A modified treatment for pressure boundary conditions in DSMC is shown, The microscale backward-facing gas flow is computed by a partitioned domain DSMC method and a general flow construction is obtained. It is shown that the recirculating flow region attached to the backward-facing step exists in the microscale flow with proper conditions while the region of separation on upper side does not. A discussion about the effect of flow parameters is given and a relationship between reattachment length and Reynolds number is obtained.

A Lagrangian finite element method is ued to simulate a uniformly heated film flowing down an inclined plate. An example with periodic inlet disturbances of different frequencies is computed,and the agreement with the linear stability theory shows that the Lagrangian finite element method has good resolution.The film flow is fully developed to saturated periodic wave,quasiperiodic wave,multipeaked wave and solitary hump.

A high-resolution interface tracking method is applied to simulate compressible multi-fluid flows with general equation of state in one-dimension. It captures the interface by using Level Set technique with conservative numerical discretization at interface. It uses high-order PPM scheme and two-shock approximation for GEOS Riemann problem. Results show that the computation is high-order accurate and there are no numerical oscillation and smearing at multi-fluid interface.

A high order Piecewise Parabolic Method (PPM) is applied to simulate compressible multifluids flows with a stiffened gas equation of state in multi dimensions, which allows high density ratios and strong shock waves. Several test problems are presented for one and two dimensions.

Gas flows driven by pressure in a microchannel are computed with the direct simulation Monte Carlo (DSMC) method. The rarefied effect is observed and slip velocity exists at solid boundaries. Temperature is almost constant in the whole flow field. The Mach number of the flow is very low. Density and pressure vary significantly along the channel while they are nearly invariant transversely. Nonlinearity of pressure distribution along the channel due to compressibility is found and reduces as the Knudsen number increases.

An approach combining the adaptive unstructured grids and the high order Godunov type scheme based on the finite volume method is applied to simulate the evolution of the interface between two layers of fluid with different densities.The research focuses on Richtmyer Meshkov instability and baroclinic effect in the evolution of the interface.The perturbation growth rates of the interface are also presented.