An explicit characteristic finite volume element method for non-divergence free convection–diffusion-reaction equation

Abstract

A second-order accurate characteristic-based finite volume element method, for analyzing time-dependent scalar convection–diffusion-reaction equation in two dimensions, is presented. The concept of the characteristic-based scheme is applied to solve the convection-diffusion-reaction equation. The finite volume method is employed to establish the discretized equations for the spatial domain, while the weighted residuals finite element technique is used to estimate the gradient quantities at the cell faces and cell-centered of the control volume. Numerical test cases have shown that the method reduces spurious oscillations and does not require an explicit artificial diffusion for improving the solution stability. The efficiency, robustness and convergence order of the method are investigated by using available analytical and numerical solutions of convection–diffusion–reaction problems.