# A high order bound preserving finite difference linear scheme for incompressible flows

## TL;DR

This paper introduces a high-order finite difference scheme with a bound-preserving flux limiter for incompressible flows, offering high resolution and reduced dissipation compared to WENO schemes, suitable for oscillatory problems.

## Contribution

A novel high-order linear scheme with a maximum-principle-preserving flux limiter for incompressible flows, combining efficiency, high resolution, and controlled oscillations.

## Key findings

- Less dissipative than WENO schemes
- High resolution due to Hermite reconstruction
- Effective control of numerical oscillations

## Abstract

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.