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EQUATIONS: Fix calculation of the fluxes in SRMHD.

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The fluxes of the momenta had the second terms wrongly calculated. The
new calculation uses equations from Mignone & Bodo (2006).

Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
This commit is contained in:
Grzegorz Kowal 2015-04-25 17:13:39 -03:00
parent 8aa56efe21
commit 4c7e526a4b
1 changed files with 32 additions and 26 deletions
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58
src/equations.F90
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@ -4482,7 +4482,12 @@ module equations
!
! References:
!
! [1] van der Holst, B., Keppens, R., Meliani, Z.
! [1] Mignone, A., Bodo, G.,
! "An HLLC Riemann solver for relativistic flows -
! II. Magnetohydrodynamics",
! Monthly Notices of the Royal Astronomical Society,
! 2006, Volume 368, Pages 1040-1054
! [2] van der Holst, B., Keppens, R., Meliani, Z.
! "A multidimentional grid-adaptive relativistic magnetofluid code",
! Computer Physics Communications, 2008, Volume 179, Pages 617-627
!
@ -4509,7 +4514,8 @@ module equations
!
integer :: i, nr
real(kind=8) :: vv, bb, vb, vm, vs
real(kind=8) :: rh, ww, wt, b2, pm, pt, bx, v1, v2
real(kind=8) :: bx, by, bz, b2, pm, pt
real(kind=8) :: rh, v1, v2
real(kind=8) :: ca, cc, c2, gn, rt, zm, zp
real(kind=8) :: fa, fb, fc, fd, fe, ff, fg
@ -4536,38 +4542,29 @@ module equations
bb = sum(q(ibx:ibz,i) * q(ibx:ibz,i))
vb = sum(q(ivx:ivz,i) * q(ibx:ibz,i))
! calculate the Lorentz factor
! calculate (1 - |V|²)
!
vm = 1.0d+00 - vv
vs = sqrt(vm)
! calculate specific and total enthalpies
! calculate magnetic field components of the magnetic four-vector divided by
! the Lorentz factor (eq. 3 in [1])
!
rh = q(idn,i) + q(ipr,i) / gammaxi
ww = rh / vm
wt = ww + bb
bx = q(ibx,i) * vm + vb * q(ivx,i)
by = q(iby,i) * vm + vb * q(ivy,i)
bz = q(ibz,i) * vm + vb * q(ivz,i)
! calculate magnetic and total pressures
! calculate magnetic and total pressures (eq. 6 in [1])
!
b2 = bb * vm + vb * vb
pm = 0.5d+00 * b2
pt = q(ipr,i) + pm
! calculate additional coefficients
!
rt = rh + b2
! calculate temporary variables
!
bx = q(ibx,i) * vs + vb * q(ivx,i) / vs
fc = bx * vs
! calculate the relativistic hydrodynamic fluxes (eq. 2 in [1])
! calculate the relativistic hydrodynamic fluxes (eq. 13 in [1])
!
f(idn,i) = u(idn,i) * q(ivx,i)
f(imx,i) = u(imx,i) * q(ivx,i) - fc * q(ibx,i) + pt
f(imy,i) = u(imy,i) * q(ivx,i) - fc * q(iby,i)
f(imz,i) = u(imz,i) * q(ivx,i) - fc * q(ibz,i)
f(imx,i) = u(imx,i) * q(ivx,i) - q(ibx,i) * bx + pt
f(imy,i) = u(imy,i) * q(ivx,i) - q(ibx,i) * by
f(imz,i) = u(imz,i) * q(ivx,i) - q(ibx,i) * bz
f(ibx,i) = q(ibp,i)
f(ibp,i) = cmax2 * q(ibx,i)
f(iby,i) = q(ivx,i) * q(iby,i) - q(ibx,i) * q(ivy,i)
@ -4580,9 +4577,14 @@ module equations
!
if (vv > 0.0d+00) then
! check if the normal component of magnetic field Bx is larger than zero
! calculate additional coefficients
!
if (q(ibx,i) /= 0.0d+00) then ! Bx ≠ 0
rh = q(idn,i) + q(ipr,i) / gammaxi
vs = sqrt(vm)
! check if the normal component of magnetic field Bₓ is larger than zero
!
if (q(ibx,i) /= 0.0d+00) then ! Bₓ ≠ 0
! prepare parameters for this case
!
@ -4614,9 +4616,9 @@ module equations
!
x(1:nr) = sign(1.0d+00, q(ivx,i)) * (abs(v1) + x(1:nr) * vs)
else ! Bx ≠ 0
else ! Bₓ ≠ 0
! special case when Bx = 0, then the quartic equation reduces to quadratic one
! special case when Bₓ = 0, then the quartic equation reduces to quadratic one
!
! prepare parameters for this case
!
@ -4643,6 +4645,10 @@ module equations
!
! prepare parameters for this case
!
rh = q(idn,i) + q(ipr,i) / gammaxi
vs = sqrt(vm)
bx = q(ibx,i) * vs + vb * q(ivx,i) / vs
rt = rh + b2
c2 = gamma * q(ipr,i) / rh
ca = bx * bx