Boundary Conditions and Face Closures

Boundary conditions in CMPS are assembled as face flux/state closures in the same residual/Jacobian framework used for internal faces. The active physical boundary families are summarized below.

Wall

Walls impose no penetration relative to the moving wall,

For a viscous no-slip wall,

The tangential relative velocity used by the wall treatment is

The thermal closure then supplies either zero heat flux, a prescribed wall temperature, or the selected conjugate/external heat-transfer relation.

Inlets

Stagnation inlet. Total pressure and total temperature are prescribed and a consistent static inflow state is recovered. For an ideal gas,

For a stiffened gas, the pressure relation uses the shifted thermodynamic pressure,

Mass-flow inlet. The entering state is constrained by

Velocity inlet. The boundary velocity is prescribed directly, \(\mathbf u_b=\mathbf u_{specified}\), together with the required thermal/composition data.

Pressure outlet

A pressure outlet applies the requested static pressure,

For outward carrier flow, transported composition is taken from the interior. For backflow, stored boundary species/turbulence/VOF data define the incoming state.

Far field

The compressible far-field closure constructs incoming/outgoing characteristic information from the interior and prescribed free-stream state. The VOF far-field path evaluates the homogeneous-mixture EOS directly; it does not average constituent sound speeds.

Symmetry and axis

For a symmetry plane, normal velocity is removed while tangential velocity is retained,

Scalar quantities use the corresponding zero-normal-gradient closure,

Axis boundaries provide the analogous regularity condition for two-dimensional axisymmetric domains.

Interior and partition interfaces

Fluid interior, solid interior, internal wall and fluid–solid wall faces use the two-sided finite-volume stencil appropriate to their adjacent zones. Partition interfaces preserve the same numerical face formulation while the neighbor state is supplied by the adjacent MPI rank.

Solid-propellant surface

The pressure-dependent propellant branch uses a Saint-Robert-type regression law. With regression coefficient \(a_b\), exponent \(n_b\), propellant density \(\rho_p\), and condensed-product mass fraction \(f_c\), the produced gas mass flux is

The boundary-normal gas velocity and integrated mass flow follow as

The injected energy flux uses the produced-gas enthalpy,

while a time-defined mass-flow branch replaces the pressure law with the configured time polynomial.

Boundary profiles

Scalar boundary values may be constant or supplied by the configured user-function path. The same mechanism is used for time- or position-dependent boundary data where a field supports profile evaluation.

Wall thermal-condition families

The boundary model contains adiabatic, prescribed-temperature, convective heat-transfer, prescribed heat-flux, external-radiation, external mixed thermal, and one-dimensional charring wall conditions. Fluid–solid interface walls separately distinguish adiabatic, non-adiabatic and charring thermal coupling. Homogeneous VOF currently accepts only the adiabatic ordinary/interior/interface-wall branches.

Audited VOF boundary readiness

Whenever a VOF boundary requires composition, the stored vector represents every physical phase and satisfies

At open boundaries, the conservative phase flux is tied exactly to the carrier mass flow:

A new default composition is deterministic: unit volume fraction in the reference phase and zero in every other phase.