Numerical Approximation of One-Dimensional Transport Model Using an Hybrid Approach in Finite Volume Method

Abstract

A finite volume method is a well-known and appropriate approach for numerical approximation of governing problems. This article proposes a finite volume approach to simulate the one-dimensional convection–diffusion transport problem. New expressions for interface approximation are constructed by combining the assumption of step-wise profile and piece-wise linear profile. In addition, a new numerical technique is developed based on these new interface approximations. This new numerical algorithm produces consistent results for numerical approximation of the governing problem and gives second-order accuracy along space and time. In order to justify the effectiveness of our numerical technique, numerical experiments are conducted for various magnitudes of convection and diffusion coefficients. The numerical results of the proposed algorithm are also compared to the finite volume method and the finite difference method. Based on this comparison, our numerical scheme presents stable and highly accurate results compared to the alternatives.