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.

Sub-division method based on support operator is used to solve diffusion equation with three-dimensional non-conformal mesh and non-planar mesh.Numerical experiments show that the method is second-order accurate on general non-conformal mesh.For curved-face mesh and non-planar-face mesh, the method is more accurate than traditional plane-approximation method.For non-conformal orthogonal mesh, the method can obtain accurate solutions of linear problems.

In distributed parameter contact algorithm on three-dimensional contact surface,a method for smoothing three-dimensional contact surface is developed. In the method,a smooth contact surface is interpolated with bi-cubic parametric patches. A bi-cubic parametric patch is defined by using local information such as coordinates and normals of vertexes of patch. The smoothing technique provides an accurate representation of actual contact surface which is C¹ continuous in patches and G¹continuous(tangent plane continuous) between adjacent patches. Then C¹ continuous smooth fields of normal pressure and density on smoothed surface are interpolated. And contact points on smoothed contact surface are calculated with Newton-Raphson iteration. Finally,contact constraints are computed with distributed parameter contact algorithm. Numerical examples demonstrate that smoothed contact surface alleviates‘chatter’of nodes and improves convergence behavior.

An artificial viscosity is presented for Lagrangian hydrodynamics method.The formulation is based on artificial viscosity first presented by Lew.It contains a limiter switching off viscosity for shockless compression.The artificial viscosity reduces dependence of solution on relation of grid to flow structure.The eigenvalue viscosity limiter controls magnitude of the artificial viscosity.By the limiter it is able to distinguish between adiabatic compression and shock compression.The formulation is applicable to any dimensions and to logically rectangular or unstructured grids.

Based on the velocity remapping strategy of the SALE algorithm, three methods are proposed to improve the accuracy and monotonicity of momentum flux calculation on a 1D staggered grid: the SUR method which employs the upwind-type slope and a repairing procedure; the SM method which employs a minmod slope limiter; and the SLR method which employs a new slope limiter and a repairing procedure. These methods are second-ordered, conservative and bound-preserving. They inherit advantages of simplicity and high efficiency of the SALE algorithm. They are easily generalized to the two-dimensional case.