Mixed cells are introduced in multi-material arbitrary Lagrangian-Eulerian (MMALE) method to capture material interfaces. An energy-preserving closure model on mixed cells for diffusion equation is proposed. Based on closure model, a method for coupling multiple material radiation diffusion simulation and hydrodynamics MMALE simulation is proposed. Numerical experiment with analytical solution shows accuracy of the method for diffusion equation. Results of Sedov and spherical implosion problems show that the method is effective and robust. Comparisons with traditional Lagrangian method prove advantages of the method.

To develop a methodology to fulfill hydraulic analysis on asymmetry and irregular topology structure networks, we proposed a method that can fully adapt on 3D asymmetric and irregular topology structure of networks. The modeling approach is illustrated in detail and compared with traditional methods using a district heating scenario. It provides instructions for other researches.

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 E-H TDFEM method derived directly from Maxwell's curl equations, Crank-Nicolson difference scheme is implemented for time-partial differential equation to obtain an unconditionally stable algorithm. Curvilinear tetrahedral elements are applied to discretize computational domain and electric and magnetic fields are expanded with same hierarchical vector basis functions. A sphere cavity and a cylindrical cavity partially filled with dielectric rod are simulated. It shows that curvilinear tetrahedral elements can reach higher accuracy with same mesh numbers, compared with tetrahedral elements. Better results can be obtained by curvilinear tetrahedral elements combined with 1.0 order hierarchical basis functions with fewer unknowns than that combined with 0.5 order hierarchical basis functions.

We present E-H time-domain finite-element method using hierarchical high-order vector basis functions. Electric fields and magnetic fields are computed together and Crank-Nicolson difference scheme is implemented to obtain an unconditionally stable algorithm. Meanwhile, perfectly matched layers are used for truncation of unbounded regions. Three-dimensional cavity and waveguide structures are simulated. It shows that accuracy is improved by E-H TDFEM method with higher-order basis functions.

A high-order discontinuous Galerkin time-domain finite-element method based on Maxwell's curl equations is presented. It is a kind of domain decomposition method. Crank-Nicolson difference scheme is used for time-partial equation. Electric and magnetic fields are expanded using high-order vector basis functions with same order. Three-dimensional cavities are simulated to demonstrate accuracy and efficiency of the method. It shows that time step size is no longer restricted by Courant-Friedrich-Levy(CFL) condition.High-order vector basis function could improve accuracy compared with Whitney 1-form vector basis function.

In distributed parameter contact algorithm on three-dimensional contact surface,a method for smoothing three-dimensional contact surface is developed. In the method,a smooth contact surface is interpolated with bi-cubic parametric patches. A bi-cubic parametric patch is defined by using local information such as coordinates and normals of vertexes of patch. The smoothing technique provides an accurate representation of actual contact surface which is C¹ continuous in patches and G¹continuous(tangent plane continuous) between adjacent patches. Then C¹ continuous smooth fields of normal pressure and density on smoothed surface are interpolated. And contact points on smoothed contact surface are calculated with Newton-Raphson iteration. Finally,contact constraints are computed with distributed parameter contact algorithm. Numerical examples demonstrate that smoothed contact surface alleviates‘chatter’of nodes and improves convergence behavior.

A brief introduction to development history of computational electromagnetics(CEM) and numerical methods in CEM is provided. In addition, we discuss up-to-date progress of CEM in scientific researches, commercial softwares and proprietary softwares. Considering applications of electromagnetics environmental effects (E3), we present development of our numerical simulation platform of E3. Finally, future trends of development in E3 are shown.

An approach is proposed for calibrating hydraulic network models.The proposed procedure could reconcile results of all scenarios under various operation conditions and utilize prior information selectively.To achieve more accurate roughness with a faster processing,a hybridoptimization technique was developed to exploit advantages of genetic algorithm and active set method.The algorithm was applied to two sample networks,and resulting calibrated model was compared to counterpart in previous literature.The proposed approach was shown stable and estimated parameters were more accurate.

An algorithm based on object-oriented(00) method is proposed.All pipe components in network topology structure are given special object,properties.Hydraulic calculation models are expressed by object methods.Boundary conditions variations are reflected by object events.Then hydraulic calculation can be solved as traversing all pipe components.Two cases are calculated and analyzed.It indicates that the method can effectively handle hydraulic imbalance caused in structure or in heat sources of a multi-source looped-pipe network with small deviations.

With Maxwell equations and electron fluid equations Gaussian,damped sinusoidal broadband high-power microwave(HPM) propagation in air is analyzed by using finite difference time domain(FDTD) method.At each time grid,according to electronic velocity of narrow-band pulse,effective electric field of broadband pulse is solved with discrete Fourier transform(DFT) method.Ionization parameters at each spatial grid are updated by substituting effective electric field and pressure into corresponding formulas.Calculation accuracy is improved.It shows that broadband HPM pulse amplitude,pulse width,height above sea level have significant effect on air breakdown.Tail loss is resulted from air breakdown.As propagation distance increases,HPM pulse tail decay increases and spectrum of pulse is broadened,splited,and center frequency shifts.

A failure cascading model for power systemes is proposed,in which energy dissipation and capability expansion are considered.Simulations are performed on both regular grids and scale-free networks.Self-organized critical phenomenon is observed in both cases.It means that energy dissipation and capability expansion are important factors in self-organized critical status.In addition,it shows that the maximum size of cascading failures in scale-free networks is much larger than that in regular networks.

Tension simulations of[001]monocrystalline face-centered cubic SiC(β-SiC) and C-doped β-SiC bulks are performed with molecular dynamics method to investigate intrinsic deformation mechanisms and mechanical behaviors of β-SiC under strain rates of 5×10⁸/s,1×10⁹/s,1×10¹⁰/s.It is found that Si-C sp³ and C-C sp³ bonds respectively transform to Si-C sp² and C-C sp² bonds as soon as the strains reach certain critical values.As certain amounts of sp² bonds are formed,instable fractures emerge in β-SiC.Since C-C sp² bonds are formed earlier than Si-C sp² bonds,the doping of C elements leads to the decrease of strength,Young's modulus and tension fracture strain of β-SiC.In addition,it is found that the strain rates have effects on tensile-strength,but not on Young's modulus.

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.

We propose a one-dimensional sandpile model with avalanche probability.The simulation is performed with the cellular automata method.As the local slope closes to the critical slope sands avalanche with a probability.The avalanche size and the average local slope are studied at different avalanche probabilities. The self-organized critical (SOC) behavior is studied at critical exponent α=1.50±0.02 as the avalanche probability is between 0.05 and 0.98.The average local slope descends with the increase of collapse probability.A sharp transition occurs between the trival behavior and SOC behavior in this model.The SOC phenomenon in one-demensional rice-pile experiment is well explained.

Based on the velocity remapping strategy of the SALE algorithm, three methods are proposed to improve the accuracy and monotonicity of momentum flux calculation on a 1D staggered grid: the SUR method which employs the upwind-type slope and a repairing procedure; the SM method which employs a minmod slope limiter; and the SLR method which employs a new slope limiter and a repairing procedure. These methods are second-ordered, conservative and bound-preserving. They inherit advantages of simplicity and high efficiency of the SALE algorithm. They are easily generalized to the two-dimensional case.

A new subgrid eddy viscosity model is proposed. The new subgird eddy viscosity is proportional to the skewness of longitudinal velocity increment, which characterizes the transportation of turbulent momentum bteween resolved and unresolved turbulence. The new model is verified by a DNS data bank of isotropic turbulence, and has been applied to the turbulent channel flow. The results show to be in good agreement with DNS ones.

A numerical method is described for solving the kinetic bollooning mode eigenequation with three components. The effect of high velocity particles on ballooning mode instability is investigated. The obtained results are in good agreement with experiments.