Solving convection-diffusion-reaction equation by adaptive finite volume element method

A finite volume element method is combined with an adaptive meshing technique to solve the two-dimensional unsteady convection-diffusion-reaction equation. The finite volume method is used to derive the discretized equations while concept of the finite element technique is applied to determine the gradient quantities at cell faces. Second-order accuracy in both space and time are achieved by applying the Taylor’s series expansion along the local characteristic lines. 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 adaptive finite volume element method is evaluated by the examples of pure-convection, convection-diffusion, convection-reaction, and diffusion-reaction problems.