Applicability of Dynamic, Local, and Diffusive Wave Models for Unified Depth-Averaged Fluid Flow Interaction with Porous Media

Abstract

A comparative study concerning dynamic, local, and zero inertia variants of volume-averaged depth-integrated porous shallow water equations has been presented. The first two hyperbolic models are resolved through an explicit augmented approximate Riemann solver, and the diffusive parabolic model employs an implicit formulation. Three benchmark tests are simulated and compared through all three counterparts. The diffusive wave model offers a wide range of time-step choices and, subsequently, lesser computational cost when the temporal variation of flow depth/velocity is relatively small. However, explicit hyperbolic models outperform in the case of rapidly varied flow interaction with granular media.