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riemann.f90
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module riemann_module
implicit none
contains
subroutine hllc(Uleft, Uright, Dir, Flux)
use sim_data, only: gamma
use eos_module, only: eos_gete
use misc_module, only: to_upper
implicit none
real(8), dimension(5), intent(in) :: Uleft, Uright
character(len=1), intent(in) :: Dir
real(8), dimension(5), intent(out) :: Flux
real(8), dimension(5) :: FL, FR, UL, UR, FstarL, FstarR, UstarL, UstarR
real(8) :: dL, udL, vdL, wdL, pL
real(8) :: dR, udR, vdR, wdR, pR
real(8) :: sdR, sdL, ufL, ufR, vfL, vfR, wfL, wfR
real(8) :: eL, eR, HL, HR, cL, cR
real(8) :: ubar, vbar, wbar, Hbar, cbar
real(8) :: qL, qR, qbar, SL, SR, SM
real(8) :: dstarL, dstarR, pstar
real(8) :: dustarL, dustarR, dvstarL, dvstarR
real(8) :: dwstarL, dwstarR, estarL, estarR
real(8), dimension(3) :: n
dL = Uleft(1)
ufL = Uleft(2)
vfL = Uleft(3)
wfL = Uleft(4)
pL = Uleft(5)
dR = Uright(1)
ufR = Uright(2)
vfR = Uright(3)
wfR = Uright(4)
pR = Uright(5)
select case (to_upper(Dir))
case ('X')
n = (/1.00, 0.00, 0.00/)
case ('Y')
n = (/0.00, 1.00, 0.00/)
case ('Z')
n = (/0.00, 0.00, 1.00/)
case default
print *, "Wrong!! Direction should be X, Y, Z"
stop
end select
sdR = sqrt(dR)
sdL = sqrt(dL)
udL = ufL * dL
udR = ufR * dR
vdL = vfL * dL
vdR = vfR * dR
wdL = wfL * dL
wdR = wfR * dR
eL = eos_gete((/dL, ufL, vfL, wfL, pL/))
eR = eos_gete((/dR, ufR, vfR, wfR, pR/))
HL = (eL + pL) / dL
HR = (eR + pR) / dR
cL = sqrt(gamma * pL / dL)
cR = sqrt(gamma * pR / dR)
ubar = (ufL * sdL + ufR * sdR) / (sdL + sdR)
vbar = (vfL * sdL + vfR * sdR) / (sdL + sdR)
wbar = (wfL * sdL + wfR * sdR) / (sdL + sdR)
Hbar = (HL * sdL + HR * sdR) / (sdL + sdR)
cbar = sqrt((gamma - 1.00) * (Hbar - 0.50 * (ubar**2 + vbar**2 + wbar**2)))
qL = sum((/ufL, vfL, wfL/) * n)
qR = sum((/ufR, vfR, wfR/) * n)
qbar = sum((/ubar, vbar, wbar/) * n)
SL = min(qL - cL, qbar - cbar)
SR = max(qR + cR, qbar + cbar)
SM = ((dR * qR * (SR - qR) - dL * qL * (SL - qL)) + pL - pR) / (dR * (SR - qR) - dL * (SL - qL))
FL = (/dL * qL, &
dL * ufL * qL + pL * n(1), &
dL * vfL * qL + pL * n(2), &
dL * wfL * qL + pL * n(3), &
qL * (eL + pL)/)
FR = (/dR * qR, &
dR * ufR * qR + pR * n(1), &
dR * vfR * qR + pR * n(2), &
dR * wfR * qR + pR * n(3), &
qR * (eR + pR)/)
dstarL = dL * (SL - qL) / (SL - SM)
dstarR = dR * (SR - qR) / (SR - SM)
pstar = pL + dL * (qL - SL) * (qL - SM)
dustarL = (dL * ufL * (SL - qL) + (pstar - pL) * n(1)) / (SL - SM)
dustarR = (dR * ufR * (SR - qR) + (pstar - pR) * n(1)) / (SR - SM)
dvstarL = (dL * vfL * (SL - qL) + (pstar - pL) * n(2)) / (SL - SM)
dvstarR = (dR * vfR * (SR - qR) + (pstar - pR) * n(2)) / (SR - SM)
dwstarL = (dL * wfL * (SL - qL) + (pstar - pL) * n(3)) / (SL - SM)
dwstarR = (dR * wfR * (SR - qR) + (pstar - pR) * n(3)) / (SR - SM)
estarL = ((eL * (SL - qL) - pL * qL) + pstar * SM) / (SL - SM)
estarR = ((eR * (SR - qR) - pR * qR) + pstar * SM) / (SR - SM)
UstarL = (/dstarL, dustarL, dvstarL, dwstarL, estarL/)
UstarR = (/dstarR, dustarR, dvstarR, dwstarR, estarR/)
UL = (/dL, dL * ufL, dL * vfL, dL * wfL, eL/)
UR = (/dR, dR * ufR, dR * vfR, dR * wfR, eR/)
FstarL = FL + SL * (UstarL - UL)
FstarR = FR + SR * (UstarR - UR)
if (0.000 < SL) then
Flux = FL
else if (SL <= 0.000 .and. 0.000 < SM) then
Flux = FstarL
else if (SM <= 0.000 .and. 0.000 <= SR) then
Flux = FstarR
else
Flux = FR
end if
return
end subroutine hllc
subroutine hlle(Uleft, Uright, Dir, Flux)
use sim_data, only: gamma
use eos_module, only: eos_gete
use misc_module, only: to_upper
implicit none
real(8), dimension(5), intent(in) :: Uleft, Uright
character(len=1), intent(in) :: Dir
real(8), dimension(5), intent(out) :: Flux
real(8), dimension(5) :: FL, FR, UL, UR, Fstar
real(8) :: dL, udL, vdL, wdL, pL
real(8) :: dR, udR, vdR, wdR, pR
real(8) :: sdR, sdL, ufL, ufR, vfL, vfR, wfL, wfR
real(8) :: eL, eR, HL, HR, cL, cR
real(8) :: ubar, vbar, wbar, Hbar, cbar
real(8) :: qL, qR, qbar, SL, SR
real(8), dimension(3) :: n
dL = Uleft(1)
ufL = Uleft(2)
vfL = Uleft(3)
wfL = Uleft(4)
pL = Uleft(5)
dR = Uright(1)
ufR = Uright(2)
vfR = Uright(3)
wfR = Uright(4)
pR = Uright(5)
select case (to_upper(Dir))
case ('X')
n = (/1.00, 0.00, 0.00/)
case ('Y')
n = (/0.00, 1.00, 0.00/)
case ('Z')
n = (/0.00, 0.00, 1.00/)
case default
print *, "Wrong!! Direction should be X, Y, Z"
stop
end select
sdR = sqrt(dR)
sdL = sqrt(dL)
udL = ufL * dL
udR = ufR * dR
vdL = vfL * dL
vdR = vfR * dR
wdL = wfL * dL
wdR = wfR * dR
eL = eos_gete((/dL, ufL, vfL, wfL, pL/))
eR = eos_gete((/dR, ufR, vfR, wfR, pR/))
HL = (eL + pL) / dL
HR = (eR + pR) / dR
cL = sqrt(gamma * pL / dL)
cR = sqrt(gamma * pR / dR)
ubar = (ufL * sdL + ufR * sdR) / (sdL + sdR)
vbar = (vfL * sdL + vfR * sdR) / (sdL + sdR)
wbar = (wfL * sdL + wfR * sdR) / (sdL + sdR)
Hbar = (HL * sdL + HR * sdR) / (sdL + sdR)
cbar = sqrt((gamma - 1.00) * (Hbar - 0.50 * (ubar**2 + vbar**2 + wbar**2)))
qL = sum((/ufL, vfL, wfL/) * n)
qR = sum((/ufR, vfR, wfR/) * n)
qbar = sum((/ubar, vbar, wbar/) * n)
SL = min(min(qL - cL, qbar - cbar), 0.0)
SR = max(max(qR + cR, qbar + cbar), 0.0)
FL = (/dL * qL, &
dL * ufL * qL + pL * n(1), &
dL * vfL * qL + pL * n(2), &
dL * wfL * qL + pL * n(3), &
qL * (eL + pL)/)
FR = (/dR * qR, &
dR * ufR * qR + pR * n(1), &
dR * vfR * qR + pR * n(2), &
dR * wfR * qR + pR * n(3), &
qR * (eR + pR)/)
UL = (/dL, dL * ufL, dL * vfL, dL * wfL, eL/)
UR = (/dR, dR * ufR, dR * vfR, dR * wfR, eR/)
Fstar = (SR * FL - SL * FR + (SL * SR * (UR - UL))) / (SR - SL)
if (0.000 < SL) then
Flux = FL
else if (SL <= 0.000 .and. 0.000 <= SR) then
Flux = Fstar
else
Flux = FR
end if
return
end subroutine hlle
end module riemann_module