共查询到10条相似文献,搜索用时 128 毫秒
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In this paper, we propose a robust finite volume scheme to numerically solve
the shallow water equations on complex rough topography. The major difficulty of this
problem is introduced by the stiff friction force term and the wet/dry interface tracking.
An analytical integration method is presented for the friction force term to remove the
stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by
introducing an empirical parameter, the water depth tolerance, as extensively adopted
in literatures. We propose a problem independent formulation for this parameter, which
provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The
method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency. 相似文献
3.
This paper proposes a fluid-solid coupled finite element formulation for the transient simulation of water-steam energy systems with phase change due to boiling and condensation. As it is commonly assumed in the study of thermal systems, the transient effects considered are exclusively originated by heat transfer processes. A homogeneous mixture model is adopted for the analysis of biphasic flow, resulting in a nonlinear transient advection-diffusion-reaction energy equation and an integral form for mass conservation in the fluid, coupled to the linear transient heat conduction equation for the solid. The conservation equations are approximated applying a stabilized Petrov-Galerkin FEM formulation, providing a set of coupled nonlinear equations for mass and energy conservation. This numerical model, combined with experimental heat transfer coefficients, provides a comprehensive simulation tool for the coupled analysis of boiling and condensation processes. For the treatment of enthalpy discontinuities traveling with the flow, a novel explicit-implicit time integration method based on Crank-Nicolson scheme is proposed, analyzing its accuracy and stability properties. To reduce problem size and enhance numerical efficiency, a modal superposition method with balanced truncation is applied to the solid equations. Finally, different example problems are solved to demonstrate the capabilities, flexibility and accuracy of the proposed formulation. 相似文献
4.
The truncated singular value decomposition (TSVD) is a popular solution method for small to moderately sized linear ill-posed
problems. The truncation index can be thought of as a regularization parameter; its value affects the quality of the computed
approximate solution. The choice of a suitable value of the truncation index generally is important, but can be difficult
without auxiliary information about the problem being solved. This paper describes how vector extrapolation methods can be
combined with TSVD, and illustrates that the determination of the proper value of the truncation index is less critical for
the combined extrapolation-TSVD method than for TSVD alone. The numerical performance of the combined method suggests a new
way to determine the truncation index.
In memory of Gene H. Golub. 相似文献
5.
Computational Discretization Algorithms for Functional Inequality Constrained Optimization 总被引:6,自引:0,他引:6
In this paper, a functional inequality constrained optimization problem is studied using a discretization method and an adaptive scheme. The problem is discretized by partitioning the interval of the independent parameter. Two methods are investigated as to how to treat the discretized optimization problem. The discretization problem is firstly converted into an optimization problem with a single nonsmooth equality constraint. Since the obtained equality constraint is nonsmooth and does not satisfy the usual constraint qualification condition, relaxation and smoothing techniques are used to approximate the equality constraint via a smooth inequality constraint. This leads to a sequence of approximate smooth optimization problems with one constraint. An adaptive scheme is incorporated into the method to facilitate the computation of the sum in the inequality constraint. The second method is to apply an adaptive scheme directly to the discretization problem. Thus a sequence of optimization problems with a small number of inequality constraints are obtained. Convergence analysis for both methods is established. Numerical examples show that each of the two proposed methods has its own advantages and disadvantages over the other. 相似文献
6.
The damping of laminar fluid transients in piping systems is studied numerically using a two-dimensional water hammer model. The numerical scheme is based on the classical fourth order Runge–Kutta method for time integration and central difference expressions for the spatial terms. The results of the present method show that the damping of transients in piping systems is governed by a non-dimensional parameter representing the ratio of the Joukowsky pressure force to the viscous force. In terms of time scales, this non-dimensional parameter represents the ratio of the viscous diffusion time scale to the pipe period. For small values of this parameter, the damping of the fluid transient becomes more pronounced while for large values, the fluid transient is subjected to insignificant damping. Moreover, the non-dimensional parameter is shown to influence other important transient phenomena such as line packing, instantaneous wall shear stress values and the Richardson annular effect. 相似文献
7.
分析了N.M.Newmark和E.L.Wilson等按位移作变量逐步积分法的主要特点.提出以速度为变量求解动力学问题的速度元法.针对无阻尼系统,构造了一种简化格式,讨论了稳定性.由于该格式在无阻尼和拟静力阻尼情况下为显式,每个时刻,不求解代数方程组,其计算量与Newmark等方法比较,显著减少.对非线性动态问题,该计算格式可作为取得较好迭代初值的一个办法.文中,就任意阻尼系统,列出了速度元法的推广形式.相应非线性情况,提供了速度增量迭代格式并证明了收敛性.文末,附录了典型问题的数值检验结果. 相似文献
8.
《Chaos, solitons, and fractals》2006,27(3):748-757
This paper investigates bifurcation and chaos in transverse motion of axially accelerating viscoelastic beams. The Kelvin model is used to describe the viscoelastic property of the beam material, and the Lagrangian strain is used to account for geometric nonlinearity due to small but finite stretching of the beam. The transverse motion is governed by a nonlinear partial-differential equation. The Galerkin method is applied to truncate the partial-differential equation into a set of ordinary differential equations. When the Galerkin truncation is based on the eigenfunctions of a linear non-translating beam subjected to the same boundary constraints, a computation technique is proposed by regrouping nonlinear terms. The scheme can be easily implemented in practical computations. When the transport speed is assumed to be a constant mean speed with small harmonic variations, the Poincaré map is numerically calculated based on 4-term Galerkin truncation to identify dynamical behaviors. The bifurcation diagrams are present for varying one of the following parameter: the axial speed fluctuation amplitude, the mean axial speed and the beam viscosity coefficient, while other parameters are unchanged. 相似文献
9.
Based on a weighted average of the modified Hellinger-Reissner principle and its dual, the combined hybrid finite element (CHFE) method was originally proposed with a combination parameter limited in the interval (0, 1). In actual computation this parameter plays an important role in adjusting the energy error of discretization models. In this paper, a novel expression of the combined hybrid variational form is used to show the relationship between the resultant method and some Galerkin/least-squares stabilized finite scheme for plate bending problems. The choice of combination parameter is then extended to (−∞, 0) ? (0, 1). Existence, uniqueness and convergence of the solution of discrete schemes are proved, and the advantage of the parameter extension in computation is discussed. As an application, improvement of Adini’s rectangular element by the CHFE approach is performed. 相似文献
10.
Summary. In this paper we study the numerical behaviour of elliptic
problems in which a small parameter is involved and an example
concerning the computation of elastic arches is analyzed using this
mathematical framework. At first, the statements of the problem and its
Galerkin approximations are defined and an asymptotic
analysis is performed. Then we give general conditions ensuring that
a numerical scheme will converge uniformly with respect to the small
parameter. Finally we study an example in
computation of arches working in linear elasticity conditions. We build one
finite element scheme giving a locking behaviour, and another one
which does not.
Revised version received October 25, 1993 相似文献