Second order velocity reconstruction on unstructured grids
Summary
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.