Explicit characteristic finite volume method for convection–diffusion equation on rectangular grids

Abstract

An explicit characteristic-based finite volume method (CFVM) for solving two-dimensional scalar convection–diffusion equations is presented. The time-dependent convection–diffusion equation is derived from characteristic coordinates using the characteristic-based scheme, while the finite volume method is employed for deriving the discretized equations. Robustness and accuracy of the method have been evaluated by pure-convection, and convection-dominated diffusion problems. Numerical test cases have shown that the method provides good computational stability and can capture high-gradient solutions.