Maximum-Principle-Preserving High-Order Conservative Difference Schemes for Convection-Dominated Diffusion Equations

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 highorder 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 convectiondominated diffusion and incompressible flow problems.