Improvement of anisotropic porosity models with a merging technique

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.