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.

In a sparse linear system derived from two-dimensional three-temperature energy equations, the diagonal dominan varies greatly from row to row and so is the magnitude of the elements. We provide a new scaling method to improve the diagonal dominance. As ILUT is used to the derived linear system, it reserves the number of elements in each row and several relatively large elements related to the photon are dropped due to the large difference among elements. To improve the equality of the ILUT, we provide a new method named multiple row ILUT (MRILUT), in which multiple rows are computed before dropping. The provided methods are embedded into a preconditioned Krylov subspace method to solve the actual two-dimensional energy equations with three temperatures. The number of iteration at each time step and the total computation time are both greatly reduced.

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.