Author(s): Jingming Hou; Franz Simons; Tobias Busse; Reinhard Hinkelmann
Keywords: Daptive method; Adaptive grid; Transport equation; Shallow water
Abstract: The simulation of flow and transport processes in hydro-and environmental systems has become an important means to assess the impacts of varying boundary conditions such as contaminations, engineering measures or climate change. Therefore, they are an important tool to predict flow and water quality in rivers under current and future conditions. In this contribution, one and two-dimensional flow and transport processes are modeled with the Finite-Volume Method which is applied to quadtree grids and embedded in an object-orientated framework. The low order fully upwind scheme chosen here or coarse grids induce numerical diffusion and numerical dispersion in the concentration distribution, and strongly influence the solution accuracy. To overcome these problems, adaptive methods have been developed for the quadtree-based grid. They aim at high solution accuracy with low computational effort by adapting the numerical solution accuracy through mesh refinement and coarsening based on an adaptive indicator which is a representative difference of the concentration gradient between the object cell and adjacent cells. An appropriate adaptive criterion is determined here in a one-dimensional case by being compared with analytic results, different mesh resolutions, refinement and coarsening levels. The ideal method should be the one with a wide range of refinement levels as well as a low adaptive criterion, which depend both on the problem. The performance of the chosen methods is demonstrated using two examples. One is a quasi one-dimensional channel where a sharp front is spreading and where an analytical solution is available. In the second example, the spreading of a tracer plume in a part of a river is investigated.