HIGHER-ORDER ACCURATE,NON-OSCILLATORY,THREE-NODES CENTRAL DIFFERENCE SCHEME FOR THE CONVECTIVE-DIFFUSION EQUATION CONSTRUCTED BY USING PHYSICAL VISCOSITY
Several higher-order accurate, non-oscillatory, three-nodes central difference schemes for the convective-diffusion equation are given by perturbationally reconstructing the diffusion scheme in the second-order accurate central difference scheme (2-CDS). Excellent properties of higher-order accurate and high resolution of the present new schemes (diffusion perturbation schemes, DPS) are verified by theoertical analyses and three numerical tests which include one-dimensional linear and non-linear and two-dimensional convective-diffusion equations. In all numerical tests, the 2-CDS oscillates and diverges on coarse grids, while part of DPS do not oscillates and can capture discontinuities with high resolution. The mean square root L2 errors of all DPS are greatly less than those of 2-CDS in all numerical tests. The DPS are the results of introducing diffusion-motion law (i. e. physical viscosity smoothing out space-distribution of diffusion quantities) into 2-CDS. The present method is obviously different from the well-known those of constructing high-order accurate and high resolution schemes. In addition, we prove that DPS are completely consistent with those schemes of introducing convection-motion law (i. e. law of that the downstream does not affect the upstream) into 2-CDS, to show that the perturbational operation to 2-CDS not only raises the scheme's accurate and stability but also reveals intrinsic relation between the convective discrete scheme and diffusion discrete scheme, and that the upstream-downstream splitting is a very useful method for reconstructing high-order accurate, high resolution CFD scheme without artificial viscosity or limiter.
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