Gradient-Adaptive-Sigma (GAS) Grid for 3D Mass-Transport Modeling

Abstract

The accuracy of three-dimensional (3D) mass transport modeling strongly relies on how well the vertical structures of the transport processes are resolved with the model resolution. The widely used vertical “stair-stepped” and topography following sigma (σ)-coordinate systems are fixed in time and space. Hence, these techniques often fail to resolve the details of the time varying, and highly nonlinear, activities in the water column. To better capture the geometrical details of these activities, a new vertical solution-adaptive grid method is introduced in this paper. The method takes into account the gradient variation of a selected variable in the mass transport field as an additional controlling factor in σ-coordinate transformation and so the new transformed grid is called a Gradient-Adaptive-Sigma (GAS) grid. The transformed grid spacing automatically adjusts in time and space according to the local solution gradient of the selected variable and converges in the high gradient regions for better resolution. The solution-adaptive method is implemented in a surface water numerical model to transform Cartesian coordinates into GAS coordinates. The model is established on the basis of an operator splitting scheme coupled with a Eulerian-Lagrangian method. Four numerical experiments describing the sediment transport activities of net entrainment and net deposition, and also pollutant dispersion, are performed with the transformed model. The computed results agree with the laboratory measurements. A comparison between the results computed by the GAS-gridded model and a σ-gridded model show that using the GAS-grid arrangement can improve the solution accuracy by as much as one-fold in regions of high solution gradients.