Fractional Steps Scheme of Finite Analytic Method for Advection–Diffusion Equation

Abstract

For simply finding local analytic solution, the time derivative in the traditional finite analytic (FA) method is generally replaced with a first-order finite difference approximation as a source term. However, this may induce excessive numerical diffusion, especially for advection-dominated transport problems. In this paper, a fractional steps scheme of the FA method without using the finite difference approximation to time derivative is proposed by applying the one-dimensional FA method whose local analytic solution is obtained from both spatial and time domains, together with the method of fractional steps. Four hypothetical examples, including two-dimensional and three-dimensional cases, are employed to investigate this newly proposed method as compared with the traditional FA method, the optimal unsteady FA method, and the alternating direction scheme of the hybrid FA method. The results show that the fractional steps scheme of the FA method can greatly diminish numerical diffusion and is superior to the other methods compared herein.