Free surface flow through rigid porous media -- An overview and comparison of formulations

TL;DR

This paper reviews various formulations for modeling free surface flow through rigid porous media, compares their simulation results with experimental data, and finds differences are small for most practical applications, especially at low Reynolds numbers.

Contribution

It provides a comprehensive review and quantitative comparison of different mathematical formulations for free surface flow through rigid porous media.

Findings

Differences between formulations are minimal at low Reynolds numbers.

Most formulations yield similar results for practical applications.

Efficient algorithms can be used without significant loss of accuracy.

Abstract

In many applications free surface flow through rigid porous media has to be modeled. Examples refer to coastal engineering applications as well as geotechnical or biomedical applications. Albeit the frequent applications, slight inconsistencies in the formulation of the governing equations can be found in the literature. The main goal of this paper is to identify these differences and provide a quantitative assessment of different approaches. Following a review of the different formulations, simulation results obtained from three alternative formulations are compared with experimental and numerical data. Results obtained by 2D and 3D test cases indicate that the predictive differences returned by the different formulations remain small for most applications, in particular for small porous Reynolds number ReP < 5000. Thus it seems justified to select a formulation that supports an efficient algorithm and coding structure.