PERTURBATIONAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION

作     者：Gao, Zhi Hu, Li-Min 

作者机构：Lab. of High Temp. Gas Dynamics Inst. of Mech. Chinese Acad. of Sci. Beijing 100080 China 

出 版 物：《Journal of Hydrodynamics》 (水动力学研究与进展B辑（英文版）)

年 卷 期：2002年第14卷第2期

页      面：51-57页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：ThisresearchwassupportedbytheNationalNaturalScienceFoundationofChina .(GrantNo:10 0 32 0 5 0 ) 

主　　题：Diffusion Finite difference method Incompressible flow Navier Stokes equations Perturbation techniques Reynolds number Two dimensional 

摘      要：The Perturbational Finite Difference (PFD) method is a kind of high-order-accurate compact difference method, but its idea is different from the normal compact method and the multi-nodes method. This method can get a Perturbational Exact Numerical Solution P(PENS) scheme for locally linearized Convection-Diffusion (CD) equation. The PENS scheme is similar to the Finite Analytical (FA) scheme and Exact Difference Solution (EDS) scheme, which are all exponential schemes, but PENS scheme is simpler and uses only 3,5 and 7 nodes for 1-, 2- and 3-dimensional problems, respectively. The various approximate schemes of PENs scheme are also called Perturbational-High-order-accurate Difference (PHD) scheme. The PHD schemes can be got by expanding the exponential terms in the PENS scheme into power series of grid Reynolds number, and they are all upwind schemes and remain the concise structure form of first-order upwind scheme. For 1-dimensional (1-D) CD equation and 2-D incompressible Navier-Stokes equation, their PENS and PHD schemes were constituted in this paper, they all gave highly accurate results for the numerical examples of three 1-D CD equations and an incompressible 2-D flow in a square cavity.