A high order bound preserving finite difference linear scheme for incompressible flows
For computational fluid dynamics researchers, this provides a more efficient and less dissipative alternative to WENO schemes for incompressible flows with oscillatory structures.
The paper proposes a high order finite difference linear scheme with a bound-preserving MPP flux limiter for incompressible flows, achieving less dissipation and lower cost than WENO schemes while maintaining high resolution. Numerical tests on Vlasov-Poisson, guiding-center, and incompressible Euler systems demonstrate good performance.
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 structure 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 reconstruction. Spurious numerical oscillations can be controlled by the 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 will demonstrate the good performance of our proposed approach.