The RKDG(Runge-Kutta Discontinuous Galerkin) finite element method,the Level Set method and the Ghost Fluid method are applied to compressible multimedia fluids.We discretizes Euler equations,the Level Set equation and the reinitialization equation by a DG(Discontinuous Galerkin) method in space and by a Runge-Kutta method in time.Two dimensional compressible two-fluid flows such as air-air,air-liquid are computed.High resolution ratio computational results are obtained.

The RKDG finite element method, Level Set method and modified Ghost Fluid method with Isentropic fix are used to simulate a one-dimensional compressible multicomponent Euler equation. A third-order accurate RKDG finite element method is used to solve the Euler equation, the Level Set equation and the re-initiation equation. Numerical tests on one-dimensional compressible two-fluid flows are made and satisfactory results are obtained.

Two kinds of algebraic multigrid (AMG) algorithms with three-dimensional equal algebraic structures are constructed on the basis of a two-dimensional coarsing technique.The AMG method and the corresponding algebraic multigrid-preconditioned CG method are applied to elliptic boundary value problems with smooth coefficients and anisotropic problems.Numerical results show that the AMG algorithm is efficient and robust.

The discontinuous finite element method with first, second and third order accuracy on triangular meshes on two-dimensional domain is applied to simulate hydrodynamic equations. The calculation results are compared with those from difference methods. It is reckoned that the discontinuous finite element method has advantages in solving hydrodynamic problems with complicated boundary conditions or a domain with a complicated boundary.

Two numerical schemes of discontinuous finite element methods are presented for Hamilton Jacobi equations which are obtained by using the different basic functions. The numerical solutions of these schemes converge to weak solutions of the Hamilton Jacobi equation under some conditions. Numerical tests given illustrate the accuracy and resolution of discontinuity for the two different schemes.

Computation of three dimensional fluid interface instability with random perturbation is performed on a 8 CPU personal parallel computer system.The parallel computation platform is a message passage interface (MPI).A second order TVD scheme with Ghost method is applied with a fully parallel algorithm to the 3D Euler equations.Level Set function is used to track the motion of a fluid interface in an Eulerian framework.Buffer zone and data communication are discussed.The number of computation meshes is about 1 million.Bubble evolution with random perturbation in Rayleigh Taylor instability is obtained by numerical simulation.

In the numerical simulation of the interfacial instability, the schemes in [1,4~8] were limited probiems in one medium with different densities or two media with homologous adiabatic exponent.If the schemes are used in computing the disturbance of different medium interfaces with homologous adiabatic exponent, the physical guantities on interfaces may give rise to nonphysical oscillation.To overcome the problem, this paper introduces the front tracking scheme ^[2] into the Level Set method, name y the contact discontinuous boundary conditions are coercively added on interfaces so that the nonphysical oscillation is avoided.The evolution of Rayleigh-Taylor instability is examined by the three-dimensional TVD/AC program under the single wave.The disturbed figures with time are given.

A scheme is hroposed for solving hyperboilc conservation laws by the Taylor-Galerkin finite element method. The scheme is obtained by discretizing hyperbolic conservation laws related to the Hamilton-Jacobi's equations. The scheme satisfies the TVD properties under the isometry meshes by modifying the numerical flux, whose idea is from the difference scheme construction. Numerical examples are given.