Constraint Preserving Schemes Using Potential-Based Fluxes. II. Genuinely Multidimensional Systems of Conservation Laws

@article{Mishra2011ConstraintPS,
title={Constraint Preserving Schemes Using Potential-Based Fluxes. II. Genuinely Multidimensional Systems of Conservation Laws},
author={Siddhartha Mishra and Eitan Tadmor},
journal={SIAM J. Numerical Analysis},
year={2011},
volume={49},
pages={1023-1045}
}

We introduce a class of numerical schemes that preserve a discrete version of vorticity in conservation laws which involve grad advection. These schemes are based on reformulating finite volume schemes in terms of vertex centered numerical potentials. The resulting potential-based schemes have a genuinely multidimensional structure. A suitable choice of potentials leads to discrete vorticity preserving schemes that are simple to code, computationally inexpensive, and proven to be stable. We… CONTINUE READING