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.