Constraint Preserving Schemes Using Potential-Based Fluxes. I. Multidimensional Transport Equations (PREPRINT)

The authors consider constraint-preserving multidimensional evolution equations. A prototypical example is provided by the magnetic induction equation of plasma physics. The constraint of interest is the divergence of the magnetic field. They design finite volume schemes that approximate these equations in a stable manner and preserve a discrete version of the constraint. The schemes are based on reformulating standard edge centered finite volume fluxes in terms of vertex-centered potentials. The potential-based approach provides a general framework for faithful discretizations of constraint transport and they apply it to both divergence-preserving as well as curl-preserving equations. The authors present benchmark numerical tests which confirm that their potential-based schemes achieve high resolution while being constraint preserving.