Constraint Preserving Schemes Using Potential-Based Fluxes I Multidimensional Transport Equations (Communications in Computational Physics, 2011)
We consider constraint preserving multidimensional evolution equations.A prototypical example is provided by the magnetic induction equation of plasmaphysics. The constraint of interest is the divergence of the magnetic field. We designfinite volume schemes which approximate these equations in a stable manner andpreserve a discrete version of the constraint. The schemes are based on reformulatingstandard edge centered finite volume fluxes in terms of vertex centered potentials.The potential-based approach provides a general framework for faithful discretizationsof constraint transport and we apply it to both divergence preserving as well as curlpreserving equations. We present benchmark numerical tests which confirm that ourpotential-based schemes achieve high resolution, while being constraint preserving.