Optimizing finite difference schemes in spectral space is important for numerical simulations in unsteady flow and aeroacoustics.It is proved that optimized schemes are not always better than high order schemes(in the sense of Taylor expansion).There exists a distance R_cr.Only before the numerical wave traveling this distance,its accumulating error is less than that of a higher order scheme.Beyond this distance,the regularity is reversed.This distance is called here the critic distance of an optimized scheme.It is necessary to control this distance in scheme optimizing.The conventional optimizing objective functions are based on amplification factor revealing the error after one time step,by which it is impossible to specify this distance.In this paper,a new class of objective functions is developed based on accumulating errors,which can control the critic distance directly.

A multispecies,multispeeds lattice Boltzmann model is presented to study the mass diffusion properties.The diffusion equations are derived by the Chapman-Enskog method.The one dimensional simulations for the sinusoidal concentration distributions are compared with the theoretical results,showing good agreement.The numerical simulations for 2-D convection diffusion problems are also presented.

A new reconstruction method for the difference of primitive function derivation is developed on structure meshes.Such a scheme is based on a finite volume discretization.It achieves 3-order spatial accuracy with upwind compact difference.Numerical experiment of transonic channel flow is presented and discussed.

The nontraditional method of space time conservation element and solution element (CE/SE), developed by chang S C in 1995, is modified. A new constructing method is used to obtain the calculating schemes. These new schemes not only have all the features which the CE/SE method has, but also are simpler, more accurate and have very high resolution of discontinuities.

A derivate's formula is presented based on the analytical discrete method and can achieve arbitrary order of accuracy firstly.It is combinated with Roe's flux differential splitting technique and high accuracy flux filter midmod,to construct a kind of nonoscillatory shock-capturing method with high order of accuracy and high resolution.

One kind of Generalized Finite Element Method-Taylor-Galerkin has been improved on convergences of velocity and stability.Using the improved method two dimensional transonic flow in turbomachinery is studied.Numerical results compared with that of experiment exhibit the advantages of this method.

This paper presents an unfactored efficient algorithm for 3-D Euler equationsbased on the implicit flux-splitting and the line Gauss-Seidel iteration. In the algorithm the explicit terms on the right side of the discretization equation are treated in second order accuracy and to solve the implicit discretization equation one back-and-forth sweep in the main flow direction is taken and an alternating direction line G-S interation is carried out in the other two directions. The numerical calculations of 3-D transonic cascade inviscid blow tave shown that the algorithm has a quite high convergent rate.