Advection-Diffusion Equation on Unstructured Adaptive Grids

Discretizations based on unstructured grids have been widely used in other scientific disciplines for modeling problems bounded by complex geometries. Solution-adaptive techniques are relatively easy to implement on unstructured grids and in addition they provide a convenient way to model the multi-scale spanning nature of atmospheric flows. This paper describes the implementation of a higher-order Godunov-type scheme on unstructured adaptive grids for the advection-diffusion equation in two dimensions. Validation of the numerical scheme and the solution-adaptive technique against exact solutions of benchmark cases is discussed. It is shown that the scheme is conservative, exhibits little numerical diffusion and is well suited for modeling Eulerian transport. The improvement in computational efficiency while maintaining the accuracy of the solution via solution-adaptive techniques is also demonstrated.