Numerical perturbation higher-order accurate reconstruction of quick scheme for the convective-diffusion equation

In this paper some higher-order accurate reconstructionschemes for the convective-diffusion discrete equations, in which theviscous and convection terms are discreted respectively as second-ordercenter and QUICK scheme, are developed by using the numerical perturbationalgorithm presented by Professor Gao Zhi. The reconstruction methods includethe global reconstruction using all node-information in a discrete element,up-stream and down- stream reconstruction using upstream and downstreamnode-information, respectively. By using those two reconstructions, twokinds of numerical perturbation higher-order accurate schemes are obtainedand called as Gao's QUICK scheme (G-QUICK scheme). Simplicity of G-QUICKscheme is the same as QUICK scheme.Gao's algorithm was early used to reconstruct three node schemes of theconvective-diffusion equations. The research in this paper shows that, Gao'salgorithm is also effective for reconstruction of multi-node scheme likeQUICK scheme. Compared with QUICK scheme, G-QUICK schemes for globalreconstruction, up-stream and down-stream reconstructions, have the higherorder accurate and wider stable region. For global reconstruction, G-QUICKschemes and QUICK scheme are conditionally stability; however for the up-and down- stream reconstruction, G-QUICK schemes contain some absolutelysteady schemes. Excellent properties of G-QUICK schemes are proved byanalysis and numerical tests. The G-QUICK schemes of up- and down- streamreconstruction provide a new way for QUICK scheme without artificialviscosity. Multi-node high order accuracy upwind and central schemes havebeen widely used in the calculation of turbulent. New schemes developed inthis paper have the same high order accuracy but the less node, and theiradvantages and effectiveness in calculation of turbulent are worthy offurther study.