The Research Of Numerical Perturbation Algorithm In Computational Fluid Dynamics

Computational ffuid dynamics(CFD) have wide application in many scienceand technology fields, and constructing calculation schemes and algorithm havebeen the research focus of CFD. The numerical perturbation algorithm presentedby Gao Zhi is one of the general method for constructing high-accurate and highresolution CFD schemes, which have excellent properties of high accurate, highresolution, large stable range and high effciency.The numerical perturbation reconstruction schemes (call them Gao's schemesfor brevity) are obtained by operating the equations and reconstruction schemes,introducing the convection law of downstream doing not affect the upstream andeliminating the truncation error of terms in the modified differential equationof reconstruction scheme. Obviously, Gao's schemes of hyperbolic equation, Eu-ler equations, convective-diffusion equation and Navier-Stokes(NS) equations willform a scheme family with a large members. Some important family memberslike three nodes Gao's schemes have been proposed, but many schemes which canbe expected like multi-nodes Gao's schemes have not yet built out.The thesis is divided into two parts:1.Some higher-order accurate reconstruction schemes for the convective-diffusiondiscrete equations, in which the viscous and convection terms are discreted respec-tively as second-order center and QUICK scheme in common use, are developed byusing the numerical perturbation algorithm. The reconstruction methods includethe global reconstruction using all nodes in a discrete element and the up- anddown- stream reconstruction using respectively upstream and downstream nodes,that introduce the convection law of downstream doing not affect upstream intothe reconstruction schemes. By using those two reconstructions, two kinds ofnumerical perturbation higher-order accurate schemes are obtained; call themGao's QUICK scheme (G-QUICK scheme). Simplicity of G-QUICK schemes isthe same as QUICK scheme.Both global reconstruction G-QUICK schemes andQUICK scheme are conditionally stability; however the up- and down- streamreconstruction G-QUICK schemes contain some absolute steady schemes. Excel-lent properties of G-QUICK schemes are proved by analysis and numerical tests.The G-QUICK schemes of up- and down- stream reconstruction provide a new way for QUICK scheme in common use doing not use artificial viscosity.2.Some subsonic-transonic ffows in cavities with different ratio of length todepth are simulated numerically using Gao's upwind finite-volume schemes(GUVS)coupling with compressible and incompressible SIMPLE algorithm in this paper,GUVS is product of reconstructing first order upwind finite volume(FV) schemeby Gao's algorithm. Some subsonic-transonic ffows in cavities with different ratioof length to depth are simulated numerically using Gao's sixth-order upwind FVscheme on structured and unstructured collocated grids. Some excellent numer-ical results are obtained. For examples, the numerical results for subsonic ffowsin rectangle cavity (i.e lid-driven cavity ffows) are quite well agreement with thebenchmark solutions given by Ghia etal using multigrid technique, ffow charac-teristics of subsonic-transonic ffows in cavities with different ratio of length todepth are also presented. Excellent properties of GUVS are proved by analysisand numerical tests.