Euler方程解的间断面的虚拟区域方法

用高分辨率激波捕捉格式求解Euler方程时，不可避免地会用到间断面两侧的点，从而在间断面附近发生数值耗散，降低分辨率．此文应用一种虚拟区域，将Level Set方法与高分辨率激波捕捉方法结合起来求解Euler方程，不使用间断面两侧的点，从而提高了分辨率．通过激波管问题的数值实验，可以看到这种方法的优越性．     

移动最小二乘微分求积法解Helmholtz方程

用一种新型的数值方法--移动最小二乘微分求积法（MLSDQ）求解二维Helmholtz方程。MLSDQ方法是一种直接将微分方程离散的方法，它是将未知函数的各阶偏导数在离散点处的值用域内各配点的函数值加权组合来表示，权系数则直接用移动最小二乘Galerkin法中的形函数求导得到，通过MLSDQ技术将Helmholtz方程和相应的边界条件转化成为一组关于各配点位势的线性代数方程组，求解这组代数方程，便可得到各配点的位势，通过求解几个具有精确解的算例，讨论了方法的收敛性和数值精度，结果表明：该方法较适合于求解小波数的Helmholtz方程,对高波数的方程，需要设置大量的域内配点才能有较好的数值结果。     

加导叶喷水推进器水动力特性研究

用数值方法计算了加导叶喷水推进器的水动力特性.在质量守恒定理和动量守恒定理的基础上建立不可压缩流体的积分方程,以SIMPLE为基本算法,结合速度修正方程和压力修正方程,求解喷水推进器的内部速度场和压力场,采用基于二方程雷诺数时均方程方法研究喷水推进的湍流模型.用数值方法建立喷水推进器的三维数学模型,用混合网格布置方法提高计算精度.分析了不同流量下加导叶喷水推进器的流量和扬程、功率和效率的关系.     

车路协同系统仿真信息多分辨率交互方法

车路协同系统仿真研究对于交通系统的发展具有重要的意义.为了研究车路协 同系统的仿真关键技术并构建车路协同系统仿真平台,本文提出信息多分辨率交互方法 解决基于HLA的系统仿真过程中的网络拥塞问题,建立了高分辨率车辆行驶状态信息模 型、中分辨率车队状态信息模型、低分辨率交通流信息模型,运用聚合解聚法实现不同信 息分辨率间的仿真过程,采用模糊预测发送缓冲区信息排队长度方法确定多分辨率模型 间的聚合解聚时机.通过仿真管理器联邦成员的运行结果分析表明,该方法能够有效减少 系统属性吞吐量,从而较好控制网络拥塞,降低系统属性延时,提高仿真效率.     

Maxwell方程特征值问题的谱方法

在传统微分方程求解中,多区域谱方法由于仅在局部单元独立构造方程的逼近格式,不同的单元通过惩罚边界或者边界上的数值流函数来进行信息交换,在基函数的选取和网格的剖分方面具有很好的灵活性和较高的精度。文章主要基于多区域谱方法对Maxwell微分方程的数值解进行研究,为了进一步降低求解方程的计算量,又引入了各种差分数值通量格式,当使用迎风通量时,格式支持的混杂模式的尺度被减小,尽管不能除去非物理特征值,但对谱得到了很清楚的分离,从而使得将物理模式与混合模式分离成为可能,使其适应于任意网格剖分的高精度、高效率算法,同时数值算例验证了该算法的有效性。     

超声速脉冲风洞起动过程数值模拟

为研究超声速脉冲风洞起动激波的传播过程和流场建立过程中流场结构的变化,对其起动过程进行了数值模拟.包含组分扩散的控制方程为二维粘性、可压缩、非定常的守恒型Navier-Stokes方程.用中心有限体积法进行空间离散,用隐式双时间步方法处理非定常时间项.计算结果与试验结果基本一致.研究表明,起动激波速度由于内型面的变化而改变,并在隔离段中达到最大值.     

一种求解线性二层规划的修正Frank-Wolf方法

利用迭代点校正方法，将非线性规划中的Frank—Wolf方法应用于线性二层规划问题，从而提出了一种求解线性二层规划的简单算法，同时给出了算法的收敛性．数值结果表明，给出的算法是可行有效的．     

船体粘性流场加速求解策略研究

为了在保证数值预报精度的前提下提高船体粘性流场数值求解速度,分析了基于数值求解RANS方程的时间步、网格节点数和离散格式对计算结果的影响,提出了加速求解策略.在最大时间步长限制下,采用缓慢增加时间步方法加速求解.对于低、中、高航速下的粘性流场求解,选择不同的协调因子比例.对自由液面位置赋合理初值.     

求解高维非线性方程的一种简便方法

将试探函数方法扩展应用于求解高维非线性偏微分方程.通过引入变换和选准试探函数,把难于求解的高维非线性偏微分方程化为易于求解的代数方程,然后用待定系数法确定相应的常数,从而简洁地求得了方程的解析解.     

弹性地基板自由振动的样条函数解

本文提出一种用样条函数分析弹性地基板自由振动的新方法。按。‘er恤方法导出 弹性地羞板系统翻率方程的标准形式,避免了求解二次特征值间题.本法程序简单, 非常适合于徽机计算。数据准备工作量及方程阶次均明显少于其他方法。数值算例表 明,本文方法是经济而且有效的.’      

Steady state analysis of towed marine cables

Efficient numerical schemes were presented for the steady state solutions of towed marine cables. For most of towed systems, the steady state problem can be resolved into two-point boundary-value problem, or initial value problem in some special cases where the initial values are available directly. A new technique was proposed and attempted to solve the two-point boundary-value problem rather than the conventional shooting method due to its algorithm complexity and low efficiency. First, the boundary conditions are transformed into a set of nonlinear governing equations about the initial values, then bisection method is employed to solve these nonlinear equations with the aid of 4th order Runge-Kutta method. In common sense, non-uniform (sheared) current is assumed, which varies in magnitude and direction with depth. The schemes are validated through the DE Zoysa's example, then several numerical examples are also presented to illustrate the numerical schemes.     

Numerical Investigation of the Dynamics for Low Tension Marine Cables

This paper presents a numerical investigation into the dynamics of marine cables which are extensively used in offshore industry. In this numerical study, the Euler-Bernoulli beam model is adopted to develop the governing equations of the cable. Bending stiffness is considered to cope with the low tension problem in local area of towing cable, and thus a more accurate solution with the consideration of the axial elongation can be given.The derived strongly-coupled and nonlinear governing equations are solved by a second-order accurate, implicit,and large time step stable central finite difference method. The quadratically convergent Newton-Raphson iteration method is applied to solving the discrete nonlinear algebraic equations. Then a towed array sonar system(TASS)problem is studied. The numerical solutions agree reasonably well with the experimental data and the simulated results of the references. The specified program of the present paper shows great robustness with high efficiency.     

Numerical Solution for Stiff Dynamic Equations of Flexible Multibody System

A nonlinear numerical integration method, based on forward and backward Euler integration methods, is proposed for solving the stiff dynamic equations of a flexible multibody system, which are transformed from the second order to the first order by adop- ring state variables. This method is of A0 stability and infinity stability. The numerical solutions violating the constraint equations are corrected by Blajer's modification approach. Simulation results of a slider-crank mechanism by the proposed method are in good a- greement with ones from other literature.     

An Iterative Stabilized Scheme for Unsteady Incompressible Viscous Flow

An efficient iterative algorithm is presented for the numerical solution of viscous incompressible NavierStokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and liddriven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.     

Adomian’s Method applied to solve ordinary and partial fractional differential equations

This paper presents a method to solve the problems of solutions for integer differential and partial differential equations using the convergence of Adomian’s Method. In this paper, we firstly use the convergence of Adomian’s Method to derive the solutions of high order linear fractional equations, and then the numerical solutions for nonlinear fractional equations. we also get the solutions of two fractional reaction-diffusion equations. We can see the advantage of this method to deal with fractional differential equations.     

断裂力学中奇异积分方程的数值求解方法

对断裂力学中奇异积分方程的数值求解技术进行了综述。重点论述了第一类和第二类Cauchy型奇异积分方程以及超奇异积分方程的数值解法。这些方法的主要思想都是通过将奇异积分方程中的未知函数表示为多项式形式连续函数与特定形式权函数的乘积,然后借助Cauchy主值积分定义与超奇异积分的有限部积分定义,将奇异积分方程的求解归结为求解一组线性代数方程。本文拟结合一些具体的数值算例,对奇异积分方程中未知函数的不同表达方式、特点进行了评述,并比较了各种算法的优缺点。最后,指出了求解奇异积分方程的数值解法研究的未来发展方向。     

可转换债券定价模型的RBF数值解

基于相机权益分析方法,建立了信用风险影响下的可转换债券定价模型及相应的初边值条件,并采用径向基配置法对该定价模型进行了数值求解.通过数值模拟讨论了信用风险对可转换债券价值的影响,并对桂冠转债的定价作了实证研究.结果表明,考虑信用风险的可转换债券定价模型能有效地提高定价精度.     

Finite Element Methods for Coupled Stokes and Darcy Problems

We derived and analyzed a new numerical scheme for the coupled Stokes and Darcy problems by using H(div) conforming elements in the entire domain. The approach employs the mixed finite element method for the Darcy equations and a stabilized H(div) finite element method for the Stokes equations. Optimal error estimates for the fluid velocity and pressure are derived. The finite element solutions from the new scheme not only feature a full satisfaction of the continuity equation, which is highly demanded in scientific computing, but also satisfy the mass conservation.