Mixed cells are introduced in multi-material arbitrary Lagrangian-Eulerian (MMALE) method to capture material interfaces. An energy-preserving closure model on mixed cells for diffusion equation is proposed. Based on closure model, a method for coupling multiple material radiation diffusion simulation and hydrodynamics MMALE simulation is proposed. Numerical experiment with analytical solution shows accuracy of the method for diffusion equation. Results of Sedov and spherical implosion problems show that the method is effective and robust. Comparisons with traditional Lagrangian method prove advantages of the method.

A 2D cell-centered multi-material arbitrary Lagrangian-Eulerian(MMALE) method based on moment of fluid(MOF) interface reconstruction is developed. Hydrodynamic equations are discretized and solved by cell-centered Lagrangian scheme. Tipton's pressure relaxation model is adopted as closure model for mixed cells. MOF method is simplified and improved to reconstruct interface in mixed cells. A conservative integral remapping algorithm based on cell-intersection is used in remapping phase. Several numerical examples are given, such as 2D periodic vortex problem, Sedov problem, interaction of a shock wave with an helium bubble,a strong water shock impacting on a cylindrical air bubble in water,2D Rayleigh-Taylor instability, etc.It shows that the method is of second order accurate, and is capable of computing problems involving large density and/or pressure ratios across interface. Its robustness is better than that of staggered MMALE method and it is applicable to complex multi-material hydrodynamic problems.

We present a second order cell-centered finite volume method of 2D Lagrangian hydrodynamics based on semi-discrete framework.Velocity and pressure on vertex of a cell are computed with characteristics theory,Then,they are used to compute numerical flux through cell interface by trapezoidal integration rule.With a reconstruction procedure,the method is extended to second order.Several numerical experiments confirm convergence and symmetry of the method.The method permits large CFL numbers and can be applied on structured and unstructured grids.It is robust in multi-material flow simulations.

A multi-material arbitrary Lagrangian-Eulerian method is developed.Fluid equations are discretized by a compatible finite element method.A two-dimensional closure model for multi-material cells is presented.It is based on approximate Riemann solver HLLC and isentropic assumption.Interface in mixed cells is constructed by MOF methods.An accurate,conservative integration remapping method is used as mesh is rezoned.Example calculations are presented to show accuracy and robustness of the method.

We present an explicit compatible finite element method for fluid dynamics problems in three-dimensional Cartesian geometry.Trilinear brick elements with a staggered-grid placement of the spatial variables are used to discretize fluid equations.An edge-centered artificial viscosity whose magnitude is regulated by local velocity gradients is used to capture shocks.Subzonal perturbed pressure is adopted to resist spurious grid motions.Artificial viscosity forces and subzonal pressure forces agree well with general compatibility.Numerical examples show accuracy and robustness of the method.

ALE (Arbitrary Lagrangian Eulerian) finite volume method for compressible fluid flows on moving quadrilateral meshes in two dimensional planar coordinates and axisymmetric coordinates is studied.A vertex-centered finite volume method and an HLLC numerical flux adapted to various equations of state are employed.A second order accuracy in space is achieved by using a reconstruction of primitive variables based on WENO approach.An explicit two-stage Runge-Kutta time-stepping scheme is used in discretization of time.The method offers accurate and robust solutions in capturing strong shock,contact discontinuities and material interface on arbitrarily moving grids.