Divergence- and curl-preserving prolongation and restriction formulas
Journal of Computational Physics
Finite volume evolution Galerkin methods for nonlinear hyperbolic systems
Journal of Computational Physics
Journal of Computational Physics
Discrete, vorticity-preserving, and stable simplicial fluids
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Vorticity-preserving schemes for the compressible Euler equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Vorticity Preserving Finite Volume Schemes for the Shallow Water Equations
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
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In numerical solutions of fluid flow, vorticity can be generated by truncation errors. We analyze this phenomenon for linearized equations and give conditions for preventing it. The Lax--Wendroff method that meets these constraints is essentially unique, although there are two distinct interpretations, and also turns out to have optimal properties regarding stability and truncation error. The extension of the scheme to unstructured grids is given, together with some discussion of practical problems to which these schemes might bring improvement.