Combined Adaptive Meshing Technique and a Characteristic-based Finite Volume Element Method for Solving Convection-Diffusion-Reaction Equation

A finite volume element method is combined with an adaptive meshing technique to solve the two-dimensional unsteady convection-diffusion-reaction equation. The characteristic-based scheme is used to derive the governing equation and then the finite volume method is employed to discretize the characteristic equation. Concept of the weighted residual method in the finite element method is applied to evaluate the gradient quantity at the cell faces. Finally, an adaptive meshing technique is applied to further improve the solution accuracy, and to minimize the computational time and computer memory requirement. The efficiency of the combined method is evaluated by the examples of pure-convection, convection-diffusion, convection-diffusion, and diffusion-reaction problems