A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows (Communications in Computational Physics, 2022)
We propose a high order finite difference linear scheme combined with ahigh order bound preserving maximum-principle-preserving (MPP) flux limiter tosolve the incompressible flow system. For such problem with highly oscillatory structure but not strong shocks, our approach seems to be less dissipative and much lesscostly than a WENO type scheme, and has high resolution due to a Hermite reconstruction. Spurious numerical oscillations can be controlled by the weak MPP fluxlimiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guiding-center model and the incompressible Euler system. The comparison between the linearand WENO type schemes, with and without the MPP flux limiter, will demonstrate thegood performance of our proposed approach.
Keywords: Finite difference scheme; high order Hermite reconstruction; MPP flux limiter; incompressible flow; Vlasov-Poisson.