Constraint Preserving Schemes Using Potential-based Fluxes. Ii. Genuinely Multi-dimensional Central Schemes for Systems of Conservation Laws

We propose an alternative framework for designing genuinely multi-dimensional (GMD) finite volume schemes for systems of conservation laws in two space dimensions. The approach is based on reformulating edge centered numerical fluxes in terms of vertex centered potentials. Any consistent numerical flux can be used to define the potentials. Suitable choices of potentials result in schemes that preserve discrete forms of interesting constraints like vorticity and divergence. The schemes are very simple to code, robust and have low computational costs. Numerical examples for scalar conservation laws, system wave equations and Euler equations of gas dynamics are presented to illustrate the efficiency of the schemes.