In multidimensional fluid dynamics, methods based on mesh meet difficulties frequently, especially in problems with multimaterial media and large deformation grids.In this paper, a new meshless Lagrangian finite point method to compute unsteady compressible flows is presented. In this method discrete points are distributed in the physical domain, and are regarded as Lagrangian points with mass, velocity and energy. At a given point, a "cloud" of points in the vicinity are chosen and the relations between them are set. The Lagrangian fluid equations other than the SPH ones are discreted with the Godunov method in which the interface is in a position of connect line between the given point and its neighbors. To enhance robustness and accuracy of the algorithm, more neighbor cloud points are introduced and the least square approximation is facilitated in the simulation. Computed results are good for classical examples.

A series of adaptive corrdinate transformation methods are proposed in which the grid angles are preserved approximately,and the material interface is kept to be Lagrangian description and a minimum difference (in the least-squares sense) between the mesh velocity and the fluid velocity is achieved.The new coordinate system is adapted to important features of flow fields.

Discussion is given on the domain decomposition parallel iterative algorithm,which is aimed at the implicit difference equation under 3-D Cartesian coordination and the error estimates for both the serial and the parallel iteration are provided.The analysis and comparison about the numerical results indicate that the parallel iterative algorithm is highly parallelizable and scalable.

It is well known that lattice Boltzmann methods(LBM) make great success in many computational physics fields,expecially in fluid mechanics.A lattice Boltzmann method with BGK model is developed to solve Burgers equation.Detailed analysis shows that the calculating scheme is a three level nonlinear finite difference one.The maximum value principle has been proved and the existence,uniqueness and stability are also discussed.The computational results agree with second order finite difference solutions very well.

By the design of new parallel algorithm and the organization of grid mapping, a serial code Lared-Ⅰ has been successfully parallelized for numerical simulations of 2-dimension three temperature hydrodynamics with the message passing programming environment. Moreover, a dynamic load balance method is also designed according to the physical and the code executing characteristics, which can significantly improve the parallel performance. The numerical results under both parallel computing environments are given as well.