Combined finite volume and finite element method for convection-diffusion-reaction equation

Abstract

A combined finite volume and finite element method is presented for solving the unsteady scalar convection-diffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusion-reaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor’s series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convection-diffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability.