TY - JOUR
T1 - A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows
AU - Zhang , Guoliang
AU - Xiong , Tao
JO - Communications in Computational Physics
VL - 1
SP - 126
EP - 155
PY - 2022
DA - 2022/07
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2021-0248
UR - https://global-sci.org/intro/article_detail/cicp/20790.html
KW - Finite difference scheme, high order Hermite reconstruction, MPP flux limiter, incompressible flow, Vlasov-Poisson.
AB - <p style="text-align: justify;">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 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.</p>