共查询到19条相似文献,搜索用时 62 毫秒
1.
构造了浅水方程组的二阶精度的TVD格式。格式由简单的TVD Runge-Kutta型时间离散和有坡度限制的空间对称离散格式组成。数值耗散项用局部棱柱化河道流的特征变量构造。格式的主要优点是能够计算天然河道中浅水方程组的弱解并且构造简单。格式能够求出天然河道或非平底部渠道中的精确静水解。给出了渠道溃坝问题数值解与解析解的比较,验证格式精度高。实际天然河道型梯级水库溃坝的数值实验表明格式稳定,适应性强。 相似文献
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本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性. 相似文献
3.
王泽军 《数学年刊A辑(中文版)》2005,(4)
本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性. 相似文献
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本文采用有限体积法结合高分辨率的TVD(总变差不增)格式,对平面激波遇矩形、三角形障碍物问题进行数值模拟,采用Schwarz变换生成计算网格,可使网格线在尖角处较密集且网格设置符合流场物理特性。初始阶段的流场复杂且粘性影响的尺度很小,模型中可以忽略流体的粘性。计算结果描述了平面无粘可压流中,由于弓形激波后熵与温度的不均匀性引起的尖角下游不定常集中涡的产生过程。数值计算与应我们要求所做激波管实验的光测结果相符合。 相似文献
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对复Schrdinger场和实Klein-Gordon场相互作用下一类耦合方程组的初边值问题进行了数值研究,提出了一个高效差分格式,该格式非耦合且为半显格式,因此比隐格式具有更快的计算速度,而且便于并行计算;同时,该格式很好地模拟了初边值问题的守恒性质,保证了格式计算的可靠性,从而便于长时间计算.细致讨论了格式的守恒性质,并在先验估计的基础上运用能量方法分析了差分格式的收敛性. 相似文献
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非线性演化方程显式精确解的新算法 总被引:1,自引:0,他引:1
本文给出了一种求解非线性演化方程的新算法 .将这种算法运用于变形浅水波方程 ,获得了八组显式精确解 ,其中包括新的孤波解和周期解 .借助于 Mathematica软件 ,这种算法能够在 Computer上实现 . 相似文献
10.
对复Schr(o)dinger场和实Klein-Gordon场相互作用下一类耦合方程组的初边值问题进行了数值研究,提出了一个高效差分格式,该格式非耦合且为半显格式,因此比隐格式具有更快的计算速度,而且便于并行计算;同时,该格式很好地模拟了初边值问题的守恒性质,保证了格式计算的可靠性,从而便于长时间计算.细致讨论了格式的守恒性质,并在先验估计的基础上运用能量方法分析了差分格式的收敛性. 相似文献
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The finite volume scheme of Vijayasundaram and Osher-Solomon type for shallow water equations are proposed. The numerical results with discontinuous initial condition and the comparison with Lax-Friedrichs numerical flux are presented for homogeneous case. The extension of the method for the inhomogeneous case is described. 相似文献
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M. V. Buntina V. V. Ostapenko 《Computational Mathematics and Mathematical Physics》2008,48(12):2241-2253
For the shallow water equations in the first approximation (Saint-Venant equations), a TVD scheme is developed for shock-capturing computations of open channel flows with discontinuous waves. The scheme is based on a special nondivergence approximation of the total momentum equation that does not involve integrals related to the cross-section pressure force and the channel wall reaction. In standard divergence difference schemes, most of the CPU time is spent on the computation of these integrals. Test computations demonstrate that the discontinuity relations reproduced by the scheme are accurate enough for actual discontinuous wave propagation to be numerically simulated. All the qualitatively distinct solutions for a dam collapsing in a trapezoidal channel with a contraction in the tailwater area are constructed as an example. 相似文献
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Abdul-Majid Wazwaz 《Applied mathematics and computation》2011,217(21):8840-8845
A variety of shallow water waves equations in (1 + 1) and (2 + 1) dimensions are investigated. We first show that these models are completely integrable. We next determine multiple-soliton solutions for each equation. The simplified Hirota’s bilinear method developed by Hereman will be employed to achieve this goal. A comparison between dispersion relations and the phase shifts will be conducted. (But possess the same coefficients for the polynomials of exponentials.) 相似文献
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Simulations of blood flows in arteries require numerical solutions
of fluid-structure interactions involving Navier-Stokes equations
coupled with large displacement visco-elasticity for the vessels.
Among the various simplifications which have been proposed, the
surface pressure model leads to a hierarchy of simpler models
including one that involves only the pressure. The model exhibits
fundamental frequencies which can be computed and compared with the
pulse. Yet unconditionally stable time discretizations can be
constructed by combining implicit time schemes with
Galerkin-characteristic discretization of the convection terms in
the Navier-Stokes equations. Such problems with prescribed pressure
on the walls will be shown to be efficient and accurate as an
approximation of the full fluid structure interaction problem. 相似文献
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Finite volume methods for dam-break flows over erodible sediment beds require a monotone numerical flux. In the present study we present a new flux-limiter scheme based on the Lax–Wendroff method coupled with a non-homogeneous Riemann solver and a flux limiter function. The non-homogeneous Riemann solver consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The proposed method satisfy the conservation property such that the discretization of the flux gradients and the source terms are well-balanced in the numerical solution of suspended sediment models. The flux-limiter method provides accurate results avoiding numerical oscillations and numerical dissipation in the approximated solutions. Several standard test examples are considered to verify the performance and the accuracy of the proposed method. 相似文献
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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
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浅水流动与污染物扩散的高分辨率计算模型 总被引:3,自引:0,他引:3
将组合型TVD格式应用于守恒型的浅水方程和污染物扩散方程,建立了二者耦合求解的高分辨率有限体积计算模型。给出了溃坝水流、明渠突扩流和污染物输运计算的典型算例,并与实验数据或其它数值结果进行了比较,证实了该模型的有效性,表明它不但能处理有激波的非恒定流问题,也能较好地计算具有任意边界的一般的浅水流动和污染物扩散问题,为浅水流动和水环境模拟提供了精度高、稳定性好、普适性强的数值方法。 相似文献
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Solving problems with free surface often encounters numerical difficulties related to excessive mesh distortion as is the case of dambreak or breaking waves. In this paper the Natural element method (NEM) is used to simulate a 2D shallow water flows in the presence of theses strong gradients. This particle-based method used a fully Lagrangian formulation based on the notion of natural neighbors. In the present study we consider the full non-linear set of Shallow Water Equations, with a transient flow under the Coriolis effect. For the numerical treatment of the nonlinear terms we used a Lagrangian technique based on the method of characteristics. This will allow avoiding divergence of Newton-Raphson scheme, when dealing with the convective terms. We also define a thin area close to the boundaries and a computational domain dedicated for nodal enrichment at each time step. Two numerical test cases were performed to verify the well-founded hopes for the future of this method in real applications. 相似文献
19.
In this paper, a finite difference method is used to approximate for the solution of the parabolic partial differential equation of order 2n and error of the method is determined. The resulting system is solved by efficient implicit iterations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method. 相似文献