共查询到19条相似文献,搜索用时 62 毫秒
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热传导方程的一类无网格方法 总被引:1,自引:0,他引:1
构造求解热传导方程的一类无网格方法,只要选择好每个节点的适当的邻点集合,便可利用节点信息顺利进行计算.作为特殊情形,也可在各种结构或非结构网格上进行计算.在矩形或均匀平行四边形网格上进行计算时具有二阶精度,当在任意的不规则四边形或三角形网格上计算时仍然是守恒的和相容的,且至少具有一阶精度.作为数值试验,将该方法用于在不规则四边形网格上及四边形与三角形混合网格上求解二维非线性抛物型方程,并在不规则四边形网格上求解二维三温辐射热传导方程,均获得了较为理想的数值结果. 相似文献
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本文采用不规则网格的差分方法,对平面油水模型进行了数值模拟,并用IMPES方法计算了两个实例。例1的计算结果与精确解吻合良好,比Pedrosa的局部加密网格法使用的网格数少而且计算更简便。例2为矩形网格难以计算的问题,应用本文方法也得出了较好的结果。这表明本文的不规则网格差分方法是可靠而简便的,它可以有效地应用于复杂外边界和复杂地层结构的油藏模拟问题。 相似文献
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耦合径向基函数与多项式基函数的无网格方法 总被引:3,自引:1,他引:2
耦合径向基函数和多项式基函数,形成一种新的近似函数.该近似函数对散乱分布的离散数据点进行逼近时,只需节点信息,不需要划分网格.详细描述了耦合近似函数的建立、属性、插值行为及其形函数和形函数导数的性质.最后引入修正变分原理和单位分解积分技术求解边值问题,并给出了计算实例,表明耦合径向基函数和多项式基函数是一种非常有效的方法. 相似文献
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在移动最小二乘法的基础上,提出了复变量移动最小二乘法.复变量移动最小二乘法的优点是采用一维基函数建立二维问题的逼近函数,所形成的无网格方法计算量小.然后,将复变量移动最小二乘法应用于弹性力学的无网格方法,提出了复变量无网格方法,推导了复变量无网格方法的公式.与传统的无网格方法相比,复变量无网格方法具有计算量小、精度高的优点.最后给出了数值算例.
关键词:
移动最小二乘法
复变量移动最小二乘法
无网格方法
弹性力学
复变量无网格方法 相似文献
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陈文 《工程物理研究院科技年报》2003,(1):438-439
现在,有效的仿真能力在快速可靠的产品设计,实验数据处理,新的物理模型的建立等方面是—个重要工具。可是,在处理高维、自由表面、非常不规则几何域、多尺度大变形问题时,划分和再划分网格非常费时费力,甚至无法运行。网格型有限元,有限体积,有限差分和边界元方法对这些高难度问题不是非常有效。最近十几年,无网格方法的研究开始得到广泛的重视。基于径向基函数的数值离散算法在它的基函数中运用距离变量,因而对任意高维复杂几何问题原则上可以运用无网格散点数据求解。该方法数学简单,运用和编程也很容易。但是,传统的欧几里得距离变量是各向同性的。因而,此方法长期仅被用于各向同性问题。此外,各种常用的径向基函数和偏微分方程没有明显的内在联系,其应用的效率和可靠性因问题而异。 相似文献
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Local Collocation Approach for Solving Turbulent Combined Forced and Natural Convection Problems 下载免费PDF全文
Robert Vertnik & Božidar &Scaron arler 《advances in applied mathematics and mechanics.》2011,3(3):259-279
An application of the meshless Local Radial Basis Function Collocation
Method (LRBFCM) [22, 30–33] in solution of incompressible turbulent combined
forced and natural convection is for the first time explored in the present paper.
The turbulent flow equations are described by the low-Re number $k − ε$ model with
Launder and Sharma [23] and Abe et al. [1] closure coefficients. The involved temperature,
velocity, pressure, turbulent kinetic energy and dissipation fields are represented
on overlapping 5-noded sub-domains through the collocation by using
multiquadrics Radial Basis Functions (RBF). The involved first and second order
partial derivatives of the fields are calculated from the respective derivatives of the
RBF's. The involved equations are solved through the explicit time stepping. The
pressure-velocity coupling is based on Chorin's fractional step method [11]. The
adaptive upwinding technique, proposed by Lin and Atluri [27], is used because
of the convection dominated situation. The solution procedure is represented for
a 2D upward channel flow with differentially heated walls. The results have been
assessed by achieving a reasonable agreement with the direct numerical simulation
of Kasagi and Nishimura [20] for Reynolds number 4494, based on the channel
width, and Grashof number 9.6 × 105. The advantages of the represented mesh-free
approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward
applicability in non-uniform node arrangements. 相似文献
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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique. 相似文献
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A. Tadeu C. S. Chen J. Antόnio & Nuno Simõ es 《advances in applied mathematics and mechanics.》2011,3(5):572-585
Fourier transform is applied to remove the time-dependent variable in the
diffusion equation. Under non-harmonic initial conditions this gives rise to a
non-homogeneous Helmholtz equation, which is solved by the method of
fundamental solutions and the method of particular solutions. The particular
solution of Helmholtz equation is available as shown in [4, 15].
The approximate solution in frequency domain is then inverted
numerically using the inverse Fourier transform algorithm. Complex frequencies
are used in order to avoid aliasing phenomena and to allow the computation of
the static response. Two numerical examples are given to illustrate the
effectiveness of the proposed approach for solving 2-D diffusion equations. 相似文献
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针对带电导体附近急剧变化的位函数和场函数这一难于处理的边界条件,将小波函数的紧支撑特性和全域径向基函数(RBF)的高精度逼近能力相结合,提出电磁场边值问题求解的耦合方法并应用于接地金属槽/箱的数值计算中;将径向基函数无网格方法引入波导本征值的计算中,给出其求解本征问题的思路,建立相应的离散方程,分析矩形、圆形和脊形波导的本征值并与有限元方法进行比较.数值仿真实验表明,径向基函数及其耦合方法在分析电磁场边值和本征值问题时是有效的且具有实现简单、节点少和精度高的优势. 相似文献
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Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts. 相似文献
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三维粗糙面电磁双站散射的直接型区域分解计算 总被引:3,自引:0,他引:3
提出三维粗糙面双站电磁散射的直接型有限元-区域分解方法.首先建立含有迭代Robin边界条件(IRBC)的区域分解法耦合模型,再用内视法导出高度稀疏分块的分区耦合矩阵,之后给出缩减耦合矩阵带宽的子区域排序方法和IRBC的FFT加速算法.用有限元-完全匹配层和未分区的有限元-IRBC方法验证数值结果. 相似文献
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复合外场中磁光材料(BiTm)_3(FeGa)_5O_(12)薄膜畴壁运动特性的研究 总被引:1,自引:1,他引:0
通过对 (BiTm) 3 (FeGa) 5O12 膜施工加低频交变磁场 ,匀速率增加的直流磁场和同时对该膜施加这两种磁场 (复合外场 ) ,用照相划线读数方法和通过电荷耦合器件 (CCD) 计算机作数字化处理获得磁畴壁 (DW)的相对百分数。结果表明 :( 1 )复合外场下DW运动规律中存在交互作用项 ;( 2 )低频交变磁场幅值 ( 1 4 0A/m)远低于等效阻力场 ( 1 0 3 A/m)时 ,DW可以运动 ,但不同步 ,频率大于 1Hz时明显滞后 ,( 3 )利用图像转换有利于提高实验结果的分辨率。 相似文献