Finite element modelling of the thermal outflow of three power plants in Huelva Estuary

A simple explicit, characteristic-based finite element method for the numerical simulation of the dispersion of the thermal outflow in Huelva estuary is considered in this paper. The derivation involves a local Taylor expansion of the convection–diffusion equation. The numerical model used was originally designed to simulate the dispersion of pollutants in the open sea and has now been reconfigured to simulate the dispersion of the thermal outflow of some power plants which may be constructed in Huelva estuary in the near future. Numerical results obtained are presented.     

Mixed Volume Element-Characteristic Fractional Step Difference Method for Contamination from Nuclear Waste Disposal

A nonlinear system with boundary-initial value conditions of convection–diffusion partial differential equations is presented to describe incompressible nuclear waste disposal contamination in porous media. The flow pressure is determined by an elliptic equation, the concentrations of brine and radionuclide are formulated by convection–diffusion equations, and the transport of temperature is defined by a heat equation. The pressure appears in convection–diffusion equations and heat equation in the form of Darcy velocity and controls the physical processes. The fluid pressure and velocity are solved by the conservative mixed volume element and the computation accuracy of Darcy velocity is improved one order. A combination method of the mixed volume element and the approximation of characteristics is applied to solve the brine and heat, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computation stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. Larger time-steps along the characteristics are shown to result in smaller time-truncation errors than those resulting from standard methods. The mixed volume element method has the property of conservation on each element and it can obtain numerical solutions of the brine and adjoint vectors. The radionuclide is solved by a coupled method of characteristics and fractional step difference. The computational work is reduced greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and using the algorithm of speedup. Using numerical analysis of priori estimates of differential equations, we demonstrate an optimal second order estimate in \(l^2\) norm. Numerical data are appropriate with the scheme and it is shown that the method is a powerful tool to solve the well-known problems in porous media.     

On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods

In this work we study the dispersion and dissipation characteristics of a higher-order finite volume method based on Moving Least Squares approximations (FV-MLS), and we analyze the influence of the kernel parameters on the properties of the scheme. Several numerical examples are included. The results clearly show a significant improvement of dispersion and dissipation properties of the numerical method if the third-order FV-MLS scheme is used compared with the second-order one. Moreover, with the explicit fourth-order Runge–Kutta scheme the dispersion error is lower than with the third-order Runge–Kutta scheme, whereas the dissipation error is similar for both time-integration schemes. It is also shown than a CFL number lower than 0.8 is required to avoid an unacceptable dispersion error.     

Application of the USGS diffusion hydrodynamic model (DHM) in evaluation of estuary flow circulation

Many of the hydrodynamic models used for tidal flow regime and storm surge analysis are based upon use of the two-dimensional hydrodynamic equations, which are obtained from the parent three-dimensional flow equations by averaging with respect to the vertical coordinates. Various numerical techniques, such as finite difference, finite element, and the method of characteristics have been used to solve these mathematical models.

The USGS diffusion hydrodynamic model has been developed to simulate two-dimensional surface water flows, and solves the governing flow equations by neglecting the inertia terms. The DHM has previously been applied to a hypothetical bay study with results comparable to those obtained using the method of characteristics. In the current work, the DHM is applied to the Batiquitos Lagoon located in the City of Encinitas, California for the purposes of evaluation of tidal flow characteristics. The main objective is to determine local flow velocities and circulation patterns in the lagoon caused by the incoming and outgoing tide.     

光子晶体光纤模式折射率的分析

模式折射率是分析光子晶体光纤色散特性的一个基本参数,其快速而较准确的计算有助于对不同结构参数的分析比较,便于工程应用,但用时域有限差分法等数值方法分析传输特性通常需要较长的计算时间,为此,文中以六角形空气孔排列的光子晶体光纤为例,用时域有限差分法分析在不同的结构参数和传播常数的组合情况下的模式折射率,并利用分析所得数据,得到了模式折射率和结构参数、传播常数之间的拟合函数.利用所得拟合公式可得光子晶体光纤的模式折射率,并在通信和传感的应用场合下为PCF的设计提供一定的理论依据.     

Production control of manufacturing systems: a multiple time scaleapproach

In this note, a stochastic production model containing processes with different time scales is developed. It is shown that if the time scales of the processes are very different, some hierarchical algorithms that are much more efficient than the standard policy iteration method can be developed to find the optimal production control. Moreover, if the time scales fall far apart, the optimal control of a deterministic limiting problem depending only on the mean characteristics of the processes can be used to approximate the optimal control of the original problem. The limiting problem has much lower dimension than its original counterpart and thus is much easier to solve. A numerical example is used to illustrate the potential of the proposed approach     

Analytic solutions to optimal control problems in crystal growth processes

A unified approach to optimal control of univariate and multivariate crystallization particulate processes with size-independent or/and size-dependent growth rate kinetics is developed by utilizing the minimum principle and the method of characteristics in conjunction with novel approximate integro-differential and ordinary differential equation computational schemes. The proposed theoretical approach leads to simple analytic solutions involving numerical boundary value problems with few unknown parameters.     

A novel numerical dispersion formulation of the 2D ADI‐FDTD method

A novel dispersion formulation of the 2D alternating‐direction implicit (ADI) finite‐difference time‐domain (FDTD) method is presented. The formulation is based on an increasing process analysis of the monochromatic wave in free space. A numerical experiment scheme is designed to verify the accuracy of the proposed formulation. The results obtained from the proposed formulation are in a good agreement with those from the numerical experiments, and the proposed formulation is more accurate than those reported in the literature. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

Optimized meshfree methods for acoustics

When the Helmholtz equation is solved by numerical methods as, e.g., the finite element method (FEM), the solution suffers from the so-called pollution effect. The pollution is mainly caused by the dispersion, meaning that the numerical wave number disagrees with the wave number of the exact solution. This leads to inaccurate results, especially for high wave numbers. In order to obtain acceptable results also for higher wave numbers, either a high element resolution or elements of a higher order can be used. For either option the consequence is an increased computation time and memory capacity.Meshfree methods as the element free Galerkin method (EFGM) and the radial point interpolation method (RPIM) are not dispersion-free either, but it has been shown that meshfree methods are able to reduce the dispersion significantly. Both methods offer several parameters, which can be modified in order to obtain optimal results with respect to the dispersion effect. This work presents an exhaustive parameter study on both the EFGM and the RPIM. It is shown, that the methods can be significantly improved if certain parameters as, e.g., weighting functions, shape parameters, size of the influence domain, are chosen appropriately.     

Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations

In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation (NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well as other applications, and discuss their dynamical properties ranging from time reversible, time transverse invariant, mass and energy conservation, and dispersion relation to soliton solutions. Then, we review and compare different numerical methods for solving the NLSE/GPE including finite difference time domain methods and time-splitting spectral method, and discuss different absorbing boundary conditions. In addition, these numerical methods are extended to the NLSE/GPE with damping terms and/or an angular momentum rotation term as well as coupled NLSEs/GPEs. Finally, applications to simulate a quantized vortex lattice dynamics in a rotating BEC are reported.     

Manifold method coupled velocity and pressure for Navier-Stokes equations and direct numerical solution of unsteady incompressible viscous flow

Numerical manifold method (NMM) application to direct numerical solution for unsteady incompressible viscous flow Navier-Stokes (N-S) equations was discussed in this paper, and numerical manifold schemes for N-S equations were derived based on Galerkin weighted residuals method as well. Mixed covers with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. The patch test demonstrated that mixed covers manifold elements meet the stability conditions and can be applied to solve N-S equations coupled velocity and pressure variables directly. The numerical schemes with mixed covers have also been proved to be unconditionally stable. As applications, mixed cover 4-node rectangular manifold element has been used to simulate the unsteady incompressible viscous flow in typical driven cavity and flow around a square cylinder in a horizontal channel. High accurate results obtained from much less calculational variables and very large time steps are in very good agreement with the compact finite difference solutions from very fine element meshes and very less time steps in references. Numerical tests illustrate that NMM is an effective and high order accurate numerical method for unsteady incompressible viscous flow N-S equations.     

Computer simulation of polarization rotation characteristics of graphene

The magnetically biased graphene has the polarization rotation characteristics which is useful to design the polarizer. But this characteristic is difficult to simulate by using the finite‐difference time‐domain (FDTD) method, not only due to the graphene's thin layer which confines the time step size, but also because of graphene's isotropic surface conductivity when it is biased by static magnetic field. To solve this problem, this study presents an anisotropic hybrid implicit‐explicit FDTD method. This method uses auxiliary difference equations to represent graphene's conductivity, and removes the confinement of graphene's thickness on time step size by using hybrid implicit‐explicit technique. So, compared with FDTD method, the presented method can save a large number of computational time, which are validated by numerical examples.     

Modelling surface radioactive,chemical and oil spills in the Strait of Gibraltar

A model that simulates the dispersion of chemical/radioactive and oil spills in the Strait of Gibraltar has been developed. Water currents over the Strait have been obtained from a hydrodynamic model. Computed tides and residual currents have been compared with observations in the area. The dispersion model, based on a particle-tracking technique, is solved off-line. Standard tidal analysis, carried out over results provided by the hydrodynamic model, is applied to obtain currents at any time and position of the Strait. Specific processes for each contaminant (decay of radioactive material, oil evaporation and decomposition) are included and simulated by means of a stochastic method. A Monte Carlo method is applied for turbulent diffusion. The model can deal with instantaneous and continuous releases. MatLab graphic user interfaces have been developed to introduce input data and visualize simulation results. Some dispersion calculations have been carried out. In general, contaminants are flushed towards the east due to the residual currents. Nevertheless, dominant east winds tend to retain contamination in the Strait and to enhance mixing. This is also the case if the release occurs close to the coast, where currents are weaker than in the central part of the Strait.     

Flux-based method of characteristics for contaminant transport in flowing groundwater

A numerical method for treating advection-dominated contaminant transport in flowing groundwater is described. This method combines advantages of numerical discretizations by finite volume methods (like local mass conservation and the positivity of solutions) and by methods of characteristics (like larger time steps and reduced artificial numerical dispersion). For one-dimensional problems the method can produce equivalent algebraic systems as the finite volume Eulerian-Lagrangian localized adjoint method [13] and the flux-based modified method of characteristics [23] (and some other methods). An extension of the "flux-based methods of characteristics" for complex transport problems on multidimensional unstructured computational grids is the main contribution of this paper. Numerical results are included for a well established test example using a flux-based method of characteristics with aligned finite volumes.     

A new FDTD scheme analysis for the characteristics of the magnetic‐anisotropic EBG structure

In this article, the new grid finite‐difference time‐domain (NG‐FDTD) method is applied to calculate the dispersion curves of electromagnetic band‐gap structures, and the dispersion characteristics of three magnetic‐anisotropic medium EBG structure are obtained using the NG‐FDTD method. According to these results, we can conclude that the EBG structure of a magnetic‐anisotropic medium, in which the permeability of nondiagonal elements is real, has a much larger band‐stop than that of isotropic EBG. Other magnetic‐anisotropic EBG structures can also increase the first band‐stop. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005.     

复合负泊松比蜂窝超结构板低频减振特性研究

为实现低频宽带减振,将星型蜂窝与内凹六边形蜂窝组合,形成复合负泊松比蜂窝结构.利用多物理场软件COMSOL Multiphysics通过施加Floquet周期性边界条件获得了复合蜂窝元胞的色散曲线,并计算有限周期结构的传输特性,验证色散曲线中带隙的存在.设计并制备了复合蜂窝超结构板样件,通过试验分析其弹性波激励下的响应,验证有限元分析结果.以低频宽带为目标,利用遗传算法对结构参数进行优化,在1000~2000Hz打开了多条宽频带隙,可以为带隙设计提供有益指导.最后,将地铁实车测试获取的地板振动频谱作为激励,对超结构的减振性能进行了仿真测试,结果表明,复合蜂窝超结构板能够有效衰减列车地板1000~2000Hz的振动峰值.     

Full‐wave analysis of circular guiding structures using the finite difference frequency domain method

In this article, a general full‐wave two dimensional finite difference frequency domain (2D‐FDFD) method is presented that could be used to analyze general circular multi‐layered multi‐conductor guiding structures. The FDFD method is mainly used to get the dispersion curves for these structures. The results which are obtained using the FDFD equations come through solving an eigen‐value problem, where the obtained eigen‐values and eigen‐vectors are used to produce the propagation constants, distribution of the fields and the characteristic impedances for these structures. Several examples ranging from simple coaxial lines to coupled circular microstrip lines are presented. The FDFD results are compared with those obtained through other analytical and numerical techniques. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

Gas-kinetic numerical study of complex flow problems covering various flow regimes

The Boltzmann simplified velocity distribution function equation, as adapted to various flow regimes, is described on the basis of the Boltzmann–Shakhov model from the kinetic theory of gases in this study. The discrete velocity ordinate method of gas-kinetic theory is studied and applied to simulate complex multi-scale flows. On the basis of using the uncoupling technique on molecular movements and collisions in the DSMC method, the gas-kinetic finite difference scheme is constructed by extending and applying the unsteady time-splitting method from computational fluid dynamics, which directly solves the discrete velocity distribution functions. The Gauss-type discrete velocity numerical quadrature technique for flows with different Mach numbers is developed to evaluate the macroscopic flow parameters in the physical space. As a result, the gas-kinetic numerical algorithm is established for studying the three-dimensional complex flows with high Mach numbers from rarefied transition to continuum regimes. On the basis of the parallel characteristics of the respective independent discrete velocity points in the discretized velocity space, a parallel strategy suitable for the gas-kinetic numerical method is investigated and, then, the HPF (High Performance Fortran) parallel programming software is developed for simulating gas dynamical problems covering the full spectrum of flow regimes. To illustrate the feasibility of the present gas-kinetic numerical method and simulate gas transport phenomena covering various flow regimes, the gas flows around three-dimensional spheres and spacecraft-like shapes with different Knudsen numbers and Mach numbers are investigated to validate the accuracy of the numerical methods through HPF parallel computing. The computational results determine the flow fields in high resolution and agree well with the theoretical and experimental data. This computing, in practice, has confirmed that the present gas-kinetic algorithm probably provides a promising approach for resolving hypersonic aerothermodynamic problems with the complete spectrum of flow regimes from the gas-kinetic point of view for solving the mesoscopic Boltzmann model equation.     

A parallel ETD algorithm for large-scale rate theory simulation

Rate theory (RT) is a commonly used method to simulate the evolution of material defects. A promising numerical method, exponential time difference (ETD), can reduce the stiff RT equations to explicit ordinary differential equations (ODEs). Previous implementations of ETD on the “Sunway TaihuLight” supercomputer suffer from high computation cost and poor parallel efficiency while solving a large amount of ODEs. This paper improves the algorithm with hybrid MPI+SIMD and additional instruction-level optimizations by taking advantage of the architecture of “Sunway TaihuLight”. The execution time of a single iteration is reduced by about 40%. Scaling from 64 to 4096 processes, the parallel efficiency of the new algorithm achieves 33.5% and 50.6% in strong and weak scalability, which corresponds to 21.4 and 32.4 in speedup, respectively.

     

雨雾淞导线覆冰理论模型数值模拟研究

导线覆冰的理论模型及数值模拟是研究覆冰过程机理的必要手段。 本文基于国际公认的导线覆冰理论模型框架,采用合理的覆冰过程物理参数化方法,构建了一套完整的数值计算方案,并利用其对雨雾淞导线覆冰过程进行了数值模拟研究,探讨了雨凇、雾淞及雨雾凇混合覆冰过程的机理及其演变特征。数值模拟结果表明：雾凇覆冰过程的增长曲线呈对数曲线变化特征,覆冰在开始阶段增长很快而随时间逐渐变慢; 而雨淞覆冰则随时间持续增长,且覆冰质量增长比覆冰厚度增长更为明显; 雨雾淞混合覆冰状态下覆冰的增长与单纯雨淞或雾凇覆冰的增长曲线均不同,由于干、湿覆冰机制的转换使覆冰增长过程呈现复杂的变化,而开始阶段无论是雨淞覆冰还是雾凇覆冰都可能表现出明显的湿增长特征。本文的研究结果揭示了雨雾凇导线覆冰过程的机理及其演变特征,具有较大的理论参考价值。