A characteristic/finite element algorithm for time-dependent 3-D advection-dominated transport using unstructured grids

Abstract

An algorithm based on operator splitting has been successfully implemented for solving unsteady, advection-dominated transport problems in 3-D. Specifically, the general operator-integration-factor splitting method of Maday et al. is applied to the unsteady advection–diffusion equation with source/sink terms. The algorithm incorporates a 3-D characteristic Galerkin scheme to treat advection, and a standard Galerkin treatment of the diffusion and source/sink terms. Up to third-order operator splitting was implemented and validated against several analytical solutions. The algorithm showed the expected error behaviour and good performance in modeling advection-dominated transport problems. The practical utility and effectiveness of the proposed numerical scheme was further demonstrated by solving the Graetz–Nusselt problem, i.e. high Peclet number mass/heat transport in a fully developed pipe flow.