Diffusion Wave Approximation of Depth-Averaged Flow Interaction with Porous Media

Abstract

A two-dimensional diffusive wave framework is proposed for modeling interaction between flow through and outside porous media. The depth-integrated parabolic model was developed with an assumption of zero temporal/convective accelerations, making it appropriate for field-scale simulations. The effects of bed shear arising from the bathymetry, roughness, and properties of granular media are consolidated into a single hydraulic diffusivity coefficient. The equation is resolved in a structured finite-volume grid with implicit time stepping. The proposed framework was validated with a standard analytical solution and small-scale experimental results. A synthetic test case containing irregular ground surface demonstrated the capability of the proposed model for real-time simulation.