Improvement of anisotropic porosity models with a merging technique

Martin Bruwier,Sébastien Erpicum,Pierre Archambeau,Michel Pirotton,Benjamin Dewals,A Paquier,N Rivière

doi:10.1051/e3sconf/20184006023

Abstract

Anisotropic porosity shallow-water models are used to take into account detailed topographic information through porosity parameters multiplying the various terms of the shallow-water equations. A storage porosity is assigned to each cell to reflect the void fraction in the cell and a conveyance porosity is used at each edge to reproduce the impact of subgrid obstacles on the flux terms. To guaranty the numerical stability, the time step depends on the value of the porosity parameters. This may hamper severely the computational efficiency in the presence of cells with low values of storage porosity. Cartesian grids are particularly sensitive to such a case since the meshing stems directly from the choice of the grid size. In this paper, this problem is addressed by using an original merging technique consisting in merging cells with a storage porosity lower than a threshold value with neighbouring cells. The model was tested for modelling a prismatic channel with different orientations between the Cartesian computational grid and the channel direction. The results show that the standard anisotropic porosity model (without merging) improves the reproduction of the flow characteristics; but at the cost of a significantly higher computational time. In contrast, the computational time is drastically reduced and the accuracy preserved when the merging technique is used with the porosity model.

Highlights

Anisotropic porosity models were introduced by [1] for the simulation of floods in urban areas at a coarse scale, using porosity parameters to reproduce the effect of obstacles at a finer scale on water storage and flow conveyance
A key issue in the use of porosity-based models on a Cartesian grid is the handling of computational cells with low values of the storage porosity, which leads to a significant increase in the computational time to maintain the numerical stability
Based on simulations of a uniform rectangular channel with different orientations with respect to a fixed Cartesian grid, the aim of this paper is twofold: (1) showing that anisotropic porosity models improve the reproduction of oblique boundaries on a Cartesian grid and (2) showing the benefit of adding a merging technique to the porosity-based model to handle properly the cells with low values of storage porosity

Summary

Introduction

Anisotropic porosity models (or integral porosity models) were introduced by [1] for the simulation of floods in urban areas at a coarse scale, using porosity parameters to reproduce the effect of obstacles at a finer scale on water storage and flow conveyance. A key issue in the use of porosity-based models on a Cartesian grid is the handling of computational cells with low values of the storage porosity, which leads to a significant increase in the computational time to maintain the numerical stability. Based on simulations of a uniform rectangular channel with different orientations with respect to a fixed Cartesian grid, the aim of this paper is twofold: (1) showing that anisotropic porosity models improve the reproduction of oblique boundaries on a Cartesian grid and (2) showing the benefit of adding a merging technique to the porosity-based model to handle properly the cells with low values of storage porosity

Objectives

Results

Conclusion