@Article{NMTMA-17-855, author = {Liu , LeleZhang , HongQian , Xu and Song , Songhe}, title = {Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2024}, volume = {17}, number = {4}, pages = {855--881}, abstract = {
This paper proposes a high-order maximum-principle-preserving (MPP) conservative scheme for convection-dominated diffusion equations. For high-order spatial discretization, we first use the fifth-order weighted compact nonlinear scheme (WCNS5) for the convection term and the sixth-order central difference scheme for the diffusion term. Owing to the nonphysical oscillations caused by the high-order scheme, we further adopt a parameterized MPP flux limiter by modifying a high-order numerical flux toward a lower-order monotone numerical flux to achieve the maximum principle. Subsequently, the resulting spatial scheme is combined with third-order strong-stability-preserving Runge-Kutta (SSPRK) temporal discretization to solve convection-dominated diffusion problems. Several one-dimension (1D) and two-dimension (2D) numerical experiments show that the proposed scheme maintains up to fifth-order accuracy and strictly preserves the maximum principle. The results indicate the proposed scheme’s strong potential for solving convection-dominated diffusion and incompressible flow problems.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2023-0165}, url = {http://global-sci.org/intro/article_detail/nmtma/23644.html} }