Jump momentum boundary condition at a fluid–porous dividing surface: Derivation of the closure problem

The method of volume averaging is used to derive a stress jump boundary condition that takes the formεβω-1∂〈vβ〉ω∂y-∂〈vβ〉η∂y=-K-1avs〈vβ〉ω.Here K-1K-1 is the tangential component of a mixed stress tensor which combines the global and Brinkman stresses at the dividing surface. The computation of the Brinkman stress at the boundary is carried out by using polynomial functions describing the spatial changes of the porosity. Local closure problems are derived for the determination of the global stress contribution at the inter-region. At this stage, an alternative methodology is proposed in order to estimate the mixed stress tensor, which has been related to the stress jump coefficient proposed in the literature. Results for the jump coefficient are found to be in good agreement with previous calculations.