A finite volume method for numerical simulation of shallow water models with porosity

• We presents a simple finite volume method to solve the SWE with porosity.
• The scheme consists of two stages (predictor–corrector).
• First stage (predictor) depends on a local parameter allowing to control diffusion.
• Numerical results are presented for shallow water equation with porosity.
• It is found that the scheme offers a robust and accurate approach for solving SWE.

In the current work, we present a new finite volume method for numerical simulation of one and two dimensions of shallow water equations with porosity. The introduction of a porosity into shallow water equations leads to modified expressions for the fluxes and source terms. The proposed method consists of two stages, which can be viewed as a predictor–corrector procedure. The first stage (predictor) of the scheme depends on a local parameter allowing to control diffusion, which modulate by using the limiters theory. The second stage (corrector) recovers the conservation equation. Numerical results are presented for shallow water equations with porosity. It is found that the proposed finite volume method offers a robust and accurate approach for solving shallow water equations with source term and porosity.