Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
On WAF-type schemes for multidimensional hyperbolic conservation laws
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
A simple finite difference scheme for multidimensional magnetohydrodynamical equations
Journal of Computational Physics
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
The &Dgr; • = 0 constraint in shock-capturing magnetohydrodynamics codes
Journal of Computational Physics
Evolution Galerkin methods for hyperbolic systems in two space dimensions
Mathematics of Computation
Vorticity-Preserving Lax--Wendroff-Type Schemes for the System Wave Equation
SIAM Journal on Scientific Computing
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems
Journal of Computational Physics
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
AN APPROXIMATE RIEMANN SOLVER FOR MAGNETOHYDRODYNAMICS (That Works in More than One Dimension)
High Order Fluctuation Schemes on Triangular Meshes
Journal of Scientific Computing
Constraint-Preserving Upwind Methods for Multidimensional Advection Equations
SIAM Journal on Numerical Analysis
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Locally Divergence-preserving Upwind Finite Volume Schemes for Magnetohydrodynamic Equations
SIAM Journal on Scientific Computing
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Vorticity Preserving Finite Volume Schemes for the Shallow Water Equations
SIAM Journal on Scientific Computing
Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws
Journal of Computational Physics
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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 extend our discussion to other classes of genuinely multidimensional schemes. Numerical examples for linear grad advection equations, linear and nonlinear wave equation systems, and the Euler equations of gas dynamics are presented.