In the framework of diffuse interface method (DIM), an efficient hybrid method for muhiphase flows with large density ratios is proposed. Lattice Boltzmann method is employed to obtain information of flow field. Cahn-Hilliard (C-H) equation is directly solved to identify the interface. In order to maintain stabihty of calculation at large density ratios, convection term of C-H equation is discretized by using second order unwind scheme. Numerical simulations of Rayleigb-Taylor (R-T) instability, bubble rising in liquid and droplet impact on a dry surface are implemented. The results agree well with data in literature.

In order to ensure conservative precision and monotonicity of a remapping algorithm and discontinuity with high resolution, a new kind of conservative RBF remapping algorithm is developed based on radial based function interpolation. Conservative precision is tested with a conservative error remapping algorithm. Numerical results are obtained for smooth and discontinuous functions. Compared with other remapping methods,the method gives good numerical results.

Riemann problems are constructed at interface in front tracking (FT) method for multi-fluid flows to study application of shock limiter.In gas-gas and gas-water problems,shock limiter parameter is selected about 0.3 considering average conservation error,L₁ error and strength of the shock.It is indicated that in order to obtain better solutions the back shock wave should be selected as an original state for Riemann problems at the interface as a shock is close to a material interface.

We summarize conservative remapping algorithms based on ENO (essentially non-oscillatory) interpolation. Three numerical techniques in computational fluid dynamics are discussed:overlapping mesh method, adaptive refinement mesh method and moving mesh method. Physical quantities transfer between meshes. Conservativeness is important, especially in computing shock and contact discontinuity. We propose a remapping algorithm based on ENO which is conservative and accurate in transferring physical quantities between meshes and give numerical examples. It shows that the algorithm has ability of resolving conservative problems with above mesh techniques in computational fluid dynamics.

A finite volume scheme is developed for Lagrangian equations in hydrodynamics.With ENO(essentially non-oscillatory) interpolating polynomials on structure grids,a high accurate finite volume scheme is constructed by modifying a first order finite volume scheme on rectangular meshes.Numerical experiments are made with an adaptive moving mesh and arbitrary Lagrangian-Eulerian method.It shows effectiveness of the method.

The Level-Set discontinuity tracking technology is extended to the simulation of general compressible multimaterial flows.A Level-Set function is used to keep the track of the interface and discontinuity.A conservative high order accurate WENO scheme is employed.The ghost fluids are constructed in the narrow band region with solution of the Riemann problem.The GFM (ghost fluid method) is implemented for the study of material interface and general discontinuity such as detonation discontinuities.The algorithm is applied to simulate multi-material fluid flows and satisfactory numerical results are obtained.

By predicting the real fluid status rather than the ghost fluid status with a Riemann problem,a simple and efficient extension of the ghost fluid method in multi-dimension is introduced. Riemann problems are constructed at the interface and solved to define boundary conditions of fluid on both sides of the interface.Since the Riemann problem solvers describe fluid state reasonably and the normal velocity and pressure are continuous across the interface,a more accurate interface boundary condition is obtained. Conservation error shows that the method incurs minor errors. Numerical experiments show that this method captures the interface and shock waves correctly.

A high-order,high resolution,conservative TVD difference scheme is presented for one dimensional hyperbolic conservation equations.The basic idea is as follows.Firstly,the computation domain is divided into many non-overlapping subdomains,and then each subdomain is further subdivided into small cells according to the required accuracy; Secondly,by the flow direction,flux splitting is introduced,and high-order approximation in the subdomain are used to compute the positive/negative numerical fluxes at cell boundaries.Furthermore,TVD corrections are considered to prevent oscillations near discontinuities from the high-order interpolation.Moreover,by means of high-order TVD Runge-Kutta time discretization,a high-order fully discretization method is obtained.The extension to one dimensional systems is also carried out.Finally,numerical experiments on one dimensional Euler equations are given,and numerical results are satisfactory.

In the research of simulation for problems with large distortion in fluid dynamics, it is often required to re-construct the computational meshes. The technique transferring physical quantities between the two computatioal meshes is called as rezoning (remapping). Based on ENO interpolation idea, in this paper, a new kind of conservative ENO rezoning (remapping) algorithm is developed to structure and unstructured computational meshes. Finally, the numerical results show that the algorithm appears to be effective.

A kind of numerical simulation algorithms for instabilities of fluid interfaces,Ghost Fluid Method, is discussed.The setting of fluid variables in ghost regions is directly based on multiple dimensional cases.Moreover,non-splitting high resolution schemes are used to solve the fluid dynamic equations. At last, the algorithm is applied to the simulation of interface instabilities of fluid dyanmics,and satisfied numerical results are obtained.

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.

It uses a Level Set function to track the motion of a fluid interface in an Eulerian framework.In addition,the use of Ghost cells (actually Ghost nodes in the difference framework) can keep the density profile from smearing out,while still preserving the scheme robust 2-nd easy to program with and accuracy TVD scheme in spacial and two step Runge Kutta methods.In contrast, the references[6][7] allow the density profile smearing out.This method significantly improves the resolution at the contact discontinuity.