Take use of characteristics of inertial confinement fusion(ICF) models and associated numerical discrete schemes, we proposed multiple techniques for promoting computational efficiency of two-dimensional radiation-hydrodynamic code LARED-integration. Numerical results show that with unchanged parallel resources it is two times faster in downstream spatial sweeping of solving transport equations. Half of total running time is saved for integrated simulation of laser fusion experimental hohlraums.

In practical applications, equation of states (EOS) consists of several piecewise smooth surfaces, which leads to discontinuity at interface. As a traditional nonlinear iterative algorithm is applied to an energy equation with discontinuous EOS, it may lead to slow convergence and unphysical solutions. To overcome the difficulties, a nonlinear problem is designed, and a nonlinear iterative algorithm is proposed to solve the problem. The algorithm is fit for energy equations with discontinuous EOS of piecewise smooth functions. A parameter of energy change is defined in the algorithm so that it is unnecessary to know discontinuity position in advance. The algorithm calculates precisely net gain or leakage of energy, which can be used to assess influence of discontinuity in EOS. Typical numerical experiments verify that the algorithm converges stably, and gives physical solutions.

We analyze non-physical solutions in laser ray tracing simulation.With a system of nonlinear equations,a new algorithm for intersection is presented.A special preconditioner is used to improve numerical stability.The algorithm is suitable for any intersectant condition.Numerical experiments show that the algorithm has better precision and adaptability.Simulation in LARED code shows good performance.

Convergence of source iteration is analyzed for multi-group radiative transfer calculations. A two-level nesting transport acceleration method is developed. Numerical results show speedup factors of the scheme are higher than that of GTA method. The scheme is feasible for non-rectangle grid calculations of 2D problems with large discontinuities of material properties.

We discuss deterministic numerical methods such as discrete ordinates methods,spherical harmonic dimensional and iteration acceleration method,for particle (neutron and radiation) transport equations in one-dimensional spheric geometry and twodimesional cylindrical geometry. Recent advances on numerical methods of transport problems are briefly described,including adaptive time step discrete scheme,iterative methods for eigenvalue problems,modified subcell balance methods,simplified spherical harmonic methods,simulation methods for coupling of diffusion and transport,parallel discrete scheme with interface prediction and correction,grey transport synthetic acceleration method,etc. Based on the analysis of difficulties in numerical methods for transport equations,suggestions for future work are proposed.

We give a convergence analysis on splitting iterative (SI) algorithm of multi-group radiation diffusion equations. Spectral radii of iterative matrix is shown. Numerical computation and analysis on spectral radii formulae reveal a relation between convergence rate and radiation coefficients. Numerical results confirm theoretical results, and give applicable conditions of the algorithm.

A series of exact solutions are constructed for two-dimensional radiative transfer and radiative diffusion problems with outer source.These solutions exhibt physical characteristics with simple expressions.Moreover,transport solutions degenerate directly into solutions of corresponding diffusion equations.Test results of the diffusion model with LARED-R are presented and analyzed.

In numerical simulation of radiation hydrodynamics problems,diffusion computation costs most part of simulation time.It is urgent to construct parallel schemes which are conservative,of high precision and unconditionally stable.The aim of the paper is to devise conservative parallel schemes based on methods of "prediction and/or correction" for nonlinear diffusion equations.Numerical results are presented to examine performance of conservative parallel schemes,such as accuracy,stability and parallel speedup.

Radiative transfer in fluid flow of radiation hydrodynamics is studied.Kinetic laws under radiation condition are investigated.Practical radiation hydrodynamics process is complicated,and numerical simulation is one of primary research means.Splitting methods are often used in numerical simulation,in which fluid motion and radiation are computed separately.We discuss computational problems in radiation diffusion calculations.Diffusion schemes and nonlinear iterative methods on severely distorted meshes are studied.A brief introduction on research progress is given.

Strong-coupled multigroup radiative transfer in optically thick regions are analyzed.A simple conner balance method in 2D is presented.A grey transport acceleration scheme is generalized to accelerate source iteration convergence of differenced multigroup transport equations.

The governing equations, moving least squares (MLS) interpolant and conservative schemes for moving least squares particle hydrodynamics(MLSPH) are presented. It focuses on numerical evaluatation of area matrix to improve calculation accuracy. Numerical experiments with shock tube and Nob problems are satisfactory. The area matrix is evaluated correctly by a three-order spline integral formula.

A discrete tangential flux on grid edge in nine-point schemes for solving diffusion equations on arbitrary quadrilateral meshes is derived. The discrete tangential flux is represented as a weighted combination of difference of center values with adaptive weighted coefficients, which depend on the thermal conductivity and geometric parameters of distorted meshes.

Construction of difference schemes for parabolic equations on distorted meshes with large aspect ratio is discussed.The limitation of 9-point scheme is provided.An assistant mesh difference method is proposed for distorted meshes with large aspect ratio to improve precision and efficiency.Based on the conservation law,applying appropriate rezone methods for meshes we modify the 9-point method to reduce computation error due to poor regularity of the meshes and low precision due to the approximation to vertices values by an average of neighboring cell values.The nonlinear system obtained is a different system from the 9-point scheme.Its solution approximates to the solution with the original meshes.The designed scheme is implemented easily and adapts well to distorted meshes.Numerical experiments show good precision and stability.