In order to make conventional implicit algorithm to be applicable in large scale parallel computers,an interface correction method is introduced to solve the particle transport S_N equations.Domain decomposition is adopted in the computational domain.On the interface,an upwind explicit scheme is applied to give an incident boundary condition,which enables the subdomain problem iterated independently.The interface values are updated by an implicit scheme concurrently in iteration.The scheme shows good precision,parallelism and simplicity in numerical experiments.

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.

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.