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Volume 32, Issue 1
A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

Guoliang Zhang & Tao Xiong

DOI: 10.4208/cicp.OA-2021-0248

Commun. Comput. Phys., 32 (2022), pp. 126-155.

Published online: 2022-07

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  • 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 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.

  • Keywords

Finite difference scheme, high order Hermite reconstruction, MPP flux limiter, incompressible flow, Vlasov-Poisson.

  • AMS Subject Headings

65M06, 65M20, 35M13

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-32-126, author = {Zhang , Guoliang and Xiong , Tao}, title = {A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows}, journal = {Communications in Computational Physics}, year = {2022}, volume = {32}, number = {1}, pages = {126--155}, 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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0248}, url = {http://global-sci.org/intro/article_detail/cicp/20790.html} }
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 -

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.

Zhang , Guoliang and Xiong , Tao. (2022). A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows. Communications in Computational Physics. 32 (1). 126-155. doi:10.4208/cicp.OA-2021-0248
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