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.

The time step control in two-dimensional three-temperature hydrodynamic calculations is studied.Based on numerical stability and accuracy we propose several conditions that restrict the time step.These conditions change the time step automatically in computation so that the calculation proceeds with the most economical and reasonable time step.Numerical results are shown to demonstrate the efficiency of the method.

We developed a high performance algebraic solver for nonlinear systems discretized from two-dimensional energy equations with three temperatures by a nine point scheme.The main idea is to solve the system by an inexact Newton method and preconditioned Krylov subspace methods in the frame of PNK and JFNK methods.Numerical experiments show the efficiency of the algebraic solvers.It is shown that our PNK method is 6 times faster than the nonlinear block Gauss-Seidel method. The JFNK and PNK methods are also compared.

An effective rezoning method for two-dimensional Lagrange meshes, i.e., an integral conservative remapping method, is studied. The algorithm is described in detail. Calculation results are shown.

A new type of hybrid iterative method is presented, which is competent in solving the large scale sparse linear systems derived from the 2-dimensional 3-temperature radiation dynamic energy equations. Numerical results show that the new method is as 4 times fast as the old ones.Especially on the cases the old one doesn't converge, the new method can easily get the solution to the precision required. It can successfully complete the simulation and the final physical parameters of the simulation coincide with the theory.

The strict explanation about conservation on discrect sitiuation is given at first.Then the dilemma among different conservative variables are discussed,and a least squart method is presented to solve it.Some easily confused concepts about conservation are analysed in detail.

The compressed shapes of the pellet driven by a radiation field in a cylindrical gold hohlraum under single ring driving of incident laser beams simulated by RT3D and Lared-Ⅰ codes are given. As the position of the incident laser spots changing, the temperature distribution on the pellet surface changes as well and the pellet shapes turned out to be cake-like, sausage-like or ball-like respectively according to the different position of the laser spots. The comparison of the simulation result with the experiment carried out in LLNL and with the simulation result by Lasnex codes is given here too and it is shown that the same conclusion and the similar numerical result was obtained. Meanwhile it can also be seen that under single ring driving, it is not enough to supply a uniform and symmetrical radiation fields and it would be necessary to develop two or three laser rings driving to improve the radiation field.

By the design of new parallel algorithm and the organization of grid mapping, a serial code Lared-Ⅰ has been successfully parallelized for numerical simulations of 2-dimension three temperature hydrodynamics with the message passing programming environment. Moreover, a dynamic load balance method is also designed according to the physical and the code executing characteristics, which can significantly improve the parallel performance. The numerical results under both parallel computing environments are given as well.

In this paper, We present a numerical method for solving the transport problem with anisotropic scattaring in one-dimensoional sphere geometry. Norm estimates of approximate solution are given Finally, some results are presented.