Potential based , constraint preserving , genuinely multi - dimensional schemes for systems of conservation laws Siddhartha Mishra

We survey the new framework developed in [33, 34, 35], for designing genuinely multi-dimensional (GMD) finite volume schemes for systems of conservation laws in two space dimensions. This approach is based on reformulating edge centered numerical fluxes in terms of vertex centered potentials. Any consistent numerical flux can be used in defining the potentials. Suitable choices of the numerical potentials yield finite-volume schemes which preserve discrete form of constraints such as vorticity and divergence. The schemes are very simple to code, flexible and have low computational costs. Numerical examples for the Euler equations of gas dynamics and the ideal MHD equations are presented to illustrate the computational efficiency of the schemes.