2-D fully coupled morphodynamic modelling in vegetated environments based on the anisotropic porosity method

Previous studies for numerical representation of aquatic vegetation based on the isotropic porosity shallow water models can not only consider the effects of vegetation resistance and spatial occupation in physics, but also improve the computational efficiency in large-scale modelling. This type of models provides a promising tool to numerically study the vegetated flow and the corresponding sediment transport in practice. However, the characteristics of preferential flow among complex vegetation distributions which are often observed in nature cannot be well captured due to the isotropic assumption. Thus, we make an improvement by introducing the anisotropic porosity method in the shallow water model. Unlike the isotropic porosity method which uses only one porosity parameter to describe the vegetation spatial occupation, the anisotropic porosity method defines a cell-based porosity for volumetric occupation and an edge-based porosity for flux exchange to capture the flow heterogeneity in space. Under the framework of finite volume method, the model is solved explicitly with a hybrid LTS/GMaTS method and the Open MP techniques for fast modelling. The well-balanced property and accuracy of the developed model have been tested by a series of flume experiments with different vegetation distributions over fixed or mobile beds. In general, both velocity and deposition patterns are well reproduced. It shows that a constant vegetation drag coefficient can lead to numerical solutions of comparable accuracy as those complex empirical relations in the anisotropic porosity modelling. In addition, the stem-scale turbulence could be a critical factor affecting the sediment transport inside and around vegetation patches and its appropriate quantification in the shallow water modelling deserves further research.