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.

Based on HLLEW (Harten-Lax-Van Leer-Einfeldt-Wada) scheme, low speed preconditioning technology is introduced to develop a three-dimensional Navier-Stokes solver for flows at all Mach numbers. Low speed preconditioning techniques is introduced to reconstruct dissipative term in HLLEW scheme and preconditioning HLLEW scheme is proposed. Implicit time-marching method is constructed based on preconditioning Jacobian Matrix. Results of NACA 4412 incompressible flow and RAE 2822 transonic flow with preconditioning HLLEW scheme are compared with results by original method and experimental data. It shows that preconditioning HLLEW method improves accuracy and convergence rate for low speed flow. It can be applied for flows at all Mach numbers.

A method using stochastic response surface method is presented. It solves wave equation with uncertain parameters in shallow water. Uncertain parameters of ocean environment are expressed with standard stochastic variables. And stochastic response of coherent sound field is expressed by Hermite multinomials. An approximate expression of coherent sound field is achieved with coefficients of stochastic muhinomial solved by probabilistic collocation method. It shows that the proposed method is more accurate and efficient than Monte Carlo method and field shifting method.

Power coupled equations for a multi-wavelength broadband Raman amplifier (MBRA) are reasonably simplified.A multi-step average power method is used to compute composite Raman gain of multi-signal in a dense wavelength division multiplexed system (DWDM).A conventional simulated annealing algorithm is applied for optimization of MBRA.A simple object function is proposed considering the gain bandwidth,on-off gain,gain flatness and other characteristic parameters.Influences of the number of pump,input power and wavelength distribution on Raman gain are studied.Relations among gain bandwidth,on-off gain,gain flatness and the number of pump of MBRA are revealed.Simulation shows that the optimal signal bandwidth Δλ becomes boarder with the increasing of the number of pump and narrower with the increasing of Raman gain and the improvement of flatness.

We present an element free Galerkin method(EFGM) for nonlinear transient field involving phase change.It needs no element connectivity.Compared with other methods such as the finite element method(FEM),it is easy in tracking the growth of phase boundaries.Essential boundary conditions are enforced using a penalty function method.The MATLAB codes are developed to obtain numerical solutions.Two classical examples show that,compared with the FEM,EFGM has more advantages such as high accuracy,good convergence and simple post-process,etc.

Under a compulsive boundary condition,a simplified time-domain finite-difference beam propagation method (TD-FD-BPM) suitable for the analysis of fiber Bragg grating (FBG) is presented.In the alternating-direction implicit method (ADIM) and the generalized Douglas (GD) scheme, the time-domain beam propagation equation is discretized with a truncation error two orders lower than that of conventional finite-difference scheme.The compulsive boundary condition simplifies the boundary model,which is important in the numerical analysis of optical waveguides with open boundary conditions.We focused on the position of excitation,the shape of the pulse and its distribution in the radial direction,and the use of the one-way continuous-wave (CW) scheme.Using a modified sinusoidal pulse,a satisfactory reflective spectrum is obtained in a short symmetrical FBG through discrete Fourier transform.

A 3D trapered spot-size converter (3D-SSC) on a rib cross-sectional optical waveguide, one of the key components in photonic devices connecting with single mode optical fibers,is investigated through simulating lightwave transmission in this component based on 3D-FD beam propagation method.Geometry parameters,such as laterally boundaries,length,width of the large section,thickness and those of the transitional optical waveguide for connecting SMOF to 3D-SSC are discussed and analyzed.The simulation shows that the insert loss of 3D-SSC can be lower than 2 dB as the width in the area of 11.5 μm~13.5 μm and the thickness in the area of 4.5 μm~6.5 μm at the large end of the taper when the taper length is in the region of 200 μm~500 μm.The capability and the alignment tolerance of the 3D-SSC is better than those of the planar SSC,and the 3D-SSC with a nonlinear lateral boundary acquires lower insertion loss than that with a linear lateral boundary.It is found that the 3D-SSC converts gradually the guided modes from multi-mode to single mode finally.

The algorithm proposed here can be used in 2D two-step plane and axisymmetric Eulerian hydrodynamic method to deal with the interface of a mixed cell. It takes advantage of the idea of Youngs method: in a mixed cell, the interface is regarded as a straight line. The area fraction of eight cells surrounding the mixed cell is used to determine the normal orientation of the interface, the area fraction or the volume fraction of the mixed cell is used to determine the equation (position) of the interface, and then the flux passing across the boundary of the cell according to this interface and the area fraction or the volume fraction of the cell at next time is calculated. In the last part of this report, some numerical results are presented, which include the precision tests of interface calculation, the comparison with SLIC and the calculations of comprehensive problems.

A Probability description of an empirical method (called method A in this paper) used in simulations of high energy multiple production processes in which not only single particle momentum distribution but also energy conservation can be satisfied is presented and mathematically deduced. The applicable condition of method A is discussed.