Finite volume method for convection–diffusion–reaction equation on triangular meshes

Abstract

AbstractAn explicit high‐resolution finite volume method is proposed for solving a two‐dimensional convection–diffusion–reaction equation on triangular meshes. Taylor's series expansion is used to formulate the higher‐order reconstruction of unknown quantities at the cell faces. The concept of the finite element technique is applied to estimate the gradient quantities at the cell faces. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. The robustness and the accuracy of the method have been evaluated by using the available analytical and numerical solutions of the two‐dimensional pure‐convection, convection–diffusion, and convection–diffusion–reaction problems. Copyright © 2008 John Wiley & Sons, Ltd.