Coping with geometric discontinuities in porous shallow water models

TL;DR

This paper addresses the challenge of geometric discontinuities in porous shallow water models by comparing 1D porosity-based solutions with 2D shallow water equations, proposing an improved Riemann solver that accounts for head loss in supercritical flows.

Contribution

It introduces a systematic comparison between 1D porosity Riemann solutions and 2D shallow water solutions, and develops an approximate Riemann solver incorporating head loss for better accuracy.

Findings

The 1D SP Riemann problem can produce multiple solutions at porosity discontinuities.

Incorporating head loss is essential for accurate modeling of supercritical flows.

The proposed Riemann solver effectively selects physically consistent solutions.

Abstract

Porosity-based models are a viable alternative to classical two-dimensional (2-d) Shallow water Equations (SWE) when the interaction of shallow flows with obstacles is modelled. The exact solution of the Single Porosity (SP) Riemann problem, which is the building block of numerous porosity models solved with the Finite Volume method, exhibits an interesting feature, namely the multiplicity of solutions when a supercritical flow impinges on a sudden porosity reduction. In the present paper, this ambiguity is overcome by systematically comparing the solution of the one-dimensional (1-d) SP Riemann problem with the corresponding 2-d SWE numerical solutions at local porosity discontinuities. An additional result of this comparison is that the SP Riemann problem should incorporate an adequate amount of head loss through porosity discontinuities when strongly supercritical flows are considered. An approximate Riemann solver, able to pick the physically congruent solution among the alternatives and equipped with the required head loss amount, shows promising results when implemented in a 1-d Single Porosity Finite Volume scheme.