We introduce asymptotic order of convergence,asymptotic range of convergence and concepts under behavior of Lagrangian computations.We also introduce grid convergence index to Lagrangian computation,and give a program using GCI method.These concepts and methods are used to measure computed values away from numerical asymptotic values.

We present a closed void interface method for computational models with void interface in multi-material problems.It simulates void successfully in complicated engineering.It bases on a technique of changeable mesh topology.It avoids using a straight line to replace a curve in traditional method,and overcomes difficulty in solving contact points.Numerical simulations confirm that the technique is effective.It shows characteristic of no void connectivity.

We present a reconection-based Lagrangian+rezone(LR) method,in which connectivity of meshes can be changed in a rezone phase in order to handle geometric intersection.The method maintains more Lagrangian features of meshes than standard LR methods.Numerical examples demonstrate that the method is more robust for large defomations.It shows predictive capabilities of reconnection-based LR method.

Computing methods for perturbation corner forces in electron pressure,ion pressure and photon pressure are investigated.We propose two kinds of subzonal pressure method for Lagrangian algorithm of two-dimensional three-temperature radiation hydrodynamics.Numerical tests show that both methods work well in eliminating unphysical deformation of Lagrangian mesh.

High-energy explosive detonation diffraction is simulated with a 2D Lagrangian unstructured mesh detonation fluid program. With EOS of JWL and trinomial reaction rate, numerical result by Lagrangian program agrees with experimental result qualitatively. Phenomena of whirlpool is well simulated. Desensitization is added to reaction rate in simulation of dead zone in insensitive high explosives detonation diffraction. The dead zone is captured. The result agrees with reported data qualitatively.

With artificial viscosity and total variation diminishing advection limiter, the edge-centered artificial viscosity with structure zones is extended to unstructured grids, The limiter is constructed by neighbor edges determined by maximum angle choice. The edge-centered artificial viscosity is compared with the zone-centered artificial viscosity. Numerical results demonstrate accuracy and efficiency of the edgecentered artificial viscosity in capturing shock discontinuous.

The subzonal pressure is obtained with subzonal Lagranian masses and corresponding densities. It results in subzonal corner forces and eliminates hourglass motion and spurious vorticity.We extend the compatible Lagranian hydrodynamics algorithm including subzonal pressures to unstructured zone and develope the code.Numerical examples of Saltzman piston demonstraste that this algorithm captures shock discontinuity,eliminates hourglass motion and restraines spurious vorticity accuratly and efficiently.

Based on Noh's artificial viscosity with artificial heat flux method(Q & H),we present a Q & H scheme on arbitrary n-polygon meshes.Noh's Q & H on structured meshes is extended to unstructured meshes in two dimensions.Numerical results of Noh's problem and collision of two metals show that the Q&H method on unstructured meshes eliminates wall heating effectivly.

The moving least squares particle hydrodynamics (MLSPH) is presented and a 1D MLSPH algorithm is discussed.To reduce oscillations near contact discontinuities,two meshfree Riemann problem initial value methods with different accuracy are introduced.The effect of contact interaction between particles is decreased by the Riemann solver.Efficiency of the method is demonstrated by numerical tests of a 1D shock tube.

A scheme for unstructured quadrilateral mesh generation based on Delaunay triangulation is presented.With a front edge definition we mark a triangle mesh in the front edge.According to triangle mesh shape and directionality two triangular meshes are merged into a quadrilateral mesh. A 100% quadrilateral mesh obtained converts a quad-dominant to an allquad mesh with mesh conversion templates.Numerical results are shown.

A discrete conservative remapping algorithm based upon refinement and numerical integrals,named particle remapping algorithm,is presented.The mass density distribution is chosen as either a piecewise constant with first-order accuracy or a piecewise linear distribution with second-order accuracy.It results in a first-order and a second-order algorithm.The density gradient is evaluated by an area average method with a piecewise linear distribution.On a staggered mesh,in which velocity is vertex-centered,an auxiliary mesh is introduced,and the velocity is remapped.The particle remapping algorithm can be applied to a structured or an unstructured mesh.It does not require a one-to-one mapping between the old and the new meshes.Numerical results show that the first-order algorithm is robust but has an excessive diffusion.The second-order one is better in shape-preservation but violates the monotonicity sometimes.To improve the monotonicity,a conservative mass repair algorithm for structured grids is extended to unstructured grids preserving upper and lower bounds of the density.Several remapping results are presented and the errors are analyzed.

A new method to generate a quasi-equal distribution of particles on arbitrary domains is provided. Based on an advancing front mesh generation method, triangles are formed at the boundary. These triangle center-points are used for the boundary condition of the Delaunay mesh generation method which generates inward triangles. All vertices of triangles are the particles in meshfree methods. An adaptive method is given to readjust distribution of particles, according to the gradient of fluid density.

Conservative scheme in Lagrangian coordination is applied to compute multicomponent fluid dynamics, in which numerical flux of one order scheme is used near interface, while numerical flux of high resolution scheme is adopted in other areas. This scheme not only remains good high resolution, but also eliminates the oscillations due to common conservative scheme.

The critical temperature and the ground state fraction of weakly interacting Bose-Einstein condensation in a harmonic potential trap are calculated with numerical method. The result indicates that both are decreasing with the scattering length increasing. But, there is only a difference about 0.4% between it and that of ideal case.