Second order velocity reconstruction on unstructured grids

Abstract

The new shallow water solver D-Flow FM is being developed at the Deltares research in- stitute. It employs a discretization method on unstructured staggered grids, which requires reconstructing a velocity vector in the center of the cell. The currently employed first order method as developed by Perot forces the use of fine and/or regular grids for the modelling of advection and diffusion. To take full advantage of unstructured grids, a second order velocity vector reconstruction method is required. In this thesis, I will derive several second order meth- ods: corrections for Perot, explicit least squares and a hybrid method. We derive discretization methods for advection and diffusion, study all methods in a simplified model in Matlab and determine their convergence behaviour. One of the second order velocity reconstruction meth- ods is also studied in the shallow water solver D-Flow FM. Second order velocity reconstruction turns out to be better than Perot’s method but it needs a second order advection method for the best results.