mod_flow_projection – LowMachReact-Hex

Fractional-step projection solver for constant- and variable-density modes.

This module implements the core hydrodynamic solver for the LowMachReact-Hex framework. Constant-density mode uses params%rho and enforces $\nabla \cdot u = 0$ . Guarded variable-density low-Mach mode uses active density transport%rho and enforces $\nabla \cdot u = S$ , where $S$ is stored in fields%projection_divergence_source for the projection time level.

Predictor Step: An intermediate velocity $\mathbf{u}^*$ is calculated by advancing the momentum equation explicitly, excluding the new pressure gradient. $\frac{\mathbf{u}^* - \mathbf{u}^n}{\Delta t} = -(\mathbf{u} \cdot \nabla) \mathbf{u} + \nu \nabla^2 \mathbf{u} - \frac{1}{\rho} \nabla p^n + \mathbf{f}$
Poisson Solve: A pressure correction potential $\phi = p^{n+1} - p^n$ is found by solving the Poisson equation derived from the active continuity constraint. $\nabla^2 \phi = \frac{\rho}{\Delta t} \nabla \cdot \mathbf{u}^*$
Corrector Step: The final velocity $\mathbf{u}^{n+1}$ and pressure $p^{n+1}$ are updated using the potential gradient. $\mathbf{u}^{n+1} = \mathbf{u}^* - \frac{\Delta t}{\rho} \nabla \phi$ $p^{n+1} = p^n + \phi$

The linear system for the Poisson equation is solved using a Preconditioned Conjugate Gradient (PCG) method with a diagonal (Jacobi) preconditioner.

Uses

- mod_precision
- mod_bc
- mod_flow_fields
- mod_mesh
- mod_profiling
- mod_linear_solver
- mpi_f08
- mod_mpi_flow
- mod_cantera
- mod_input

Functions

private function boundary_density_for_cell(params, transport, cell_id) result(rho_b)

Arguments

Type	Intent		Name
type(case_params_t),	intent(in)	::	params
type(transport_properties_t),	intent(in)	::	transport
integer,	intent(in)	::	cell_id

Return Value real(kind=rk)

private function face_linear_scalar(mesh, bc, face_id, cell_id, nb, owner_value, neighbor_value) result(face_value)

Linearly interpolates a scalar field to a face.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(bc_set_t),	intent(in)	::	bc
integer,	intent(in)	::	face_id
integer,	intent(in)	::	cell_id
integer,	intent(in)	::	nb
real(kind=rk),	intent(in)	::	owner_value
real(kind=rk),	intent(in)	::	neighbor_value

Return Value real(kind=rk)

private function face_linear_vector(mesh, bc, face_id, cell_id, nb, owner_value, neighbor_value) result(face_value)

Linearly interpolates a vector field to a face.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(bc_set_t),	intent(in)	::	bc
integer,	intent(in)	::	face_id
integer,	intent(in)	::	cell_id
integer,	intent(in)	::	nb
real(kind=rk),	intent(in)	::	owner_value(3)
real(kind=rk),	intent(in)	::	neighbor_value(3)

Return Value real(kind=rk), (3)

private function face_neighbor_weight(mesh, bc, face_id, cell_id, nb) result(w_nb)

Allocates and resets temporary solver vectors. Calculates the normal distance between cell centers or cell-to-face.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh	The mesh.
type(bc_set_t),	intent(in)	::	bc	Boundary conditions.
integer,	intent(in)	::	face_id	Face index.
integer,	intent(in)	::	cell_id	Source cell index.
integer,	intent(in)	::	nb	Neighbor cell index (or 0 for boundaries).

Return Value real(kind=rk)

Subroutines

public subroutine advance_projection_step(mesh, flow, bc, params, transport, fields, stats)

Orchestrates one full fractional-step iteration.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh	Computational mesh context.
type(flow_mpi_t),	intent(inout)	::	flow	MPI parallelization data structure.
type(bc_set_t),	intent(in)	::	bc	Boundary condition patches.
type(case_params_t),	intent(in)	::	params	Configuration input parameters.
type(transport_properties_t),	intent(inout)	::	transport	Physical and thermodynamic properties (e.g. density).
type(flow_fields_t),	intent(inout)	::	fields	Flow field arrays (u, u_star, p, phi, face_flux, mass_flux) updated in-place.
type(solver_stats_t),	intent(inout)	::	stats	Solver diagnostics statistics container.

public subroutine compute_and_update_cfl(mesh, flow, params, fields, stats)

Calculates domain-wide CFL and optionally scales the timestep size.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(case_params_t),	intent(inout)	::	params
type(flow_fields_t),	intent(in)	::	fields
type(solver_stats_t),	intent(inout)	::	stats

public subroutine compute_flow_diagnostics(mesh, flow, bc, params, fields, stats)

Aggregates global raw-divergence, kinetic-energy, and boundary-flux data.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(flow_fields_t),	intent(in)	::	fields
type(solver_stats_t),	intent(inout)	::	stats

public subroutine correct_projection_to_lowmach_source(mesh, flow, bc, params, transport, fields, stats)

Performs a post-chemistry corrective pressure projection step.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh	Computational mesh context.
type(flow_mpi_t),	intent(inout)	::	flow	MPI parallelization data structure.
type(bc_set_t),	intent(in)	::	bc	Boundary condition patches.
type(case_params_t),	intent(in)	::	params	Configuration input parameters.
type(transport_properties_t),	intent(inout)	::	transport	Physical and thermodynamic properties (e.g. density).
type(flow_fields_t),	intent(inout)	::	fields	Flow field arrays corrected in-place.
type(solver_stats_t),	intent(inout)	::	stats	Solver diagnostics statistics container.

public subroutine update_lowmach_divergence_source_from_density(mesh, flow, bc, params, transport, fields, species_Y, T_state)

Update the guarded variable-density low-Mach divergence source.

Arguments

Type	Intent	Optional		Name
type(mesh_t),	intent(in)		::	mesh	Computational mesh context.
type(flow_mpi_t),	intent(inout)		::	flow	MPI parallelization communicator data.
type(bc_set_t),	intent(in)		::	bc	Boundary condition set.
type(case_params_t),	intent(in)		::	params	Global simulation configuration parameters.
type(transport_properties_t),	intent(inout)		::	transport	Thermodynamic property array containing density.
type(flow_fields_t),	intent(inout)		::	fields	Flow fields where the divergence source will be populated.
real(kind=rk),	intent(in),	optional	::	species_Y(:,:)
real(kind=rk),	intent(in),	optional	::	T_state(:)

private subroutine advance_ab2(mesh, flow, params, fields, rhs, local_ustar)

Advances velocity using the 2nd-order Adams-Bashforth scheme.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(case_params_t),	intent(in)	::	params
type(flow_fields_t),	intent(in)	::	fields
real(kind=rk),	intent(in)	::	rhs(:,:)
real(kind=rk),	intent(out)	::	local_ustar(:,:)

private subroutine balance_neumann_outlet_flux(mesh, flow, bc, params, fields, face_flux)

Adjusts flux at Neumann outlets to ensure strict global mass balance.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(flow_fields_t),	intent(in)	::	fields
real(kind=rk),	intent(inout)	::	face_flux(:)

private subroutine check_mpi(ierr, where)

Internal helper for MPI error checking.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	ierr
character(len=*),	intent(in)			::	where

private subroutine compute_boundary_flux(mesh, flow, bc, face_flux, local_flux)

Helper to integrated boundary flux on MPI-owned partitions.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
real(kind=rk),	intent(in)	::	face_flux(:)
real(kind=rk),	intent(out)	::	local_flux

private subroutine compute_face_mass_flux(mesh, flow, bc, transport, face_flux, mass_flux)

Computes density-weighted face mass flux from volumetric flux.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(transport_properties_t),	intent(in)	::	transport
real(kind=rk),	intent(in)	::	face_flux(:)
real(kind=rk),	intent(out)	::	mass_flux(:)

private subroutine compute_flux_divergence(mesh, flow, face_flux, local_div)

Computes the discrete divergence of face fluxes for each cell.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
real(kind=rk),	intent(in)	::	face_flux(:)
real(kind=rk),	intent(out)	::	local_div(:)

private subroutine compute_momentum_rhs(mesh, flow, bc, params, transport, u, p, local_rhs)

Evaluates the advective, diffusive, and pressure terms of the momentum equation.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(transport_properties_t),	intent(in)	::	transport
real(kind=rk),	intent(in)	::	u(:,:)
real(kind=rk),	intent(in)	::	p(:)
real(kind=rk),	intent(out)	::	local_rhs(:,:)

private subroutine compute_predicted_face_flux(mesh, flow, bc, params, transport, ustar, face_flux)

Linearly interpolates cell-centered intermediate velocity to mesh faces.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(transport_properties_t),	intent(in)	::	transport
real(kind=rk),	intent(in)	::	ustar(:,:)
real(kind=rk),	intent(out)	::	face_flux(:)

private subroutine correct_cell_velocity(mesh, flow, bc, params, transport, ustar, phi, local_u)

Updates cell-centered velocity using the pressure potential gradient.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(transport_properties_t),	intent(in)	::	transport
real(kind=rk),	intent(in)	::	ustar(:,:)
real(kind=rk),	intent(in)	::	phi(:)
real(kind=rk),	intent(out)	::	local_u(:,:)

private subroutine correct_face_flux(mesh, flow, bc, params, transport, predicted_flux, phi, face_flux)

Corrects face fluxes using the pressure potential gradient.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(flow_mpi_t),	intent(in)	::	flow
type(bc_set_t),	intent(in)	::	bc
type(case_params_t),	intent(in)	::	params
type(transport_properties_t),	intent(in)	::	transport
real(kind=rk),	intent(in)	::	predicted_flux(:)
real(kind=rk),	intent(in)	::	phi(:)
real(kind=rk),	intent(out)	::	face_flux(:)

private subroutine pressure_gradient_cell(mesh, bc, p, cell_id, gradp)

Calculates the pressure gradient at a cell center using Gauss's Theorem.

Arguments

Type	Intent		Name
type(mesh_t),	intent(in)	::	mesh
type(bc_set_t),	intent(in)	::	bc
real(kind=rk),	intent(in)	::	p(:)
integer,	intent(in)	::	cell_id
real(kind=rk),	intent(out)	::	gradp(3)

mod_flow_projection Module

Contents

Functions

Subroutines

Uses

Functions

private function boundary_density_for_cell(params, transport, cell_id) result(rho_b)

Arguments

Return Value real(kind=rk)

private function face_linear_scalar(mesh, bc, face_id, cell_id, nb, owner_value, neighbor_value) result(face_value)

Arguments

Return Value real(kind=rk)

private function face_linear_vector(mesh, bc, face_id, cell_id, nb, owner_value, neighbor_value) result(face_value)

Arguments

Return Value real(kind=rk), (3)

private function face_neighbor_weight(mesh, bc, face_id, cell_id, nb) result(w_nb)

Arguments

Return Value real(kind=rk)

Subroutines

public subroutine advance_projection_step(mesh, flow, bc, params, transport, fields, stats)

Arguments

public subroutine compute_and_update_cfl(mesh, flow, params, fields, stats)

Arguments

public subroutine compute_flow_diagnostics(mesh, flow, bc, params, fields, stats)

Arguments

public subroutine correct_projection_to_lowmach_source(mesh, flow, bc, params, transport, fields, stats)

Arguments

public subroutine update_lowmach_divergence_source_from_density(mesh, flow, bc, params, transport, fields, species_Y, T_state)

Arguments

private subroutine advance_ab2(mesh, flow, params, fields, rhs, local_ustar)

Arguments

private subroutine balance_neumann_outlet_flux(mesh, flow, bc, params, fields, face_flux)

Arguments

private subroutine check_mpi(ierr, where)

Arguments

private subroutine compute_boundary_flux(mesh, flow, bc, face_flux, local_flux)

Arguments

private subroutine compute_face_mass_flux(mesh, flow, bc, transport, face_flux, mass_flux)

Arguments

private subroutine compute_flux_divergence(mesh, flow, face_flux, local_div)

Arguments

private subroutine compute_momentum_rhs(mesh, flow, bc, params, transport, u, p, local_rhs)

Arguments

private subroutine compute_predicted_face_flux(mesh, flow, bc, params, transport, ustar, face_flux)

Arguments

private subroutine correct_cell_velocity(mesh, flow, bc, params, transport, ustar, phi, local_u)

Arguments

private subroutine correct_face_flux(mesh, flow, bc, params, transport, predicted_flux, phi, face_flux)

Arguments

private subroutine pressure_gradient_cell(mesh, bc, p, cell_id, gradp)

Arguments