An Explicit Finite Volume Element Method without an Explicit Artificial Diffusion Term for Convection-Diffusion Equation on Triangular Grids

Abstract

A high-resolution finite volume method for solving two-dimensional convectiondiffusion equation on triangular meshes is presented. The concept of the finite element technique is applied to estimate the gradient quantities at the cell faces. It is shown that the method does not require any artificial diffusion to improve the solution stability. The robustness and accuracy of the method have been evaluated by using available analytical and numerical solutions of two-dimensional pure-convection and convection-diffusion problems.