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1.
作为近年来广受关注的一种数值方法,虚拟元方法具有很多优势。但在求解实际问题导出的一些辐射扩散方程时,该方法可能无法保证数值解的非负性及一般多边形网格上的局部守恒性。针对辐射扩散方程,利用非线性两点流逼近方法作为后处理措施,提出了一种基于虚拟元方法的保正守恒格式。该格式通过最低阶虚拟元方法得到数值解的单元顶点值,再利用非线性两点流逼近方法得到数值解的非负单元中心值,同时使格式满足局部守恒性。任意多边形网格上的数值结果表明,该格式具有保正性和解的近似二阶收敛速度,对于处理含强间断或非线性扩散系数的辐射扩散问题均有较强的适应性。 相似文献
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本文基于二阶导数的四阶Pade型紧致差分逼近式,并结合原方程本身,得到了三维Helmholtz方程的一种四阶精度的隐式紧致差分格式,该格式在每个空间方向上只涉及到三个点处的未知量及其二阶导数值。边界处对于二阶导数的离散格式利用四阶显式偏心格式。然后,利用Richardson外推法、算子插值法及二阶导数在边界点处的六阶显式偏心格式,将本文构造的格式精度提高到六阶。最后,通过数值实验验证了本文方法的精确性和可靠性。 相似文献
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在Banach空间利用单调迭代技巧和一个新的比较结果,研究了非线性混合型二阶微分积分方程两点边值问题耦合解的存在性及迭代逼近。 相似文献
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本文提出了一种新的最小二乘混合有限元方法求解Sobolev方程.采用了对υ和σ不同指标的有限元空间进行计算(LBB条件不需要),分析了此逼近格式的收敛性,并给出相应的误差估计.误差结果表明此种数值方法具有最优的收敛阶,并且关于时间具有二阶的收敛精度. 相似文献
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求解结构动力响应的一个新的高阶算法 总被引:3,自引:0,他引:3
本文将结构动力学问题转到状态空间中去研究并以三次Hermite插值多项式逼近状态变量,应用时间不连续的Galerkin方法推导出了一个单步递推算法公式,从对该算法公式的有限差分分析可知它是无条件强稳定、有效高精度并且有好的耗散、漂移和超调特性.给出了与Newmak的梯形法则、HHT-α及对状态变量的三次拉格朗日插值多项式逼近方法的分析和数值比较. 相似文献
6.
抛物型积分微分方程各向异性非协调有限元分析 总被引:2,自引:0,他引:2
各向异性有限元方法的显著的优点之一就是可以用较少的自由度得到与传统有限元正则剖分时同样的估计结果.然而,在这种情况下,Sobolev空间上的:Bramble-Hilbert引理在插值误差分析中不能直接应用,而且对于非协调元来说其传统边界估计技巧也不再适用.本文证明了一个非协调单元具有各向异性特征,并将它应用到研究抛物积分微分方程半离散格式下的Galerkin逼近.利用单元的特殊性,验证了Ritz-Volterra投影与有限元插值是相同的.在解适当光滑时,通过引入一些新的技巧,得到了与传统方法相同的收敛误差估计和超逼近性质.最后,通过构造适当的插值后处理算子,得到了各向异性网格下的整体超收敛结果.该文的结果对进一步探索和设计数值的自适应算法是有帮助的. 相似文献
7.
Banach空间混合型微分—积分方程极值解的存在性 总被引:3,自引:2,他引:1
在Banach空间得到了混合型二阶微分-积分方程两点边值问题的极值解,并给出了迭代逼近列。本文的结果推广了文」3「的中有关结果。 相似文献
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本文研究的是三维曲边区域上二阶椭圆型问题的等参有限元逼近。利用等参变换技巧和有限元插值理论,本文证明了等参有限元对于曲边区域边值问题具有最优收敛性,保证了等参有限元数值格式在工程应用中的可靠性和有效性。本文第二部分致力于构造简单有效的数值积分公式。文中给出的四点、五点、六点和八点六面体数值积分公式,可以简化单元刚度矩阵和荷载向量的计算,并严格证明了利用数值积分公式的等参元数值格式仍然保持最优收敛阶。 相似文献
10.
文中运用双参数法提出了一个4参数的四边形非协调有限元,讨论了该单元对纯位移边界条件下的均匀介质线弹性方程的逼近问题.证明了在材料几乎不可压时单元对弹性问题的一致最优收敛性,数值试验验证了理论分析结果.并通过构造后处理算子,得到了超收敛结果.所有的分析结果都可以推广到三维情形. 相似文献
11.
Approximating second‐order vector differential operators on distorted meshes in two space dimensions
F. Hermeline 《International journal for numerical methods in engineering》2008,76(7):1065-1089
A new finite volume method is presented for approximating second‐order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite; therefore, the most powerful linear solvers can be applied. The method has been tested on a few second‐order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second‐order accurate and locking‐free. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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L. Cea J. R. French M. E. Vzquez‐Cendn 《International journal for numerical methods in engineering》2006,67(13):1909-1932
In this paper an unstructured finite volume model for quasi‐2D tidal flow with wet–dry fronts and turbulence modelling is presented, and applied to the Crouch–Roach estuarine system (Essex, U.K.). Two depth averaged turbulence models, a mixing length model and a k–ε model, are used in the numerical computations. An additional limiter to the production of turbulence due to bed friction is introduced in order to improve the performance and numerical stability of the model near wet–dry fronts. In addition to a first‐order and a second‐order schemes, an hybrid second‐order/first‐order upwind scheme which improves the accuracy of the first‐order scheme while maintaining a good numerical stability is used to discretize the convective flux. Numerical results are compared with observed current speed and water level data, with particular reference to the ability of the model to reproduce shallow water tidal harmonics. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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A method for the numerical solution of a class of problems governed by a system of second order elliptic partial differential equations is derived. The solution to the boundary value problem is obtained in terms of an integral taken round part of the boundary of the region under consideration. Some numerical examples are considered and the results obtained are shown to be in excellent agreement with those obtained either analytically or by employing other numerical methods. 相似文献
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以轴向基础窄带随机激励悬臂梁非线性动力学方程组为分析对象。采用多尺度法,获得了系统主参激共振的非线性调谐方程组。在假设带宽较小的前提下,利用摄动法,获得了系统非平凡幅一频响应的1,2阶稳态矩近似理论表达式,并通过直接的数值积分获得了相应的曲线形式并进行了比较,取得了较好的一致性。分析结果表明:对于第1阶模态的主参激共振,其1,2阶稳态矩一频率特性呈现硬特性,而对于2阶及以上模态的主参激共振,系统1,2阶稳态矩一频率特性呈现软特性;带宽的小范围变化对1,2阶稳态矩产生的效应甚微。通过对概率密度进一步的数值计算,首次发现了系统的响应在非平凡平稳响应与平凡平稳响应间的随机跳跃现象,计算结果显示,随着带宽的增加,非平凡平稳响应处的概率密度逐渐减小,而平凡平稳响应处的概率密度随之增加。 相似文献
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研究了一类含弱非线性的改进型Boussinesq水波方程,在非交错网格下,利用有限差分法建立了混合四阶Adams-Bashforth-Moulton的预报校正格式的波浪数值模型。在数值模型中,关于空间一阶导数差分格式采用四阶精度、二阶导数差分格式采用二阶精度。针对波浪的一维、二维传播变形问题进行了数值计算,并通过与相关实验结果对比分析考察了该数值模型的适用性。 相似文献
16.
The stability of a linear oscillator with delayed state feedback driven by parametric Gaussian white noise is studied in this paper. The first and second order moment equations of the system response are derived by using moment method and Itô differential rule. Based on the moment equations, the delay-independent stable conditions of both moments are proposed: For the first order moment, the sufficient and necessary condition that guarantee delay-independent stability is identified to that of the deterministic system; for the second order moment, the sufficient condition that ensure delay-independent stability depends on noise intensity. The theoretical results are also illustrated with numerical simulations. 相似文献
17.
The Determination of Stress Distribution and Elastic Properties for Heterogeneous Materials with Hybrid Finite Element 总被引:1,自引:0,他引:1
F. Cesari F. M. Furgiuele C. Maletta 《International Journal of Mechanics and Materials in Design》2005,2(1-2):1-13
This paper describes a numerical method for evaluating the micro and macromechanical response of two-dimensional heterogeneous
materials with both periodic and random distribution of the second phase. The proposed method uses two different numerical
programs, based on the Voronoi Cell Finite Element Method, developed by the authors. Various numerical examples are executed
for validating the effectiveness of the proposed method in evaluating the overall elastic constants of heterogeneous materials,
and different comparison with analytical models and experimental results are shown. In order to validate the accuracy of the
programs for predicting the stress micro-fields around the inclusion, some comparisons with a FEM commercial numerical code
are performed. 相似文献
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The results are given of numerical experiment in processing the current–voltage characteristics of a plane probe in a plasma with an anisotropic function of velocity distribution of electrons (EVDF). In order to find the first and second moments of EVDF expansion in Legendre polynomials, the known procedures are employed to develop and approve the computer codes for numerical reconstruction of these moments by the measured first derivatives of electron current to the probe for different orientations of the latter. 相似文献