We use discontinuous finite element method to solve three-dimensional hydrodynamic equations.The domain is divided with an unstructured tetrahedral mesh.In order to overcome low efficiency of explicit scheme,especially as sizes of cells vary strongly,we use a local time stepping technique(LTS).We integrate control equations in space and time to obtain a single-step scheme.The calculation of each grid cell can be localized.It avoids excessive memory difficulties as dealing with three-dimensional problem with high order Runge-Kutta method.ADER method is used to calculate numerical flux across element boundary to improve accuracy of the hydrodynamic equations.Finally,numerical examples demonstrate stability and effectiveness of the method.

A conservative remapping algorithm based on donor-cell method for multiscale dynamic simulation is proposed which couples micro molecular dynamics (MD) simulation with macro finite element (FE) method. Since physical quantities are obtained with integral reconstruction from information of FE nodes and their underlying MD atoms, the algorithm can be applied to both structured and unstructured meshes. An auxiliary mesh is introduced for vertex-centered unknowns. Accuracy and efficiency of the method are validated with numerical experiments.

For systems of nonlinear hyperbolic conservation laws,two adaptive discontinuous Galerkin finite element methods(ADGM) generating conforming unstructured triangular meshes are proposed.The first one is for structured mesh. It is simple and fast.The second one is for both structured and unstructured meshes.Based on posteriori error estimation of nonlinear hyperbolic conservation laws,a discontinuous interfacial mesh refinement indicator is shown in generating adaptive meshes. It is shown that the methods are flexible and reliable. Computation cost is decreased.

To solve the three-dimensional transient problems,the Improved Quasi Static Method(IQS) is adopted to deal with the temporal problem,and an improvement of synthesis method(YN) is also introduced.By factorizing the neutron flux,the time step of this method is enlarged so as to decrease the number of spatial calculations.For spatial calculations,Nodal Green's Function Method(NGFM) is used to determine the distribution of shape function,so the spatial mesh of IQSYN/NGFM can be about twenty times as large as that of finite difference method.