Maximum principle preserving space and time flux limiting for diagonally implicit Runge-Kutta discretizations of scalar convection-diffusion equations (Q2162336)

The authors present two techniques to obtain maximum principle preserving (MPP) numerical schemes for scalar nonlinear convection-diffusion partial differential equations. The approach followed here is similar to that one of \textit{D. Kuzmin} et al. [J. Sci. Comput. 91, No. 1, Paper No. 21, 34 p. (2022; Zbl 07488731)] which dealt with explicit methods for hyperbolic problems. Both methodologies are based on combining a low-order MPP scheme with a high-order scheme, limiting the contribution from their difference. The study presented here is focused on using finite volumes in space and Runge-Kutta methods in time but the limiters developed here could be used with a wide range of space and time discretizations. Using these limiters with appropriate discretizations allows to obtain a scheme whose local error is of any desired order. That is, the methods are MPP for time steps of any size. Some numerical tests are presented to show the desirable properties of the resulting schemes.