1)
#define Bconsy(i,j,k) Bcons(i,j,k,2)
#define Bconsz(i,j,k) Bcons(i,j,k,3)
/*@@
@routine GRHydro_AdvectedLoopM
@date Aug 11, 2011
@author Scott Noble, Joshua Faber, Bruno Mundim
@desc
Initial data for advected loop test
@enddesc
@calls
@calledby
@history
Using GRHydro_ShockTubeM.F90 as a template.
@endhistory
@@*/
subroutine GRHydro_AdvectedLoopM(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
CCTK_INT :: i, j, k, nx, ny, nz
CCTK_REAL :: det,radius,vxval,vyval,vzval,gam
CCTK_REAL :: radius_iph, radius_imh
CCTK_REAL :: radius_jph, radius_jmh
CCTK_REAL :: radius_kph, radius_kmh
CCTK_REAL :: rhoval,pressval
CCTK_REAL :: r_loop,A_loop,pi
CCTK_REAL :: dx,dy,dz
CCTK_REAL :: range_x,range_y,range_z,range_d
CCTK_REAL :: cos_theta, sin_theta, tan_theta
CCTK_REAL :: Bvecx_d, Bvecy_d, Bvecz_d
CCTK_REAL :: x_d, y_d, z_d,diaglength
CCTK_REAL :: dx_d, dy_d, dz_d, dx_x, dz_x
!!$Adiabatic index for test:
gam = (5.0d0/3.0d0)
!!$radius of the loop:
r_loop = 0.3d0
!!$ stregth of the A-field
A_loop=1.0d-3
!!$pressure and density:
rhoval = 1.0d0
pressval = 3.0d0
if (CCTK_EQUALS(advectedloop_type,"2D")) then
!!$ Vx, Vy and Vz values:
if (CCTK_EQUALS(advectedloop_case,"V^z/=0")) then
!!$vxval=0.2d0/sqrt(6.0d0)
!!$ This new choice yields a crossing time of exactly t=24
!!$ assuming -1<x<1; -0.5<y<0.5
vxval=1.d0/12.d0
vyval=0.5d0*vxval
vzval=vyval
else if (CCTK_EQUALS(advectedloop_case,"V^z=0")) then
!!$ vxval=0.2d0/sqrt(6.0d0)
vxval=1.d0/12.d0
vyval=0.5d0*vxval
vzval=0.0d0
else
call CCTK_WARN(0,"V^z component case not recognized!")
end if
else if (CCTK_EQUALS(advectedloop_type,"3D")) then
vxval=0.2d0*sqrt(2.0d0)
vyval=0.2d0
if (CCTK_EQUALS(advectedloop_case,"V^z/=0")) then
!!$vxval=0.2d0/sqrt(6.0d0)
!!$ This new choice yields a crossing time of exactly t=5
!!$ assuming -1<x<1; -0.5<y<0.5
vzval=0.1
else if (CCTK_EQUALS(advectedloop_case,"V^z=0")) then
vzval=0.0d0
else
call CCTK_WARN(0,"V^z component case not recognized!")
end if
endif
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
dx = CCTK_DELTA_SPACE(1)
dy = CCTK_DELTA_SPACE(2)
dz = CCTK_DELTA_SPACE(3)
!!$ Note that the 3D test wasn't deviced to be used with AMR!
range_x = (cctk_gsh(1)-2*cctk_nghostzones(1))*dx
range_y = (cctk_gsh(2)-2*cctk_nghostzones(2))*dy
range_z = (cctk_gsh(3)-2*cctk_nghostzones(3))*dz
range_d = sqrt(range_z**2+range_x**2)
diaglength = range_x*range_z/range_d
!!$ For 3-d case, the grid is going to be assumed to be a cube
cos_theta = range_z/range_d
sin_theta = range_x/range_d
tan_theta = sin_theta/cos_theta
do i=1,nx
do j=1,ny
do k=1,nz
rho(i,j,k)=rhoval
press(i,j,k)=pressval
eps(i,j,k)=press(i,j,k)/(gam-1.0d0)/rho(i,j,k)
if (CCTK_EQUALS(advectedloop_type,"2D")) then
velx(i,j,k)=vxval
vely(i,j,k)=vyval
velz(i,j,k)=vzval
Bvecz(i,j,k)=0.0d0
radius = sqrt(x(i,j,k)**2+y(i,j,k)**2)
if (CCTK_EQUALS(advectedloop_delA,"Exact")) then
if(radius.le.r_loop) then
Bvecx(i,j,k)=-1.0d0*A_loop*y(i,j,k)/radius
Bvecy(i,j,k)=A_loop*x(i,j,k)/radius
else
Bvecx(i,j,k)=0.0d0
Bvecy(i,j,k)=0.0d0
endif
else if (CCTK_EQUALS(advectedloop_delA,"Numeric")) then
radius_iph = max(sqrt((x(i,j,k)+0.5d0*dx)**2+y(i,j,k)**2)-r_loop,0.d0)
radius_imh = max(sqrt((x(i,j,k)-0.5d0*dx)**2+y(i,j,k)**2)-r_loop,0.d0)
radius_jph = max(sqrt(x(i,j,k)**2+(y(i,j,k)+0.5d0*dy)**2)-r_loop,0.d0)
radius_jmh = max(sqrt(x(i,j,k)**2+(y(i,j,k)-0.5d0*dy)**2)-r_loop,0.d0)
!! if(radius.le.r_loop) then
Bvecx(i,j,k)=-1.0d0*A_loop*(radius_jph-radius_jmh)/dy
Bvecy(i,j,k)=A_loop*(radius_iph-radius_imh)/dx
!! else
!! Bvecx(i,j,k)=0.0d0
!! Bvecy(i,j,k)=0.0d0
!! endif
else
call CCTK_WARN(0,"A^b differentiation not recognized!")
end if
else if (CCTK_EQUALS(advectedloop_type,"3D")) then
!!$ tangential velocity should be parallel to (1,1,1) plus a normal component (-1,0,1)
velx(i,j,k)=cos_theta*vxval-sin_theta*vzval
vely(i,j,k)=vyval
velz(i,j,k)=cos_theta*vzval+sin_theta*vxval
Bvecz_d=0.0d0
!!$ x_d = (x+z)/sqrt(2) => x_d=0 is equivalent to x+z=0
x_d = cos_theta*x(i,j,k)+sin_theta*z(i,j,k)
y_d = y(i,j,k)
z_d = cos_theta*z(i,j,k)-sin_theta*x(i,j,k)
!!$ need to make x_d periodic!
if(x_d.gt.1.5*diaglength) then
x_d=x_d-2.0*diaglength
else if (x_d.gt.0.5*diaglength .and. x_d.lt.1.5*diaglength) then
x_d=x_d-diaglength
else if(x_d.lt.-1.5*diaglength) then
x_d=x_d+2.0*diaglength
else if (x_d.lt.(-0.5*diaglength) .and. x_d.gt.(-1.5*diaglength)) then
x_d=x_d+diaglength
endif
radius = sqrt(x_d**2+y_d**2)
if (CCTK_EQUALS(advectedloop_delA,"Exact")) then
if(radius.le.r_loop) then
Bvecx_d=-1.0d0*A_loop*y_d/radius
Bvecy_d=A_loop*x_d/radius
else
Bvecx_d=0.0d0
Bvecy_d=0.0d0
endif
Bvecx(i,j,k)=cos_theta*Bvecx_d-sin_theta*Bvecz_d
Bvecy(i,j,k)=Bvecy_d
Bvecz(i,j,k)=cos_theta*Bvecz_d+sin_theta*Bvecx_d
else if (CCTK_EQUALS(advectedloop_delA,"Numeric")) then
!! dx_d = cos_theta*dx+sin_theta*dz
!! dy_d = dy
!! dz_d = cos_theta*dz-sin_theta*dx
!! dx_d is the change in the rotated coords induced by a step in a direction over the Cartesian grid
dx_x = cos_theta*dx
dz_x = sin_theta*dz
!! These are used for exact differencing
radius_iph = max(sqrt((x_d+0.5d0*dx_x)**2+y_d**2)-r_loop,0.d0)
radius_imh = max(sqrt((x_d-0.5d0*dx_x)**2+y_d**2)-r_loop,0.d0)
radius_jph = max(sqrt(x_d**2+(y_d+0.5d0*dy)**2)-r_loop,0.d0)
radius_jmh = max(sqrt(x_d**2+(y_d-0.5d0*dy)**2)-r_loop,0.d0)
radius_kph = max(sqrt((x_d+0.5d0*dz_x)**2+y_d**2)-r_loop,0.d0)
radius_kmh = max(sqrt((x_d-0.5d0*dz_x)**2+y_d**2)-r_loop,0.d0)
!! see notes
!! if(radius.le.r_loop) then
Bvecx(i,j,k)=-1.0d0*A_loop*cos_theta*(radius_jph-radius_jmh)/dy
Bvecy(i,j,k)=A_loop*(sin_theta*(radius_kph-radius_kmh)/dz + &
cos_theta*(radius_iph-radius_imh)/dx)
Bvecz(i,j,k)=-1.0d0*A_loop*sin_theta*(radius_jph-radius_jmh)/dy
!! else
!! Bvecx(i,j,k)=0.0d0
!! Bvecy(i,j,k)=0.0d0
!! Bvecz(i,j,k)=0.0d0
!! endif
else
call CCTK_WARN(0,"A^b differentiation not recognized!")
end if
else
call CCTK_WARN(0,"Advected loop type not recognized!")
end if
det=SPATIAL_DETERMINANT(gxx(i,j,k),gxy(i,j,k),gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k))
if (CCTK_EQUALS(GRHydro_eos_type,"Polytype")) then
call Prim2ConPolyM(GRHydro_eos_handle,gxx(i,j,k),gxy(i,j,k),&
gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k),&
det, dens(i,j,k),sx(i,j,k),sy(i,j,k),sz(i,j,k),&
tau(i,j,k),Bconsx(i,j,k),Bconsy(i,j,k),Bconsz(i,j,k),rho(i,j,k),&
velx(i,j,k),vely(i,j,k),velz(i,j,k),&
eps(i,j,k),press(i,j,k),Bvecx(i,j,k),Bvecy(i,j,k),Bvecz(i,j,k),&
w_lorentz(i,j,k))
else
call Prim2ConGenM(GRHydro_eos_handle,gxx(i,j,k),gxy(i,j,k),&
gxz(i,j,k),gyy(i,j,k),gyz(i,j,k),gzz(i,j,k),&
det, dens(i,j,k),sx(i,j,k),sy(i,j,k),sz(i,j,k),&
tau(i,j,k),Bconsx(i,j,k),Bconsy(i,j,k),Bconsz(i,j,k),rho(i,j,k),&
velx(i,j,k),vely(i,j,k),velz(i,j,k),&
eps(i,j,k),press(i,j,k),Bvecx(i,j,k),Bvecy(i,j,k),Bvecz(i,j,k),&
w_lorentz(i,j,k))
end if
enddo
enddo
enddo
densrhs = 0.d0
srhs = 0.d0
taurhs = 0.d0
Bconsrhs = 0.d0
return
end subroutine GRHydro_AdvectedLoopM
|
