Local mesh refinement

Direct Numerical Simulation of the flow around an object is one of the most challenging applications of Computation Fluid Dynamics. For these simulations a very efficient and robust finite volume discretization method of the Navier-Stokes equations has been developed at the University of Groningen over the years. In the original version of the method the equations are discretized with a finite volume scheme on a regular grid. This discretization has the disadvantage that refinement in a desired region of the computational domain also alters the grid outside this region, as grid lines are continued to the boundary of the computational domain. Through this inefficient behaviour, regular grids are a major restriction. Local mesh refinement can be the solution to this problem. In this Master's thesis the development of a general applicable local mesh refinement method is described. First, the discretization of the Navier-Stokes equations on regular grids will be explained. Then local mesh refinement will be introduced and in particular the discretization at the boundary of the refinement. The main property of the discretization is energy conservation. We will examine if it is possible to conserve mass, momentum and energy also at the boundary of the refinement.