  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.
