TY - JOUR
T1 - Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations
AU - Liu , Lele
AU - Zhang , Hong
AU - Qian , Xu
AU - Song , Songhe
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 855
EP - 881
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0165
UR - https://global-sci.org/intro/article_detail/nmtma/23644.html
KW - Maximum-principle-preserving, weighted compact nonlinear schemes, parameterized MPP flux limiter, convection-dominated diffusion equations.
AB - <p style="text-align: justify;">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.</p>