Sub-division method based on support operator is used to solve diffusion equation with three-dimensional non-conformal mesh and non-planar mesh.Numerical experiments show that the method is second-order accurate on general non-conformal mesh.For curved-face mesh and non-planar-face mesh, the method is more accurate than traditional plane-approximation method.For non-conformal orthogonal mesh, the method can obtain accurate solutions of linear problems.

We present a distributed parallel SPH programming algorithm using adaptive mesh refinement background grids,in which size of a grid is decided based on maximal smoothed length of local particles. All neighboring particles of a given particle can be found in the grid the particle belongs to and in grids of same size adjoining to this grid. Searching bound is confined and as a result computational efficiency is improved. The method is validated in non-uniform smoothed length SPH simulation.

Global sensitivity analysis method based on polynomial chaos and variance decomposition is reviewed comprehensively. In order to alleviate "curse of dimensionality" coming from high-dimensional random spaces or high-order polynomial chaos expansions, several approaches such as least square regression, sparse grid quadrature and sparse recovery based on l₁ minimization (i. e. compressive sensing) are used to reduce sample size of collocation points that needed by non-intrusive polynomial chaos method. With computation of Sobol global sensitivity indices for several benchmark response models including Ishigami function, Sobol function, Corner peak function and Morris function, effective implementations of polynomial chaos method for variance-based global sensitivity analysis are exhibited.

We present a cell-centered finite volume method for 2D invicsous Lagrangian hydrodynamics.Velocity and pressure on vertex of a cell are computed with characteristics theory,which is derived from governing equations of Lagrangian form linearized by freezing Jacobian matrices about a known reference state.The velocity is used to update coordinate of vertex of a cell.Product of two variables is used to compute numerical flux through cell interface by a trapezoidal integration rule.Convergency,symmetry and conservation of total energy of the method are demonstrated.The method can be applied to structured or unstructured grids,and does well spontaneously for multi-material flows in a robust way.The scheme is one order precision,and can be easily draw on two order precision.

An artificial viscosity is presented for Lagrangian hydrodynamics method.The formulation is based on artificial viscosity first presented by Lew.It contains a limiter switching off viscosity for shockless compression.The artificial viscosity reduces dependence of solution on relation of grid to flow structure.The eigenvalue viscosity limiter controls magnitude of the artificial viscosity.By the limiter it is able to distinguish between adiabatic compression and shock compression.The formulation is applicable to any dimensions and to logically rectangular or unstructured grids.

A high order hybrid central-WENO finite difference scheme with adaptive mesh refinement (AMR) for numerical simulation of gaseous detonations is presented. Governing equations are two-and three-dimensional reactive Euler equations in a ZND detonation model. The hybrid scheme combines high order central finite difference schemes and WENO schemes effectively. In high gradient regions, WENO schemes are empolyed to capture discontinuity, while in smooth regions a more efficient and accurate central finite difference scheme is adopted. The AMR grid is based on flow field structure. Numerical results show that a hybrid scheme with AMR method has characteristics of high-order, high-resolution, and high-efficiency.