We propose a method for BN two-phase flow containing non-conservative terms. In microscopic aspect, a GKS model which matches with the BN model is constructed. Numerical fluxes are obtained with integrating particle velocity distribution function. And non-conservative terms are explicitly introduced into evolution and construction of numerical fluxes. Non-conservative terms are well handled. This method avoids complex iterative process of Riemann solver. It has high calculation efficiency. Numerical tests show high precision.

We present an explicit compatible finite element method for fluid dynamics problems in three-dimensional Cartesian geometry.Trilinear brick elements with a staggered-grid placement of the spatial variables are used to discretize fluid equations.An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks.Subzonal perturbed pressure is adopted to resist spurious grid motions.Artificial viscosity forces and subzonal pressure forces agree well with general compatibility.Numerical examples show accuracy and robustness of the method.

Variational methods are used in a unified coordinate system.The mesh spacing, smoothness,orthogonality and regularity of grids are considered to obtain an elliptic equation for h.Typical examples demonstrate that it is possible to use variational methods in a unified coordinate system,and the distribution of h satisfies different boundary conditions.

It assesses the Rayleigh inverse-iteration method and boundary layer asymptotic expansion method, and uses them into the stability equations of compressible boundary layer and the numerical method for forecasting the transition point. It gives also a stability analysis on the first mode of the boundary layer of flat plane and a forecasting of transition point. Results are discussed and compared with observations.