共查询到20条相似文献,搜索用时 187 毫秒
1.
2.
3.
4.
提出了一种基于AH(Associated Hermite)正交基函数求解对流扩散方程的无条件稳定算法。该算法将方程的时间项通过Hermite多项式作为正交基函数进行展开,利用Galerkin方法消除时间变量项,从而导出有限维AH域隐式差分方程,突破了传统显式差分格式稳定性条件的限制,最后通过对AH域展开系数的求解得到该对流扩散方程的数值解。在数值算例中,将该算法与传统显示差分法和交替方向隐式差分法进行对比分析,数值计算结果表明,算法无条件稳定且其计算精度与时间步长无关,对于具有精细结构的对流换热问题,该算法具有明显的效率优势,且保持了较高的精度。 相似文献
5.
6.
极限下限分析的正交基无单元Galerkin法 总被引:1,自引:0,他引:1
基于极限分析的下限定理,建立了用正交基无单元Galerkin法进行理想弹塑性结构极
限分析的整套求解算法.下限分析所需的虚拟弹性应力场可由正交基无单元Galerkin法直接
得到,所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模
拟.这些自平衡应力场基矢量可由弹塑性增量分析中的平衡迭代得到.通过对自平衡应力场
子空间的不断修正,整个问题的求解将化为一系列非线性数学规划子问题,并通过复合形法
进行求解.算例表明该方法有效地克服了维数障碍问题,使计算效率得到了充分的提高,是
切实可行的. 相似文献
7.
8.
具有分数导数本构关系的非线性粘弹性Timoshenko梁动力学行为分析 总被引:8,自引:0,他引:8
本文利用分数导数型本构关系建立了在有限变形情况下Timoshenko梁的控制方程并利用Galerkin方法进行简化。然后利用一种存储部分历史数据的分数积分的计算方法对梁的控制方程进行求解。考察了载荷参数和分数导数参数对梁振动的影响,并采用非线性动力学中的各种数值方法,如时程曲线、功率谱、相图、Poincare截面等,揭示了非线性粘弹性Timoshenko梁丰富的动力学行为。 相似文献
9.
10.
在迭代图胞映射方法的框架下,基于摄动微分多项式的思想讨论了常微分方程的快速求解,将所得结果与迭代图胞映射方法有机结合,有效地解决了迭代图胞映射动力系统的快速生成问题,克服了微分方程动力系统生成迭代图胞映射系统过程中耗时较多、效率低下的不足,大大提高了计算效率。通过对典型非线性系统——杜芬方程的应用分析,证实了该方法的有... 相似文献
11.
In this brief communication, Melnikov's method is adopted to study the chaotic behaviors of a two-dimensional thin panel subjected to subsonic flow and external excitation. The nonlinear governing equations of the subsonic panel system are reduced to a series of ordinary differential equations by using Galerkin method. The critical parameters for chaos are obtained. It is found that the critical parameters obtained by the theoretical analysis are in agreement with the numerical simulations. The method suggested in this paper can also be extended for other fluid-structure dynamic systems, such as the fluid-conveying system. 相似文献
12.
The dissipative quantum Zakharov equations are mainly studied. The existence and uniqueness of the solutions for the dissipative quantum Zakharov equations are proved by the standard Galerkin approximation method on the basis of a priori estimate. Meanwhile, the asymptotic behavior of solutions and the global attractor which is constructed in the energy space equipped with the weak topology are also investigated. 相似文献
13.
建立考虑横向剪切与转动惯量影响的矩形板的动力控制方程,应用Galerkin方法将其化为Mathieu方程,然后根据Lyapunov-Schmidt方法得到了系统在参数激励下的1/2亚谐分叉特性,并给出了四边简支与四边固支弹性薄板的非线性动力屈曲分叉条件。 相似文献
14.
By using the method of quasi-shells,the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral tri- angle cell are founded.By using the method of the separating variable function,the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support.The tensile force is solved out from the compati- ble equations,a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin.The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function.The existence of the chaotic motion of the single-layer shallow cylin- drical reticulated shell is approved by using the digital simulation method and Poincarémapping. 相似文献
15.
Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation
下载免费PDF全文
![点击此处可从《国际流体数值方法杂志》网站下载免费的PDF全文](/ch/ext_images/free.gif)
We present a new non‐intrusive model reduction method for the Navier–Stokes equations. The method replaces the traditional approach of projecting the equations onto the reduced space with a radial basis function (RBF) multi‐dimensional interpolation. The main point of this method is to construct a number of multi‐dimensional interpolation functions using the RBF scatter multi‐dimensional interpolation method. The interpolation functions are used to calculate POD coefficients at each time step from POD coefficients at earlier time steps. The advantage of this method is that it does not require modifications to the source code (which would otherwise be very cumbersome), as it is independent of the governing equations of the system. Another advantage of this method is that it avoids the stability problem of POD/Galerkin. The novelty of this work lies in the application of RBF interpolation and POD to construct the reduced‐order model for the Navier–Stokes equations. Another novelty is the verification and validation of numerical examples (a lock exchange problem and a flow past a cylinder problem) using unstructured adaptive finite element ocean model. The results obtained show that CPU times are reduced by several orders of magnitude whilst the accuracy is maintained in comparison with the corresponding high‐fidelity models. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
16.
In this paper we present new numerical algorithms based on a generalized nonlinear Galerkin method in order to solve coastal and oceanic circulation problems. The equations system is based on the primitive equations of the ocean under Boussinesq and hydrostatic approximations. These equations are transformed using, at the same time, the classical σ transformation and an original homogenization of the boundary conditions. We use a well adapted special basis to apply the usual Galerkin method and the nonlinear Galerkin method. This basis is built on a modelization of the energetic transfers through the different scales of flow. Two approaches are proposed to solve the continuity equation: the (nonlinear) Galerkin method and the method of the characteristics. We present the advantages and drawbacks of both methods. 相似文献
17.
In a previous work (Park HM, Lee MW. An efficient method of solving the Navier–Stokes equation for the flow control. International Journal of Numerical Methods in Engineering 1998; 41 : 1131–1151), the authors proposed an efficient method of solving the Navier–Stokes equations by reducing their number of modes. Employing the empirical eigenfunctions of the Karhunen–Loève decomposition as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear sub‐space that is sufficient to describe the observed phenomena, and consequently, reduce the Navier–Stokes equations defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. In the present work, we apply this technique, termed the Karhunen–Loève Galerkin procedure, to a pointwise control problem of Navier–Stokes equations. The Karhunen–Loève Galerkin procedure is found to be much more efficient than the traditional method, such as finite difference method in obtaining optimal control profiles when the minimization of the objective function has been done by using a conjugate gradient method. 相似文献
18.
基于伽辽金加权残值法,本文首先建立一维饱和土动力学控制微分方程的弱形式,而后分别采用微分求积法和有限元法将其空间坐标离散,得到以土体骨架位移、流体-土骨架相对位移和孔隙流体压力为自由度的单元离散方程,从而采用Crank-Nicolson 法求解.数值算例一方面通过与解析解的对比,验证了离散方程和数值程序的正确性.另一方面,通过地表位移和基底孔隙压力的收敛性分析,检验了求积元和有限元法的收敛效率.数值结果表明:所建立的弱式微分求积法在饱和土动力分析中不仅具有显著优于常规有限元法的收敛效率,而且还具有可变阶的收敛性能,为今后高效率分析提供了一种可能. 相似文献
19.
肖黎明 《应用数学和力学(英文版)》1999,20(7):801-806
1TheProposalofProblemWeconsiderafamilyoflinearelasticshelsofthicknes2ε,alhavingthesamemiddlesurfaceS=φ(ω)R3,whereωR2isaboun... 相似文献
20.
Chun-Sheng Chen Wei-Ren Chen Rean-Der Chien 《European Journal of Mechanics - A/Solids》2009,28(2):329-337
In this paper, the dynamic stability of laminated hybrid composite plates subjected to periodic uniaxial stress and bending stress is studied. The governing equations of motion of Mathieu-type are established by using the Galerkin method with reduced eigenfunctions transforms. Based on Bolotin's method the regions of dynamic instability of laminated hybrid composite plates are determined by solving the eigenvalue problems. The effects of layer thickness ratio, layer number, core material and load parameter on the dynamic instability of laminated hybrid composite plates are investigated and discussed. 相似文献