Semi-Implicit Solution of the Convection-Diffusion Problems with Applications in Fluid Dynamics

摘要

We deal with the time discretization of the system of ordinary differential equations arising from the discontinuous Galerkin discretization of a scalar convection-diffusion equation. We discuss several semi-implicit techniques, which lead to a sufficiently stable scheme and to a necessity to solve only linear problem at each time level. An extension to the system of the Navier-Stokes equations is presented and demonstrated by a numerical example.