Alternating triangular schemes for convection–diffusion problems

Abstract

Explicit–implicit approximations are used to approximate nonstationary convection–diffusion equations in time. In unconditionally stable two-level schemes, diffusion is taken from the upper time level, while convection, from the lower layer. In the case of three time levels, the resulting explicit–implicit schemes are second-order accurate in time. Explicit alternating triangular (asymmetric) schemes are used for parabolic problems with a self-adjoint elliptic operator. These schemes are unconditionally stable, but conditionally convergent. Three-level modifications of alternating triangular schemes with better approximating properties were proposed earlier. In this work, two- and three-level alternating triangular schemes for solving boundary value problems for nonstationary convection–diffusion equations are constructed. Numerical results are presented for a two-dimensional test problem on triangular meshes, such as Delaunay triangulations and Voronoi diagrams.