Flux field calculation in time-dependent problems with Monte Carlo method and associated particles transportation equation are described.The random walk principle of time station sampling(TSS) method in dynamic system is introduced.A time station importance sampling(TSIS) method is developed and applied to decrease statistical fluctuation in global flux field calculation.Alternative importance function and its unbiased weight of modification are investigated.Numerical results and analyses on methods in specific model are given.The time station importance sampling(TSIS) biased method can be used to control statistical variance of global fine mesh flux adaptively in a same level.

We develop a conservative piece-wise parabolic advecting remapping method(PPRM).The first part of it is an alternate sweeping average method(ASAM) for improving symmetrization of advecting remapping method.The second part is a piece-wise parabolic distributing function for improving order.We use one-and two-dimesional examples to test order and symmetrization of PPRM.

An AMR(adaptive mesh refinement) method is presented with different time steps in the cells at inequable levels. In order to get high accuracy in the cells on the interlace, the AMR method is adopted together with the level set method and the ghost fluid method. Euler equations is solved by a WENO algorithm which is easily realized while getting a high resolution. Compared with the method without considering AMR or the level set method, our method shows an advantage in achieving high resolution on the interface. The result indicates that these methods work well together in the numerical simulation.

A difference scheme for two-dimensional three-temperature energy equations in Cartesian coordinates is united with that in cylindrical coordinates.The LARED-H (laser radiation electron dynamic holehurm) code is extended to describe physical processes in both coordinates.Physical models are investigated for a line-focused target with different incident angles.Numerical results are given to describe the expanding process of target-plasma.