7.6.12.11.3. Porous_Muscl_Density

Syntax

Mass Balance Advective Flux [{of} SpeciesName] = Porous_Muscl_Density ([Limiter = limiter] | [Zeta = zeta] | [Use_Peclet_Blending = use_peclet_blending])

Scope

Aria Material

Summary

MUSCL scheme for advective flux in porous equations. Currently only valid for EQ porous_enthalpy / mass_balance while using CVFEM.

Description

Let $q$ be the subcontrol surface interpolated scalar and let $q_{muscl}$ be the MUSCL scalar at the subcontrol surface computed using the projected nodal gradient of the scalar and the prescribed limiter (i.e., NONE, SUPERBEE, MINDMOD, VAN_ALBADA, VAN_LEER). The scalar at the subcontrol surface is linearly interpolated as

$q_f = \chi q_{muscl} + \left(1 - \chi\right) q,$

where $\chi = \dfrac{\left(\zeta Pe\right)^2}{5 + \left(\zeta Pe \right)^2}$ is the weighting function between 0 and 1 that is based on the cell Peclet number $Pe$ and $\zeta$ , a user specified scaling. If no diffusion is present, (i.e., pure advection), $q_{muscl}$ is used. Similarly, if the cell Peclet number is near zero, then the interpolated scalar $q$ is used.

The cell Peclet number is the ratio of advective flux to diffusive flux in a cell. For the mass balance equation, it is assumed the MASS_BALANCE_DIFFUSIVE_FLUX = POROUS is used, giving a diffusive flux (if present) of the form $\mathbf{J} = -\phi \rho D_i \nabla Y_i$ , which in turn yields the following cell Pe

$Pe_{\Delta x} = \dfrac{\mathbf{u} \cdot \mathbf{\Delta x}}{\phi D_i}.$

On the other hand, for the gas phase porous enthalpy equation, it is assumed the HEAT CONDUCTION = POROUS_SIMPLIFIED_DIFFUSIVE_ENTHALPY model is used, giving a diffusive flux (if present) of the form $\mathbf{q} = -\phi \rho D \nabla h$ , which in turn for a unit Lewis number yields the following cell Pe,

$Pe_{\Delta x} = \dfrac{\mathbf{u} \cdot \mathbf{\Delta x}}{\phi \alpha}$

For the solid phase (or no phase) porous enthalpy equation, it is assumed HEAT CONDUCTION = FOURIERS_LAW is used i.e, $\mathbf{q} = -k \nabla T$ , resulting in the following cell Pe

$Pe_{\Delta x} = \dfrac{\mathbf{u} \cdot \mathbf{\Delta x}}{\alpha}.$

Note the thermal diffusivity is computed using a scalar thermal conductivity. For other cases, set the optional parameter use_pecleting_blending = 0, to turn off Peclet blending.

Parameter	Value	Default
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
limiter	“string”	VAN_LEER
zeta	real	1
use_peclet_blending	integer	–