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.

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.

A consistent linear multifrequency-grey acceleration scheme is developed to accelerate the iterative convergence speed of diamonddifferenced multigroup radiative transfer equations. A difference scheme of acceleration equation is obtained directly by applying discrete P1 approximation to differenced S_N equations. Numerical examples show that the method is effective and robust.