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181.
We use boundary value methods to compute consistent initial values for fully implicit nonlinear differential-algebraic equations.
The obtained algorithm uses variable order formulae and a deferred correction technique to evaluate the error. A rigorous
theory is stated for nonlinear index 1, 2 and 3 DAEs of Hessenberg form. Numerical tests on classical index 1, 2 and 3 DAE
problems are reported.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
182.
For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow. 相似文献
183.
Daniel T. Valentine 《国际流体数值方法杂志》1995,21(2):155-180
The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy. 相似文献
184.
本文将文献[9]提出改进的通量分裂方法,应用于随时间变化的贴体网格中,建立了可用于求解非定常Euler方程的通量分裂方法.该方法是以连续的特征值分离为基础,它具有方法简单,便于推广使用的特点.同时克服了Steger-Warming通量分裂方法存在的问题.对通量分裂后的Euler方程.利用MUSCL型迎风差分建立了具有二阶精度的有限体积方程.文中以NACA64A—10翼型为例,对其在跨音速流场中进行沉浮、俯仰及带有振动控制面引起的非定常气动载荷进行了计算.部分计算结果与相应的实验结果进行了比较,吻合良好 相似文献
185.
In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears. 相似文献
186.
A general class of Fuller modified maximum likelihood estimators are considered. It is shown that this class possesses finite moments. Asymptotic bias and asymptotic mean squared error are derived using small-σ expansions. A simulation study is carried out to compare different estimators in this class with standard estimators. 相似文献
187.
In this paper,based on the results presented in part Ⅰ of this paper[18],we present a numerical embedding algorithm for solving the nonlinear complementarityproblem, and prove its convergence carefully. Numerical experiments show that thealgorithm is successful. 相似文献
188.
Models are developed for decision making about monitoring andmaintenance of systems whose performance through time is describedby a general stochastic process. The system is monitored andpreventive and corrective maintenance actions are carried outin response to the observed system state. The decision processis simplified by using the maximum process as a decision variable.The models developed generalize age replacement models and othersimple maintenance strategies. The approach can deal with failuresthat prevent the system functioning further, and also failuresthat are defined by regulation or economic considerations. Attentionis restricted to perfect repair and inspection, but the structureprovides the framework for further developments. 相似文献
189.
Higher-order implicit strong numerical schemes for stochastic differential equations 总被引:2,自引:0,他引:2
Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined. 相似文献
190.
刘春平 《数学物理学报(A辑)》2004,4(6):661-668
该文给出了一种构造非线性发展方程显式行波解的方法并用该方法得到了Hirota-Satsuma方程组,一类非线性常微分方程以及广义耦合标量场方程组的显式行波解. 相似文献