A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem with highly oscillatory struc-ture but not strong shocks, our approach seems to be less dissipative and much less costly than a WENO type scheme, and has high resolution due to a Hermite recon-struction. Spurious numerical oscillations can be controlled by the weak MPP flux limiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guiding -center model and the incompressible Euler system. The comparison between the linear and WENO type schemes, with and without the MPP flux limiter, will demonstrate the good performance of our proposed approach.