Application of Nonlinear Monotone Finite Volume Schemes to Advection-Diffusion Problems

Abstract

Two conservative schemes for the nonstationary advection-diffusion equation featuring nonlinear monotone finite volume methods (FVMON) are considered. The first one is an operator-splitting scheme which uses discontinuous finite elements for the advection operator discretization and FVMON for the diffusion operator. The second one introduces another type of FVMON and is implicit second-order BDF in time. A brief description of the schemes and their properties is given. A numerical study is conducted in order to check their convergence and to compare them with conventional methods. © Springer-Verlag Berlin Heidelberg 2011.