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 4) Harten-Lax-van Leer Discontinuities (HLLD) - for MHD only. More...

Functions/Subroutines
subroutine, public	s_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)
	Dispatch 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 4) s_hlld_riemann_solver.

subroutine	s_compute_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)
	Dispatch 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, public	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)

subroutine, public	s_lf_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)

subroutine, public	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)
	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).

subroutine, public	s_hlld_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)
	HLLD Riemann solver resolves 5 of the 7 waves of MHD equations: 1 entropy wave, 2 Alfvén waves, 2 fast magnetosonic waves.

impure subroutine, public	s_initialize_riemann_solvers_module
	The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

subroutine	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, qr_prim_rsx_vf, qr_prim_rsy_vf, qr_prim_rsz_vf, dqr_prim_dx_vf, dqr_prim_dy_vf, dqr_prim_dz_vf, norm_dir, ix, iy, iz)
	The purpose of this subroutine is to populate the buffers of the left and right Riemann states variables, depending on the boundary conditions.

subroutine	s_initialize_riemann_solver (flux_src_vf, norm_dir)
	The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures needed to configure the chosen Riemann solver algorithm.

subroutine	s_compute_cylindrical_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)
	Computes cylindrical viscous source flux contributions for momentum and energy. Calculates Cartesian components of the stress tensor using averaged velocity derivatives and cylindrical geometric factors, then updates `flux_src_vf`. Assumes x-dir is axial (z_cyl), y-dir is radial (r_cyl), z-dir is azimuthal (theta_cyl for derivatives).

subroutine	s_compute_cartesian_viscous_source_flux (dvell_dx_vf, dvell_dy_vf, dvell_dz_vf, dvelr_dx_vf, dvelr_dy_vf, dvelr_dz_vf, flux_src_vf, norm_dir)
	Computes Cartesian viscous source flux contributions for momentum and energy. Calculates averaged velocity gradients, gets Re and interface velocities, calls helpers for shear/bulk stress, then updates `flux_src_vf`.

subroutine	s_calculate_shear_stress_tensor (vel_grad_avg, re_shear, divergence_v, tau_shear_out)
	Calculates shear stress tensor components. tau_ij_shear = ( (dui/dxj + duj/dxi) - (2/3)(div_v)delta_ij ) / Re_shear.

subroutine	s_calculate_bulk_stress_tensor (re_bulk, divergence_v, tau_bulk_out)
	Calculates bulk stress tensor components (diagonal only). tau_ii_bulk = (div_v) / Re_bulk. Off-diagonals are zero.

subroutine	s_finalize_riemann_solver (flux_vf, flux_src_vf, flux_gsrc_vf, norm_dir)
	Deallocation and/or disassociation procedures that are needed to finalize the selected Riemann problem solver.

impure subroutine, public	s_finalize_riemann_solvers_module
	Module deallocation and/or disassociation procedures.

Variables
real(wp), dimension(:, :, :, :), allocatable	vel_src_rsx_vf

real(wp), dimension(:, :, :, :), allocatable	vel_src_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	vel_src_rsz_vf

real(wp), dimension(:, :, :, :), allocatable	mom_sp_rsx_vf

real(wp), dimension(:, :, :, :), allocatable	mom_sp_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	mom_sp_rsz_vf

real(wp), dimension(:, :, :, :), allocatable	re_avg_rsx_vf

real(wp), dimension(:, :, :, :), allocatable	re_avg_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	re_avg_rsz_vf

real(wp), dimension(:), allocatable	gs_rs

real(wp), dimension(:, :), allocatable	res_gs


real(wp), dimension(:, :, :, :), allocatable	flux_rsx_vf
	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(wp), dimension(:, :, :, :), allocatable	flux_src_rsx_vf

real(wp), dimension(:, :, :, :), allocatable	flux_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	flux_src_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	flux_rsz_vf

real(wp), dimension(:, :, :, :), allocatable	flux_src_rsz_vf


real(wp), dimension(:, :, :, :), allocatable	flux_gsrc_rsx_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(wp), dimension(:, :, :, :), allocatable	flux_gsrc_rsy_vf

real(wp), dimension(:, :, :, :), allocatable	flux_gsrc_rsz_vf

Indical bounds in the s1-, s2- and s3-directions
type(int_bounds_info)	is1

type(int_bounds_info)	is2

type(int_bounds_info)	is3

type(int_bounds_info)	isx

type(int_bounds_info)	isy

type(int_bounds_info)	isz

Detailed Description

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 4) Harten-Lax-van Leer Discontinuities (HLLD) - for MHD only.

Function/Subroutine Documentation

◆ s_calculate_bulk_stress_tensor()

subroutine m_riemann_solvers::s_calculate_bulk_stress_tensor	(	real(wp), intent(in)	re_bulk,
		real(wp), intent(in)	divergence_v,
		real(wp), dimension(num_dims, num_dims), intent(out)	tau_bulk_out )

Calculates bulk stress tensor components (diagonal only). tau_ii_bulk = (div_v) / Re_bulk. Off-diagonals are zero.

Parameters

[in]	Re_bulk	Bulk Reynolds number.
[in]	divergence_v	Velocity divergence (du/dx + dv/dy + dw/dz).
[out]	tau_bulk_out	Calculated bulk stress tensor (stress on i-face, i-direction).

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◆ s_calculate_shear_stress_tensor()

subroutine m_riemann_solvers::s_calculate_shear_stress_tensor	(	real(wp), dimension(num_dims, num_dims), intent(in)	vel_grad_avg,
		real(wp), intent(in)	re_shear,
		real(wp), intent(in)	divergence_v,
		real(wp), dimension(num_dims, num_dims), intent(out)	tau_shear_out )

Calculates shear stress tensor components. tau_ij_shear = ( (dui/dxj + duj/dxi) - (2/3)*(div_v)*delta_ij ) / Re_shear.

Parameters

[in]	vel_grad_avg	Averaged velocity gradient tensor (d(vel_i)/d(coord_j)).
[in]	Re_shear	Shear Reynolds number.
[in]	divergence_v	Velocity divergence (du/dx + dv/dy + dw/dz).
[out]	tau_shear_out	Calculated shear stress tensor (stress on i-face, j-direction).

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◆ s_compute_cartesian_viscous_source_flux()

subroutine m_riemann_solvers::s_compute_cartesian_viscous_source_flux	(	type(scalar_field), dimension(num_dims), intent(in)	dvell_dx_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvell_dy_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvell_dz_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvelr_dx_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvelr_dy_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvelr_dz_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		integer, intent(in)	norm_dir )

Computes Cartesian viscous source flux contributions for momentum and energy. Calculates averaged velocity gradients, gets Re and interface velocities, calls helpers for shear/bulk stress, then updates flux_src_vf.

Parameters

[in]	velL_vf	Left boundary velocity (num_dims scalar_field).
[in]	dvelL_dx_vf	Left boundary d(vel)/dx (num_dims scalar_field).
[in]	dvelL_dy_vf	Left boundary d(vel)/dy (num_dims scalar_field).
[in]	dvelL_dz_vf	Left boundary d(vel)/dz (num_dims scalar_field).
[in]	velR_vf	Right boundary velocity (num_dims scalar_field).
[in]	dvelR_dx_vf	Right boundary d(vel)/dx (num_dims scalar_field).
[in]	dvelR_dy_vf	Right boundary d(vel)/dy (num_dims scalar_field).
[in]	dvelR_dz_vf	Right boundary d(vel)/dz (num_dims scalar_field).
[in,out]	flux_src_vf	Intercell source flux array to update (sys_size scalar_field).
[in]	norm_dir	Interface normal direction (1=x, 2=y, 3=z).
[in]	ix	X-direction loop bounds (int_bounds_info).
[in]	iy	Y-direction loop bounds (int_bounds_info).
[in]	iz	Z-direction loop bounds (int_bounds_info).

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◆ s_compute_cylindrical_viscous_source_flux()

subroutine m_riemann_solvers::s_compute_cylindrical_viscous_source_flux	(	type(scalar_field), dimension(num_dims), intent(in)	vell_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvell_dx_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvell_dy_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvell_dz_vf,
		type(scalar_field), dimension(num_dims), intent(in)	velr_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvelr_dx_vf,
		type(scalar_field), dimension(num_dims), intent(in)	dvelr_dy_vf,
		type(scalar_field), dimension(num_dims), intent(in)	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,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

Computes cylindrical viscous source flux contributions for momentum and energy. Calculates Cartesian components of the stress tensor using averaged velocity derivatives and cylindrical geometric factors, then updates flux_src_vf. Assumes x-dir is axial (z_cyl), y-dir is radial (r_cyl), z-dir is azimuthal (theta_cyl for derivatives).

Parameters

[in]	velL_vf	Left boundary velocity ($v_x, v_y, v_z$) (num_dims scalar_field).
[in]	dvelL_dx_vf	Left boundary $\partial v_i/\partial x$ (num_dims scalar_field).
[in]	dvelL_dy_vf	Left boundary $\partial v_i/\partial y$ (num_dims scalar_field).
[in]	dvelL_dz_vf	Left boundary $\partial v_i/\partial z$ (num_dims scalar_field).
[in]	velR_vf	Right boundary velocity ($v_x, v_y, v_z$) (num_dims scalar_field).
[in]	dvelR_dx_vf	Right boundary $\partial v_i/\partial x$ (num_dims scalar_field).
[in]	dvelR_dy_vf	Right boundary $\partial v_i/\partial y$ (num_dims scalar_field).
[in]	dvelR_dz_vf	Right boundary $\partial v_i/\partial z$ (num_dims scalar_field).
[in,out]	flux_src_vf	Intercell source flux array to update (sys_size scalar_field).
[in]	norm_dir	Interface normal direction (1=x-face, 2=y-face, 3=z-face).
[in]	ix	Global X-direction loop bounds (int_bounds_info).
[in]	iy	Global Y-direction loop bounds (int_bounds_info).
[in]	iz	Global Z-direction loop bounds (int_bounds_info).

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◆ s_compute_viscous_source_flux()

subroutine m_riemann_solvers::s_compute_viscous_source_flux	(	type(scalar_field), dimension(num_vels), intent(in)	vell_vf,
		type(scalar_field), dimension(num_vels), intent(in)	dvell_dx_vf,
		type(scalar_field), dimension(num_vels), intent(in)	dvell_dy_vf,
		type(scalar_field), dimension(num_vels), intent(in)	dvell_dz_vf,
		type(scalar_field), dimension(num_vels), intent(in)	velr_vf,
		type(scalar_field), dimension(num_vels), intent(in)	dvelr_dx_vf,
		type(scalar_field), dimension(num_vels), intent(in)	dvelr_dy_vf,
		type(scalar_field), dimension(num_vels), intent(in)	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,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

Dispatch 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.

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◆ s_finalize_riemann_solver()

subroutine m_riemann_solvers::s_finalize_riemann_solver	(	type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir )

Deallocation and/or disassociation procedures that are needed to finalize the selected Riemann problem solver.

Parameters

flux_vf	Intercell fluxes
flux_src_vf	Intercell source fluxes
flux_gsrc_vf	Intercell geometric source fluxes
norm_dir	Dimensional splitting coordinate direction

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◆ s_finalize_riemann_solvers_module()

impure subroutine, public m_riemann_solvers::s_finalize_riemann_solvers_module

Module deallocation and/or disassociation procedures.

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◆ s_hll_riemann_solver()

subroutine, public m_riemann_solvers::s_hll_riemann_solver	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	ql_prim_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	qr_prim_vf,
		type(scalar_field), dimension(sys_size), intent(in)	q_prim_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

The computation of c_avg does not require all the variables, and therefore the non '_avg'

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◆ s_hllc_riemann_solver()

subroutine, public m_riemann_solvers::s_hllc_riemann_solver	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	ql_prim_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	qr_prim_vf,
		type(scalar_field), dimension(sys_size), intent(in)	q_prim_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

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).

Parameters

qL_prim_vf	The left WENO-reconstructed cell-boundary values of the cell-average primitive variables
qR_prim_vf	The right WENO-reconstructed cell-boundary values of the cell-average primitive variables
dqL_prim_dx_vf	The left WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqL_prim_dy_vf	The left WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqL_prim_dz_vf	The left WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
dqR_prim_dx_vf	The right WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqR_prim_dy_vf	The right WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqR_prim_dz_vf	The right WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
gm_alphaL_vf	Left averaged gradient magnitude
gm_alphaR_vf	Right averaged gradient magnitude
flux_vf	Intra-cell fluxes
flux_src_vf	Intra-cell fluxes sources
flux_gsrc_vf	Intra-cell geometric fluxes sources
norm_dir	Dir. splitting direction
ix	Index bounds in the x-dir
iy	Index bounds in the y-dir
iz	Index bounds in the z-dir
q_prim_vf	Cell-averaged primitive variables

The computation of c_avg does not require all the variables, and therefore the non '_avg'

gamma_method = 1: Ref. Section 2.3.1 Formulation of doi:10.7907/ZKW8-ES97.

gamma_method = 2: c_p / c_v where c_p, c_v are specific heats.

The computation of c_avg does not require all the variables, and therefore the non '_avg'

gamma_method = 1: Ref. Section 2.3.1 Formulation of doi:10.7907/ZKW8-ES97.

gamma_method = 2: c_p / c_v where c_p, c_v are specific heats.

The computation of c_avg does not require all the variables, and therefore the non '_avg'

gamma_method = 1: Ref. Section 2.3.1 Formulation of doi:10.7907/ZKW8-ES97.

gamma_method = 2: c_p / c_v where c_p, c_v are specific heats.

The computation of c_avg does not require all the variables, and therefore the non '_avg'

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◆ s_hlld_riemann_solver()

subroutine, public m_riemann_solvers::s_hlld_riemann_solver	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	ql_prim_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	qr_prim_vf,
		type(scalar_field), dimension(sys_size), intent(in)	q_prim_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

HLLD Riemann solver resolves 5 of the 7 waves of MHD equations: 1 entropy wave, 2 Alfvén waves, 2 fast magnetosonic waves.

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◆ s_initialize_riemann_solver()

subroutine m_riemann_solvers::s_initialize_riemann_solver	(	type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		integer, intent(in)	norm_dir )

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures needed to configure the chosen Riemann solver algorithm.

Parameters

qL_prim_vf	The left WENO-reconstructed cell-boundary values of the cell-average primitive variables
qR_prim_vf	The right WENO-reconstructed cell-boundary values of the cell-average primitive variables
flux_vf	Intra-cell fluxes
flux_src_vf	Intra-cell fluxes sources
flux_gsrc_vf	Intra-cell geometric fluxes sources
norm_dir	Dir. splitting direction
ix	Index bounds in the x-dir
iy	Index bounds in the y-dir
iz	Index bounds in the z-dir
q_prim_vf	Cell-averaged primitive variables

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◆ s_initialize_riemann_solvers_module()

impure subroutine, public m_riemann_solvers::s_initialize_riemann_solvers_module

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

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◆ s_lf_riemann_solver()

subroutine, public m_riemann_solvers::s_lf_riemann_solver	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	ql_prim_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	qr_prim_vf,
		type(scalar_field), dimension(sys_size), intent(in)	q_prim_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

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◆ s_populate_riemann_states_variables_buffers()

subroutine m_riemann_solvers::s_populate_riemann_states_variables_buffers	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

The purpose of this subroutine is to populate the buffers of the left and right Riemann states variables, depending on the boundary conditions.

Parameters

qL_prim_vf	The left WENO-reconstructed cell-boundary values of the cell-average primitive variables
qR_prim_vf	The right WENO-reconstructed cell-boundary values of the cell-average primitive variables
dqL_prim_dx_vf	The left WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqL_prim_dy_vf	The left WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqL_prim_dz_vf	The left WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
dqR_prim_dx_vf	The right WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqR_prim_dy_vf	The right WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqR_prim_dz_vf	The right WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
gm_alphaL_vf	Left averaged gradient magnitude
gm_alphaR_vf	Right averaged gradient magnitude
norm_dir	Dir. splitting direction
ix	Index bounds in the x-dir
iy	Index bounds in the y-dir
iz	Index bounds in the z-dir

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◆ s_riemann_solver()

subroutine, public m_riemann_solvers::s_riemann_solver	(	real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	ql_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dql_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	ql_prim_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsx_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsy_vf,
		real(wp), dimension(idwbuff(1)%beg:, idwbuff(2)%beg:, idwbuff(3)%beg:, 1:), intent(inout)	qr_prim_rsz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dx_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dy_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	dqr_prim_dz_vf,
		type(scalar_field), dimension(:), intent(inout), allocatable	qr_prim_vf,
		type(scalar_field), dimension(sys_size), intent(in)	q_prim_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_src_vf,
		type(scalar_field), dimension(sys_size), intent(inout)	flux_gsrc_vf,
		integer, intent(in)	norm_dir,
		type(int_bounds_info), intent(in)	ix,
		type(int_bounds_info), intent(in)	iy,
		type(int_bounds_info), intent(in)	iz )

Dispatch 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 4) s_hlld_riemann_solver.

Parameters

qL_prim_vf	The left WENO-reconstructed cell-boundary values of the cell-average primitive variables
qR_prim_vf	The right WENO-reconstructed cell-boundary values of the cell-average primitive variables
dqL_prim_dx_vf	The left WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqL_prim_dy_vf	The left WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqL_prim_dz_vf	The left WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
dqR_prim_dx_vf	The right WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives
dqR_prim_dy_vf	The right WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives
dqR_prim_dz_vf	The right WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives
gm_alphaL_vf	Left averaged gradient magnitude
gm_alphaR_vf	Right averaged gradient magnitude
flux_vf	Intra-cell fluxes
flux_src_vf	Intra-cell fluxes sources
flux_gsrc_vf	Intra-cell geometric fluxes sources
norm_dir	Dir. splitting direction
ix	Index bounds in the x-dir
iy	Index bounds in the y-dir
iz	Index bounds in the z-dir
q_prim_vf	Cell-averaged primitive variables

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Variable Documentation

◆ flux_gsrc_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_gsrc_rsx_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.

◆ flux_gsrc_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_gsrc_rsy_vf

◆ flux_gsrc_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_gsrc_rsz_vf

◆ flux_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_rsx_vf

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.

◆ flux_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_rsy_vf

◆ flux_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_rsz_vf

◆ flux_src_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_src_rsx_vf

◆ flux_src_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_src_rsy_vf

◆ flux_src_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::flux_src_rsz_vf

◆ gs_rs

real(wp), dimension(:), allocatable m_riemann_solvers::gs_rs

◆ is1

type(int_bounds_info) m_riemann_solvers::is1

◆ is2

type(int_bounds_info) m_riemann_solvers::is2

◆ is3

type(int_bounds_info) m_riemann_solvers::is3

◆ isx

type(int_bounds_info) m_riemann_solvers::isx

◆ isy

type(int_bounds_info) m_riemann_solvers::isy

◆ isz

type(int_bounds_info) m_riemann_solvers::isz

◆ mom_sp_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::mom_sp_rsx_vf

◆ mom_sp_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::mom_sp_rsy_vf

◆ mom_sp_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::mom_sp_rsz_vf

◆ re_avg_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::re_avg_rsx_vf

◆ re_avg_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::re_avg_rsy_vf

◆ re_avg_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::re_avg_rsz_vf

◆ res_gs

real(wp), dimension(:, :), allocatable m_riemann_solvers::res_gs

◆ vel_src_rsx_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::vel_src_rsx_vf

◆ vel_src_rsy_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::vel_src_rsy_vf

◆ vel_src_rsz_vf

real(wp), dimension(:, :, :, :), allocatable m_riemann_solvers::vel_src_rsz_vf

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ s_calculate_bulk_stress_tensor()

◆ s_calculate_shear_stress_tensor()

◆ s_compute_cartesian_viscous_source_flux()

◆ s_compute_cylindrical_viscous_source_flux()

◆ s_compute_viscous_source_flux()

◆ s_finalize_riemann_solver()

◆ s_finalize_riemann_solvers_module()

◆ s_hll_riemann_solver()

◆ s_hllc_riemann_solver()

◆ s_hlld_riemann_solver()

◆ s_initialize_riemann_solver()

◆ s_initialize_riemann_solvers_module()

◆ s_lf_riemann_solver()

◆ s_populate_riemann_states_variables_buffers()

◆ s_riemann_solver()

Variable Documentation

◆ flux_gsrc_rsx_vf

◆ flux_gsrc_rsy_vf

◆ flux_gsrc_rsz_vf

◆ flux_rsx_vf

◆ flux_rsy_vf

◆ flux_rsz_vf

◆ flux_src_rsx_vf

◆ flux_src_rsy_vf

◆ flux_src_rsz_vf

◆ gs_rs

◆ is1

◆ is2

◆ is3

◆ isx

◆ isy

◆ isz

◆ mom_sp_rsx_vf

◆ mom_sp_rsy_vf

◆ mom_sp_rsz_vf

◆ re_avg_rsx_vf

◆ re_avg_rsy_vf

◆ re_avg_rsz_vf

◆ res_gs

◆ vel_src_rsx_vf

◆ vel_src_rsy_vf

◆ vel_src_rsz_vf