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m_riemann_solvers.fpp
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m_riemann_solvers.fpp
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!>
!! @file m_riemann_solvers.f90
!! @brief Contains module m_riemann_solvers
!> @brief This module features a database of approximate and exact Riemann
!! problem solvers for the Navier-Stokes system of equations, which
!! is supplemented by appropriate advection equations that are used
!! to capture the material interfaces. The closure of the system is
!! achieved by the stiffened gas equation of state and any required
!! mixture relations. Surface tension effects are accounted for and
!! are modeled by means of a volume force acting across the diffuse
!! material interface region. The implementation details of viscous
!! and capillary effects, into the Riemann solvers, may be found in
!! Perigaud and Saurel (2005). Note that both effects are available
!! only in the volume fraction model. At this time, the approximate
!! and exact Riemann solvers that are listed below are available:
!! 1) Harten-Lax-van Leer (HLL)
!! 2) Harten-Lax-van Leer-Contact (HLLC)
!! 3) Exact
#:include 'inline_riemann.fpp'
#:include 'inline_conversions.fpp'
module m_riemann_solvers
! Dependencies =============================================================
use m_derived_types !< Definitions of the derived types
use m_global_parameters !< Definitions of the global parameters
use m_mpi_proxy !< Message passing interface (MPI) module proxy
use m_variables_conversion !< State variables type conversion procedures
use m_bubbles !< To get the bubble wall pressure function
! ==========================================================================
implicit none
private; public :: s_initialize_riemann_solvers_module, &
s_riemann_solver, &
s_hll_riemann_solver, &
s_hllc_riemann_solver, &
s_finalize_riemann_solvers_module
abstract interface ! =======================================================
!> Abstract interface to the subroutines that are utilized to compute the
!! Riemann problem solution. For additional information please reference:
!! 1) s_hll_riemann_solver
!! 2) s_hllc_riemann_solver
!! 3) s_exact_riemann_solver
!! @param qL_prim_vf The left WENO-reconstructed cell-boundary values of the
!! cell-average primitive variables
!! @param qR_prim_vf The right WENO-reconstructed cell-boundary values of the
!! cell-average primitive variables
!! @param dqL_prim_dx_vf The left WENO-reconstructed cell-boundary values of the
!! first-order x-dir spatial derivatives
!! @param dqL_prim_dy_vf The left WENO-reconstructed cell-boundary values of the
!! first-order y-dir spatial derivatives
!! @param dqL_prim_dz_vf The left WENO-reconstructed cell-boundary values of the
!! first-order z-dir spatial derivatives
!! @param dqR_prim_dx_vf The right WENO-reconstructed cell-boundary values of the
!! first-order x-dir spatial derivatives
!! @param dqR_prim_dy_vf The right WENO-reconstructed cell-boundary values of the
!! first-order y-dir spatial derivatives
!! @param dqR_prim_dz_vf The right WENO-reconstructed cell-boundary values of the
!! first-order z-dir spatial derivatives
!! @param gm_alphaL_vf Left averaged gradient magnitude
!! @param gm_alphaR_vf Right averaged gradient magnitude
!! @param flux_vf Intra-cell fluxes
!! @param flux_src_vf Intra-cell fluxes sources
!! @param flux_gsrc_vf Intra-cell geometric fluxes sources
!! @param norm_dir Dir. splitting direction
!! @param ix Index bounds in the x-dir
!! @param iy Index bounds in the y-dir
!! @param iz Index bounds in the z-dir
!! @param q_prim_vf Cell-averaged primitive variables
subroutine s_abstract_riemann_solver(qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, dqL_prim_dx_vf, &
dqL_prim_dy_vf, &
dqL_prim_dz_vf, &
qL_prim_vf, &
qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf, dqR_prim_dx_vf, &
dqR_prim_dy_vf, &
dqR_prim_dz_vf, &
qR_prim_vf, &
q_prim_vf, &
flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
import :: scalar_field, int_bounds_info, sys_size, startx, starty, startz
real(kind(0d0)), dimension(startx:, starty:, startz:, 1:), intent(INOUT) :: qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf
type(scalar_field), dimension(sys_size), intent(IN) :: q_prim_vf
type(scalar_field), allocatable, dimension(:), intent(INOUT) :: qL_prim_vf, qR_prim_vf
type(scalar_field), &
allocatable, dimension(:), &
intent(INOUT) :: dqL_prim_dx_vf, dqR_prim_dx_vf, &
dqL_prim_dy_vf, dqR_prim_dy_vf, &
dqL_prim_dz_vf, dqR_prim_dz_vf
type(scalar_field), &
dimension(sys_size), &
intent(INOUT) :: flux_vf, flux_src_vf, flux_gsrc_vf
integer, intent(IN) :: norm_dir
type(int_bounds_info), intent(IN) :: ix, iy, iz
end subroutine s_abstract_riemann_solver
!> The abstract interface to the subroutines that are utilized to compute
!! the viscous source fluxes for either Cartesian or cylindrical geometries.
!! For more information please refer to:
!! 1) s_compute_cartesian_viscous_source_flux
!! 2) s_compute_cylindrical_viscous_source_flux
subroutine s_compute_abstract_viscous_source_flux(velL_vf, & ! -------------
dvelL_dx_vf, &
dvelL_dy_vf, &
dvelL_dz_vf, &
velR_vf, &
dvelR_dx_vf, &
dvelR_dy_vf, &
dvelR_dz_vf, &
flux_src_vf, &
norm_dir, &
ix, iy, iz)
import :: scalar_field, int_bounds_info, num_dims, sys_size
type(scalar_field), &
dimension(num_dims), &
intent(IN) :: velL_vf, velR_vf, &
dvelL_dx_vf, dvelR_dx_vf, &
dvelL_dy_vf, dvelR_dy_vf, &
dvelL_dz_vf, dvelR_dz_vf
type(scalar_field), &
dimension(sys_size), &
intent(INOUT) :: flux_src_vf
integer, intent(IN) :: norm_dir
type(int_bounds_info), intent(IN) :: ix, iy, iz
end subroutine s_compute_abstract_viscous_source_flux
end interface ! ============================================================
!> The cell-boundary values of the fluxes (src - source) that are computed
!! through the chosen Riemann problem solver, and the direct evaluation of
!! source terms, by using the left and right states given in qK_prim_rs_vf,
!! dqK_prim_ds_vf where ds = dx, dy or dz.
!> @{
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_rsx_vf, flux_src_rsx_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_rsy_vf, flux_src_rsy_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_rsz_vf, flux_src_rsz_vf
!> @}
!$acc declare create( flux_rsx_vf, flux_src_rsx_vf, flux_rsy_vf, &
!$acc flux_src_rsy_vf, flux_rsz_vf, flux_src_rsz_vf )
!> The cell-boundary values of the geometrical source flux that are computed
!! through the chosen Riemann problem solver by using the left and right
!! states given in qK_prim_rs_vf. Currently 2D axisymmetric for inviscid only.
!> @{
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_gsrc_rsx_vf !<
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_gsrc_rsy_vf !<
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: flux_gsrc_rsz_vf !<
!> @}
!$acc declare create( flux_gsrc_rsx_vf, flux_gsrc_rsy_vf, flux_gsrc_rsz_vf )
! The cell-boundary values of the velocity. vel_src_rs_vf is determined as
! part of Riemann problem solution and is used to evaluate the source flux.
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: vel_src_rsx_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: vel_src_rsy_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: vel_src_rsz_vf
!$acc declare create(vel_src_rsx_vf, vel_src_rsy_vf, vel_src_rsz_vf)
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: mom_sp_rsx_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: mom_sp_rsy_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: mom_sp_rsz_vf
!$acc declare create(mom_sp_rsx_vf, mom_sp_rsy_vf, mom_sp_rsz_vf)
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: Re_avg_rsx_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: Re_avg_rsy_vf
real(kind(0d0)), allocatable, dimension(:, :, :, :) :: Re_avg_rsz_vf
!$acc declare create(Re_avg_rsx_vf, Re_avg_rsy_vf, Re_avg_rsz_vf)
procedure(s_abstract_riemann_solver), &
pointer :: s_riemann_solver => null() !<
!! Pointer to the procedure that is utilized to calculate either the HLL,
!! HLLC or exact intercell fluxes, based on the choice of Riemann solver
procedure(s_compute_abstract_viscous_source_flux), &
pointer :: s_compute_viscous_source_flux => null() !<
!! Pointer to the subroutine that is utilized to compute the viscous source
!! flux for either Cartesian or cylindrical geometries.
!> @name Indical bounds in the s1-, s2- and s3-directions
!> @{
type(int_bounds_info) :: is1, is2, is3
type(int_bounds_info) :: isx, isy, isz
!> @}
!$acc declare create(is1, is2, is3, isx, isy, isz)
real(kind(0d0)), allocatable, dimension(:) :: Gs
!$acc declare create(Gs)
real(kind(0d0)), allocatable, dimension(:, :) :: Res
!$acc declare create(Res)
contains
subroutine s_hll_riemann_solver(qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, dqL_prim_dx_vf, & ! -------
dqL_prim_dy_vf, &
dqL_prim_dz_vf, &
qL_prim_vf, &
qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf, dqR_prim_dx_vf, &
dqR_prim_dy_vf, &
dqR_prim_dz_vf, &
qR_prim_vf, &
q_prim_vf, &
flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
real(kind(0d0)), dimension(startx:, starty:, startz:, 1:), intent(INOUT) :: qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf
type(scalar_field), dimension(sys_size), intent(IN) :: q_prim_vf
type(scalar_field), allocatable, dimension(:), intent(INOUT) :: qL_prim_vf, qR_prim_vf
type(scalar_field), &
allocatable, dimension(:), &
intent(INOUT) :: dqL_prim_dx_vf, dqR_prim_dx_vf, &
dqL_prim_dy_vf, dqR_prim_dy_vf, &
dqL_prim_dz_vf, dqR_prim_dz_vf
! Intercell fluxes
type(scalar_field), &
dimension(sys_size), &
intent(INOUT) :: flux_vf, flux_src_vf, flux_gsrc_vf
integer, intent(IN) :: norm_dir
type(int_bounds_info), intent(IN) :: ix, iy, iz
real(kind(0d0)), dimension(num_fluids) :: alpha_rho_L, alpha_rho_R
real(kind(0d0)) :: rho_L, rho_R
real(kind(0d0)), dimension(num_dims) :: vel_L, vel_R
real(kind(0d0)) :: pres_L, pres_R
real(kind(0d0)) :: E_L, E_R
real(kind(0d0)) :: H_L, H_R
real(kind(0d0)), dimension(num_fluids) :: alpha_L, alpha_R
real(kind(0d0)) :: Y_L, Y_R
real(kind(0d0)) :: gamma_L, gamma_R
real(kind(0d0)) :: pi_inf_L, pi_inf_R
real(kind(0d0)) :: c_L, c_R
real(kind(0d0)), dimension(6) :: tau_e_L, tau_e_R
real(kind(0d0)) :: G_L, G_R
real(kind(0d0)), dimension(2) :: Re_L, Re_R
real(kind(0d0)) :: rho_avg
real(kind(0d0)), dimension(num_dims) :: vel_avg
real(kind(0d0)) :: H_avg
real(kind(0d0)) :: gamma_avg
real(kind(0d0)) :: c_avg
real(kind(0d0)) :: s_L, s_R, s_M, s_P, s_S
real(kind(0d0)) :: xi_L, xi_R !< Left and right wave speeds functions
real(kind(0d0)) :: xi_M, xi_P
real(kind(0d0)) :: nbub_L, nbub_R
real(kind(0d0)) :: ptilde_L, ptilde_R
real(kind(0d0)) :: vel_L_rms, vel_R_rms, vel_avg_rms
real(kind(0d0)) :: blkmod1, blkmod2
real(kind(0d0)) :: rho_Star, E_Star, p_Star, p_K_Star
real(kind(0d0)) :: Ms_L, Ms_R, pres_SL, pres_SR
real(kind(0d0)) :: alpha_L_sum, alpha_R_sum
integer :: i, j, k, l, q !< Generic loop iterators
! Populating the buffers of the left and right Riemann problem
! states variables, based on the choice of boundary conditions
call s_populate_riemann_states_variables_buffers( &
qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, dqL_prim_dx_vf, &
dqL_prim_dy_vf, &
dqL_prim_dz_vf, &
qL_prim_vf, &
qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf, dqR_prim_dx_vf, &
dqR_prim_dy_vf, &
dqR_prim_dz_vf, &
qR_prim_vf, &
norm_dir, ix, iy, iz)
! Reshaping inputted data based on dimensional splitting direction
call s_initialize_riemann_solver( &
q_prim_vf, &
flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
#:for NORM_DIR, XYZ in [(1, 'x'), (2, 'y'), (3, 'z')]
if (norm_dir == ${NORM_DIR}$) then
!$acc parallel loop collapse(3) gang vector default(present) private(alpha_rho_L, alpha_rho_R, vel_L, vel_R, alpha_L, alpha_R, vel_avg, tau_e_L, tau_e_R, G_L, G_R, Re_L, Re_R, &
!$acc rho_avg, h_avg, gamma_avg, s_L, s_R, s_S)
do l = is3%beg, is3%end
do k = is2%beg, is2%end
do j = is1%beg, is1%end
!$acc loop seq
do i = 1, contxe
alpha_rho_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, i)
alpha_rho_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, i)
end do
!$acc loop seq
do i = 1, num_dims
vel_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, contxe + i)
vel_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, contxe + i)
end do
vel_L_rms = 0d0; vel_R_rms = 0d0
!$acc loop seq
do i = 1, num_dims
vel_L_rms = vel_L_rms + vel_L(i)**2d0
vel_R_rms = vel_R_rms + vel_R(i)**2d0
end do
!$acc loop seq
do i = 1, num_fluids
alpha_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)
alpha_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)
end do
pres_L = qL_prim_rs${XYZ}$_vf(j, k, l, E_idx)
pres_R = qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx)
rho_L = 0d0
gamma_L = 0d0
pi_inf_L = 0d0
rho_R = 0d0
gamma_R = 0d0
pi_inf_R = 0d0
alpha_L_sum = 0d0
alpha_R_sum = 0d0
if (mpp_lim) then
!$acc loop seq
do i = 1, num_fluids
alpha_rho_L(i) = max(0d0, alpha_rho_L(i))
alpha_L(i) = min(max(0d0, alpha_L(i)), 1d0)
alpha_L_sum = alpha_L_sum + alpha_L(i)
end do
alpha_L = alpha_L/max(alpha_L_sum, sgm_eps)
!$acc loop seq
do i = 1, num_fluids
alpha_rho_R(i) = max(0d0, alpha_rho_R(i))
alpha_R(i) = min(max(0d0, alpha_R(i)), 1d0)
alpha_R_sum = alpha_R_sum + alpha_R(i)
end do
alpha_R = alpha_R/max(alpha_R_sum, sgm_eps)
end if
!$acc loop seq
do i = 1, num_fluids
rho_L = rho_L + alpha_rho_L(i)
gamma_L = gamma_L + alpha_L(i)*gammas(i)
pi_inf_L = pi_inf_L + alpha_L(i)*pi_infs(i)
rho_R = rho_R + alpha_rho_R(i)
gamma_R = gamma_R + alpha_R(i)*gammas(i)
pi_inf_R = pi_inf_R + alpha_R(i)*pi_infs(i)
end do
if (any(Re_size > 0)) then
!$acc loop seq
do i = 1, 2
Re_L(i) = dflt_real
if (Re_size(i) > 0) Re_L(i) = 0d0
!$acc loop seq
do q = 1, Re_size(i)
Re_L(i) = alpha_L(Re_idx(i, q))/Res(i, q) &
+ Re_L(i)
end do
Re_L(i) = 1d0/max(Re_L(i), sgm_eps)
end do
!$acc loop seq
do i = 1, 2
Re_R(i) = dflt_real
if (Re_size(i) > 0) Re_R(i) = 0d0
!$acc loop seq
do q = 1, Re_size(i)
Re_R(i) = alpha_R(Re_idx(i, q))/Res(i, q) &
+ Re_R(i)
end do
Re_R(i) = 1d0/max(Re_R(i), sgm_eps)
end do
end if
E_L = gamma_L*pres_L + pi_inf_L + 5d-1*rho_L*vel_L_rms
E_R = gamma_R*pres_R + pi_inf_R + 5d-1*rho_R*vel_R_rms
H_L = (E_L + pres_L)/rho_L
H_R = (E_R + pres_R)/rho_R
if (hypoelasticity) then
!$acc loop seq
do i = 1, strxe - strxb + 1
tau_e_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, strxb - 1 + i)
tau_e_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, strxb - 1 + i)
end do
G_L = 0d0
G_R = 0d0
!$acc loop seq
do i = 1, num_fluids
G_L = G_L + alpha_L(i)*Gs(i)
G_R = G_R + alpha_R(i)*Gs(i)
end do
do i = 1, strxe - strxb + 1
! Elastic contribution to energy if G large enough
!TODO take out if statement if stable without
if ((G_L > 1000) .and. (G_R > 1000)) then
E_L = E_L + (tau_e_L(i)*tau_e_L(i))/(4d0*G_L)
E_R = E_R + (tau_e_R(i)*tau_e_R(i))/(4d0*G_R)
! Additional terms in 2D and 3D
if ((i == 2) .or. (i == 4) .or. (i == 5)) then
E_L = E_L + (tau_e_L(i)*tau_e_L(i))/(4d0*G_L)
E_R = E_R + (tau_e_R(i)*tau_e_R(i))/(4d0*G_R)
end if
end if
end do
end if
@:compute_average_state()
call s_compute_speed_of_sound(pres_L, rho_L, gamma_L, pi_inf_L, H_L, alpha_L, &
vel_L_rms, c_L)
call s_compute_speed_of_sound(pres_R, rho_R, gamma_R, pi_inf_R, H_R, alpha_R, &
vel_R_rms, c_R)
!> The computation of c_avg does not require all the variables, and therefore the non '_avg'
! variables are placeholders to call the subroutine.
call s_compute_speed_of_sound(pres_R, rho_avg, gamma_avg, pi_inf_R, H_avg, alpha_R, &
vel_avg_rms, c_avg)
if (any(Re_size > 0)) then
!$acc loop seq
do i = 1, 2
Re_avg_rs${XYZ}$_vf(j, k, l, i) = 2d0/(1d0/Re_L(i) + 1d0/Re_R(i))
end do
end if
if (wave_speeds == 1) then
if (hypoelasticity) then
s_L = min(vel_L(dir_idx(1)) - sqrt(c_L*c_L + &
(((4d0*G_L)/3d0) + &
tau_e_L(dir_idx_tau(1)))/rho_L) &
, vel_R(dir_idx(1)) - sqrt(c_R*c_R + &
(((4d0*G_R)/3d0) + &
tau_e_R(dir_idx_tau(1)))/rho_R))
s_R = max(vel_R(dir_idx(1)) + sqrt(c_R*c_R + &
(((4d0*G_R)/3d0) + &
tau_e_R(dir_idx_tau(1)))/rho_R) &
, vel_L(dir_idx(1)) + sqrt(c_L*c_L + &
(((4d0*G_L)/3d0) + &
tau_e_L(dir_idx_tau(1)))/rho_L))
else
s_L = min(vel_L(dir_idx(1)) - c_L, vel_R(dir_idx(1)) - c_R)
s_R = max(vel_R(dir_idx(1)) + c_R, vel_L(dir_idx(1)) + c_L)
end if
s_S = (pres_R - pres_L + rho_L*vel_L(dir_idx(1))* &
(s_L - vel_L(dir_idx(1))) - &
rho_R*vel_R(dir_idx(1))* &
(s_R - vel_R(dir_idx(1)))) &
/(rho_L*(s_L - vel_L(dir_idx(1))) - &
rho_R*(s_R - vel_R(dir_idx(1))))
elseif (wave_speeds == 2) then
pres_SL = 5d-1*(pres_L + pres_R + rho_avg*c_avg* &
(vel_L(dir_idx(1)) - &
vel_R(dir_idx(1))))
pres_SR = pres_SL
Ms_L = max(1d0, sqrt(1d0 + ((5d-1 + gamma_L)/(1d0 + gamma_L))* &
(pres_SL/pres_L - 1d0)*pres_L/ &
((pres_L + pi_inf_L/(1d0 + gamma_L)))))
Ms_R = max(1d0, sqrt(1d0 + ((5d-1 + gamma_R)/(1d0 + gamma_R))* &
(pres_SR/pres_R - 1d0)*pres_R/ &
((pres_R + pi_inf_R/(1d0 + gamma_R)))))
s_L = vel_L(dir_idx(1)) - c_L*Ms_L
s_R = vel_R(dir_idx(1)) + c_R*Ms_R
s_S = 5d-1*((vel_L(dir_idx(1)) + vel_R(dir_idx(1))) + &
(pres_L - pres_R)/ &
(rho_avg*c_avg))
end if
s_M = min(0d0, s_L); s_P = max(0d0, s_R)
xi_M = (5d-1 + sign(5d-1, s_L)) &
+ (5d-1 - sign(5d-1, s_L)) &
*(5d-1 + sign(5d-1, s_R))
xi_P = (5d-1 - sign(5d-1, s_R)) &
+ (5d-1 - sign(5d-1, s_L)) &
*(5d-1 + sign(5d-1, s_R))
! Mass
!$acc loop seq
do i = 1, contxe
flux_rs${XYZ}$_vf(j, k, l, i) = &
(s_M*alpha_rho_R(i)*vel_R(dir_idx(1)) &
- s_P*alpha_rho_L(i)*vel_L(dir_idx(1)) &
+ s_M*s_P*(alpha_rho_L(i) &
- alpha_rho_R(i))) &
/(s_M - s_P)
end do
! Momentum
if (bubbles) then
!$acc loop seq
do i = 1, num_dims
flux_rs${XYZ}$_vf(j, k, l, contxe + dir_idx(i)) = &
(s_M*(rho_R*vel_R(dir_idx(1)) &
*vel_R(dir_idx(i)) &
+ dir_flg(dir_idx(i))*(pres_R - ptilde_R)) &
- s_P*(rho_L*vel_L(dir_idx(1)) &
*vel_L(dir_idx(i)) &
+ dir_flg(dir_idx(i))*(pres_L - ptilde_L)) &
+ s_M*s_P*(rho_L*vel_L(dir_idx(i)) &
- rho_R*vel_R(dir_idx(i)))) &
/(s_M - s_P)
end do
else if (hypoelasticity) then
!$acc loop seq
do i = 1, num_dims
flux_rs${XYZ}$_vf(j, k, l, contxe + dir_idx(i)) = &
(s_M*(rho_R*vel_R(dir_idx(1)) &
*vel_R(dir_idx(i)) &
+ dir_flg(dir_idx(i))*pres_R &
- tau_e_R(dir_idx_tau(i))) &
- s_P*(rho_L*vel_L(dir_idx(1)) &
*vel_L(dir_idx(i)) &
+ dir_flg(dir_idx(i))*pres_L &
- tau_e_L(dir_idx_tau(i))) &
+ s_M*s_P*(rho_L*vel_L(dir_idx(i)) &
- rho_R*vel_R(dir_idx(i)))) &
/(s_M - s_P)
end do
else
!$acc loop seq
do i = 1, num_dims
flux_rs${XYZ}$_vf(j, k, l, contxe + dir_idx(i)) = &
(s_M*(rho_R*vel_R(dir_idx(1)) &
*vel_R(dir_idx(i)) &
+ dir_flg(dir_idx(i))*pres_R) &
- s_P*(rho_L*vel_L(dir_idx(1)) &
*vel_L(dir_idx(i)) &
+ dir_flg(dir_idx(i))*pres_L) &
+ s_M*s_P*(rho_L*vel_L(dir_idx(i)) &
- rho_R*vel_R(dir_idx(i)))) &
/(s_M - s_P)
end do
end if
! Energy
if (bubbles) then
flux_rs${XYZ}$_vf(j, k, l, E_idx) = &
(s_M*vel_R(dir_idx(1))*(E_R + pres_R - ptilde_R) &
- s_P*vel_L(dir_idx(1))*(E_L + pres_L - ptilde_L) &
+ s_M*s_P*(E_L - E_R)) &
/(s_M - s_P)
else if (hypoelasticity) then
!TODO: simplify this so it's not split into 3
if (num_dims == 1) then
flux_rs${XYZ}$_vf(j, k, l, E_idx) = &
(s_M*(vel_R(dir_idx(1))*(E_R + pres_R) &
- (tau_e_R(dir_idx_tau(1))*vel_R(dir_idx(1)))) &
- s_P*(vel_L(dir_idx(1))*(E_L + pres_L) &
- (tau_e_L(dir_idx_tau(1))*vel_L(dir_idx(1)))) &
+ s_M*s_P*(E_L - E_R)) &
/(s_M - s_P)
else if (num_dims == 2) then
flux_rs${XYZ}$_vf(j, k, l, E_idx) = &
(s_M*(vel_R(dir_idx(1))*(E_R + pres_R) &
- (tau_e_R(dir_idx_tau(1))*vel_R(dir_idx(1))) &
- (tau_e_R(dir_idx_tau(2))*vel_R(dir_idx(2)))) &
- s_P*(vel_L(dir_idx(1))*(E_L + pres_L) &
- (tau_e_L(dir_idx_tau(1))*vel_L(dir_idx(1))) &
- (tau_e_L(dir_idx_tau(2))*vel_L(dir_idx(2)))) &
+ s_M*s_P*(E_L - E_R)) &
/(s_M - s_P)
else if (num_dims == 3) then
flux_rs${XYZ}$_vf(j, k, l, E_idx) = &
(s_M*(vel_R(dir_idx(1))*(E_R + pres_R) &
- (tau_e_R(dir_idx_tau(1))*vel_R(dir_idx(1))) &
- (tau_e_R(dir_idx_tau(2))*vel_R(dir_idx(2))) &
- (tau_e_R(dir_idx_tau(3))*vel_R(dir_idx(3)))) &
- s_P*(vel_L(dir_idx(1))*(E_L + pres_L) &
- (tau_e_L(dir_idx_tau(1))*vel_L(dir_idx(1))) &
- (tau_e_L(dir_idx_tau(2))*vel_L(dir_idx(2))) &
- (tau_e_L(dir_idx_tau(3))*vel_L(dir_idx(3)))) &
+ s_M*s_P*(E_L - E_R)) &
/(s_M - s_P)
end if
else
flux_rs${XYZ}$_vf(j, k, l, E_idx) = &
(s_M*vel_R(dir_idx(1))*(E_R + pres_R) &
- s_P*vel_L(dir_idx(1))*(E_L + pres_L) &
+ s_M*s_P*(E_L - E_R)) &
/(s_M - s_P)
end if
! Elastic Stresses
if (hypoelasticity) then
do i = 1, strxe - strxb + 1 !TODO: this indexing may be slow
flux_rs${XYZ}$_vf(j, k, l, strxb - 1 + i) = &
(s_M*(rho_R*vel_R(dir_idx(1)) &
*tau_e_R(i)) &
- s_P*(rho_L*vel_L(dir_idx(1)) &
*tau_e_L(i)) &
+ s_M*s_P*(rho_L*tau_e_L(i) &
- rho_R*tau_e_R(i))) &
/(s_M - s_P)
end do
end if
! Advection
!$acc loop seq
do i = advxb, advxe
flux_rs${XYZ}$_vf(j, k, l, i) = &
(qL_prim_rs${XYZ}$_vf(j, k, l, i) &
- qR_prim_rs${XYZ}$_vf(j + 1, k, l, i)) &
*s_M*s_P/(s_M - s_P)
flux_src_rs${XYZ}$_vf(j, k, l, i) = &
(s_M*qR_prim_rs${XYZ}$_vf(j + 1, k, l, i) &
- s_P*qL_prim_rs${XYZ}$_vf(j, k, l, i)) &
/(s_M - s_P)
end do
! Div(U)?
!$acc loop seq
do i = 1, num_dims
vel_src_rs${XYZ}$_vf(j, k, l, dir_idx(i)) = &
(xi_M*(rho_L*vel_L(dir_idx(i))* &
(s_L - vel_L(dir_idx(1))) - &
pres_L*dir_flg(dir_idx(i))) - &
xi_P*(rho_R*vel_R(dir_idx(i))* &
(s_R - vel_R(dir_idx(1))) - &
pres_R*dir_flg(dir_idx(i)))) &
/(xi_M*rho_L*(s_L - vel_L(dir_idx(1))) - &
xi_P*rho_R*(s_R - vel_R(dir_idx(1))))
end do
if (bubbles) then
! From HLLC: Kills mass transport @ bubble gas density
if (num_fluids > 1) then
flux_rs${XYZ}$_vf(j, k, l, contxe) = 0d0
end if
end if
end do
end do
end do
end if
#:endfor
if (any(Re_size > 0)) then
if (weno_Re_flux) then
call s_compute_viscous_source_flux( &
qL_prim_vf(momxb:momxe), &
dqL_prim_dx_vf(momxb:momxe), &
dqL_prim_dy_vf(momxb:momxe), &
dqL_prim_dz_vf(momxb:momxe), &
qR_prim_vf(momxb:momxe), &
dqR_prim_dx_vf(momxb:momxe), &
dqR_prim_dy_vf(momxb:momxe), &
dqR_prim_dz_vf(momxb:momxe), &
flux_src_vf, norm_dir, ix, iy, iz)
else
call s_compute_viscous_source_flux( &
q_prim_vf(momxb:momxe), &
dqL_prim_dx_vf(momxb:momxe), &
dqL_prim_dy_vf(momxb:momxe), &
dqL_prim_dz_vf(momxb:momxe), &
q_prim_vf(momxb:momxe), &
dqR_prim_dx_vf(momxb:momxe), &
dqR_prim_dy_vf(momxb:momxe), &
dqR_prim_dz_vf(momxb:momxe), &
flux_src_vf, norm_dir, ix, iy, iz)
end if
end if
call s_finalize_riemann_solver(flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
end subroutine s_hll_riemann_solver
!> This procedure is the implementation of the Harten, Lax,
!! van Leer, and contact (HLLC) approximate Riemann solver,
!! see Toro (1999) and Johnsen (2007). The viscous and the
!! surface tension effects have been included by modifying
!! the exact Riemann solver of Perigaud and Saurel (2005).
!! @param qL_prim_vf The left WENO-reconstructed cell-boundary values of the
!! cell-average primitive variables
!! @param qR_prim_vf The right WENO-reconstructed cell-boundary values of the
!! cell-average primitive variables
!! @param dqL_prim_dx_vf The left WENO-reconstructed cell-boundary values of the
!! first-order x-dir spatial derivatives
!! @param dqL_prim_dy_vf The left WENO-reconstructed cell-boundary values of the
!! first-order y-dir spatial derivatives
!! @param dqL_prim_dz_vf The left WENO-reconstructed cell-boundary values of the
!! first-order z-dir spatial derivatives
!! @param dqR_prim_dx_vf The right WENO-reconstructed cell-boundary values of the
!! first-order x-dir spatial derivatives
!! @param dqR_prim_dy_vf The right WENO-reconstructed cell-boundary values of the
!! first-order y-dir spatial derivatives
!! @param dqR_prim_dz_vf The right WENO-reconstructed cell-boundary values of the
!! first-order z-dir spatial derivatives
!! @param gm_alphaL_vf Left averaged gradient magnitude
!! @param gm_alphaR_vf Right averaged gradient magnitude
!! @param flux_vf Intra-cell fluxes
!! @param flux_src_vf Intra-cell fluxes sources
!! @param flux_gsrc_vf Intra-cell geometric fluxes sources
!! @param norm_dir Dir. splitting direction
!! @param ix Index bounds in the x-dir
!! @param iy Index bounds in the y-dir
!! @param iz Index bounds in the z-dir
!! @param q_prim_vf Cell-averaged primitive variables
subroutine s_hllc_riemann_solver(qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, dqL_prim_dx_vf, & ! ------
dqL_prim_dy_vf, &
dqL_prim_dz_vf, &
qL_prim_vf, &
qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf, dqR_prim_dx_vf, &
dqR_prim_dy_vf, &
dqR_prim_dz_vf, &
qR_prim_vf, &
q_prim_vf, &
flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
real(kind(0d0)), dimension(startx:, starty:, startz:, 1:), intent(INOUT) :: qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf
type(scalar_field), dimension(sys_size), intent(IN) :: q_prim_vf
type(scalar_field), allocatable, dimension(:), intent(INOUT) :: qL_prim_vf, qR_prim_vf
type(scalar_field), &
allocatable, dimension(:), &
intent(INOUT) :: dqL_prim_dx_vf, dqR_prim_dx_vf, &
dqL_prim_dy_vf, dqR_prim_dy_vf, &
dqL_prim_dz_vf, dqR_prim_dz_vf
! Intercell fluxes
type(scalar_field), &
dimension(sys_size), &
intent(INOUT) :: flux_vf, flux_src_vf, flux_gsrc_vf
integer, intent(IN) :: norm_dir
type(int_bounds_info), intent(IN) :: ix, iy, iz
real(kind(0d0)), dimension(num_fluids) :: alpha_rho_L, alpha_rho_R
real(kind(0d0)) :: rho_L, rho_R
real(kind(0d0)), dimension(num_dims) :: vel_L, vel_R
real(kind(0d0)) :: pres_L, pres_R
real(kind(0d0)) :: E_L, E_R
real(kind(0d0)) :: H_L, H_R
real(kind(0d0)), dimension(num_fluids) :: alpha_L, alpha_R
real(kind(0d0)) :: Y_L, Y_R
real(kind(0d0)) :: gamma_L, gamma_R
real(kind(0d0)) :: pi_inf_L, pi_inf_R
real(kind(0d0)) :: c_L, c_R
real(kind(0d0)), dimension(2) :: Re_L, Re_R
real(kind(0d0)) :: rho_avg
real(kind(0d0)), dimension(num_dims) :: vel_avg
real(kind(0d0)) :: H_avg
real(kind(0d0)) :: gamma_avg
real(kind(0d0)) :: c_avg
real(kind(0d0)) :: s_L, s_R, s_M, s_P, s_S
real(kind(0d0)) :: xi_L, xi_R !< Left and right wave speeds functions
real(kind(0d0)) :: xi_M, xi_P
real(kind(0d0)) :: nbub_L, nbub_R
real(kind(0d0)), dimension(nb) :: R0_L, R0_R
real(kind(0d0)), dimension(nb) :: V0_L, V0_R
real(kind(0d0)), dimension(nb) :: P0_L, P0_R
real(kind(0d0)), dimension(nb) :: pbw_L, pbw_R
real(kind(0d0)), dimension(nb, nmom) :: moms_L, moms_R
real(kind(0d0)) :: ptilde_L, ptilde_R
real(kind(0d0)) :: alpha_L_sum, alpha_R_sum, nbub_L_denom, nbub_R_denom
real(kind(0d0)) :: PbwR3Lbar, Pbwr3Rbar
real(kind(0d0)) :: R3Lbar, R3Rbar
real(kind(0d0)) :: R3V2Lbar, R3V2Rbar
real(kind(0d0)) :: vel_L_rms, vel_R_rms, vel_avg_rms
real(kind(0d0)) :: blkmod1, blkmod2
real(kind(0d0)) :: rho_Star, E_Star, p_Star, p_K_Star
real(kind(0d0)) :: pres_SL, pres_SR, Ms_L, Ms_R
real(kind(0d0)) :: start, finish
integer :: i, j, k, l, q !< Generic loop iterators
integer :: idx1, idxi
! Populating the buffers of the left and right Riemann problem
! states variables, based on the choice of boundary conditions
call s_populate_riemann_states_variables_buffers( &
qL_prim_rsx_vf, qL_prim_rsy_vf, qL_prim_rsz_vf, dqL_prim_dx_vf, &
dqL_prim_dy_vf, &
dqL_prim_dz_vf, &
qL_prim_vf, &
qR_prim_rsx_vf, qR_prim_rsy_vf, qR_prim_rsz_vf, dqR_prim_dx_vf, &
dqR_prim_dy_vf, &
dqR_prim_dz_vf, &
qR_prim_vf, &
norm_dir, ix, iy, iz)
! Reshaping inputted data based on dimensional splitting direction
call s_initialize_riemann_solver( &
q_prim_vf, &
flux_vf, flux_src_vf, &
flux_gsrc_vf, &
norm_dir, ix, iy, iz)
#:for NORM_DIR, XYZ in [(1, 'x'), (2, 'y'), (3, 'z')]
if (norm_dir == ${NORM_DIR}$) then
if (model_eqns == 3) then
!ME3
!$acc parallel loop collapse(3) gang vector default(present) private(vel_L, vel_R, Re_L, Re_R, &
!$acc rho_avg, h_avg, gamma_avg, s_L, s_R, s_S, vel_avg_rms, alpha_L, alpha_R)
do l = is3%beg, is3%end
do k = is2%beg, is2%end
do j = is1%beg, is1%end
vel_L_rms = 0d0; vel_R_rms = 0d0
!$acc loop seq
do i = 1, num_dims
vel_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, contxe + i)
vel_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, contxe + i)
vel_L_rms = vel_L_rms + vel_L(i)**2d0
vel_R_rms = vel_R_rms + vel_R(i)**2d0
end do
pres_L = qL_prim_rs${XYZ}$_vf(j, k, l, E_idx)
pres_R = qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx)
rho_L = 0d0
gamma_L = 0d0
pi_inf_L = 0d0
rho_R = 0d0
gamma_R = 0d0
pi_inf_R = 0d0
alpha_L_sum = 0d0
alpha_R_sum = 0d0
if (mpp_lim) then
!$acc loop seq
do i = 1, num_fluids
qL_prim_rs${XYZ}$_vf(j, k, l, i) = max(0d0, qL_prim_rs${XYZ}$_vf(j, k, l, i))
qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i) = min(max(0d0, qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)), 1d0)
alpha_L_sum = alpha_L_sum + qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)
end do
!$acc loop seq
do i = 1, num_fluids
qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i) = qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)/max(alpha_L_sum, sgm_eps)
end do
!$acc loop seq
do i = 1, num_fluids
qR_prim_rs${XYZ}$_vf(j + 1, k, l, i) = max(0d0, qR_prim_rs${XYZ}$_vf(j + 1, k, l, i))
qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i) = min(max(0d0, qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)), 1d0)
alpha_R_sum = alpha_R_sum + qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)
end do
!$acc loop seq
do i = 1, num_fluids
qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)/max(alpha_R_sum, sgm_eps)
end do
end if
!$acc loop seq
do i = 1, num_fluids
rho_L = rho_L + qL_prim_rs${XYZ}$_vf(j, k, l, i)
gamma_L = gamma_L + qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)*gammas(i)
pi_inf_L = pi_inf_L + qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + i)*pi_infs(i)
rho_R = rho_R + qR_prim_rs${XYZ}$_vf(j + 1, k, l, i)
gamma_R = gamma_R + qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)*gammas(i)
pi_inf_R = pi_inf_R + qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + i)*pi_infs(i)
alpha_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, advxb + i - 1)
alpha_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, advxb + i - 1)
end do
if (any(Re_size > 0)) then
!$acc loop seq
do i = 1, 2
Re_L(i) = dflt_real
if (Re_size(i) > 0) Re_L(i) = 0d0
!$acc loop seq
do q = 1, Re_size(i)
Re_L(i) = qL_prim_rs${XYZ}$_vf(j, k, l, E_idx + Re_idx(i, q))/Res(i, q) &
+ Re_L(i)
end do
Re_L(i) = 1d0/max(Re_L(i), sgm_eps)
end do
!$acc loop seq
do i = 1, 2
Re_R(i) = dflt_real
if (Re_size(i) > 0) Re_R(i) = 0d0
!$acc loop seq
do q = 1, Re_size(i)
Re_R(i) = qR_prim_rs${XYZ}$_vf(j + 1, k, l, E_idx + Re_idx(i, q))/Res(i, q) &
+ Re_R(i)
end do
Re_R(i) = 1d0/max(Re_R(i), sgm_eps)
end do
end if
E_L = gamma_L*pres_L + pi_inf_L + 5d-1*rho_L*vel_L_rms
E_R = gamma_R*pres_R + pi_inf_R + 5d-1*rho_R*vel_R_rms
H_L = (E_L + pres_L)/rho_L
H_R = (E_R + pres_R)/rho_R
@:compute_average_state()
call s_compute_speed_of_sound(pres_L, rho_L, gamma_L, pi_inf_L, H_L, alpha_L, &
vel_L_rms, c_L)
call s_compute_speed_of_sound(pres_R, rho_R, gamma_R, pi_inf_R, H_R, alpha_R, &
vel_R_rms, c_R)
!> The computation of c_avg does not require all the variables, and therefore the non '_avg'
! variables are placeholders to call the subroutine.
call s_compute_speed_of_sound(pres_R, rho_avg, gamma_avg, pi_inf_R, H_avg, alpha_R, &
vel_avg_rms, c_avg)
if (any(Re_size > 0)) then
!$acc loop seq
do i = 1, 2
Re_avg_rs${XYZ}$_vf(j, k, l, i) = 2d0/(1d0/Re_L(i) + 1d0/Re_R(i))
end do
end if
if (wave_speeds == 1) then
s_L = min(vel_L(dir_idx(1)) - c_L, vel_R(dir_idx(1)) - c_R)
s_R = max(vel_R(dir_idx(1)) + c_R, vel_L(dir_idx(1)) + c_L)
s_S = (pres_R - pres_L + rho_L*vel_L(dir_idx(1))* &
(s_L - vel_L(dir_idx(1))) - &
rho_R*vel_R(dir_idx(1))* &
(s_R - vel_R(dir_idx(1)))) &
/(rho_L*(s_L - vel_L(dir_idx(1))) - &
rho_R*(s_R - vel_R(dir_idx(1))))