Combined adaptive meshing technique and finite volume element method for solving convection–diffusion equation

Abstract

A finite volume element method for solving the two-dimensional scalar convection–diffusion equation is presented. The finite volume method is used to derive the discretized equations for the convection–diffusion equation, while the finite element technique is applied to determine the gradient quantities at cell faces. Second-order accuracy in both space and time are achieved by applying the Taylor’s series expansion along the local characteristic lines. An adaptive meshing technique is incorporated to further improve the computed solution accuracy. Four numerical test cases are presented to evaluate the performance of the combined method. These test cases are the pure-convection and convection-dominated problems.