PERTURBATIONAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION |
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作者单位: | Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, China
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基金项目: | ThisresearchwassupportedbytheNationalNaturalScienceFoundationofChina .(GrantNo:10 0 32 0 5 0 ) |
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摘 要: |
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PERTURBATIONAL FINITE DIFFERENCE SCHEME OF CONVECTION-DIFFUSION EQUATION |
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Authors: | Gao Zhi HU Li-min |
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Abstract: | 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 (PENS) scheme for locally linearlized 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 Renold 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. |
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Keywords: | perturbational finite difference method convection-diffusion equation perturbational exact nemerical solution scheme perturbational high-order-accurate difference scheme |
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