共查询到20条相似文献,搜索用时 578 毫秒
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数值求解二维Euler方程的有限体积法(如k-exact,WENO重构、紧致重构等),无一例外地要进行耗时的网格单元上的二维重构.然而这些二维重构最后仅用于确定网格单元边界上高斯积分点处的解值,单元上二维重构似乎并非必需的.因此,文章提出用网格边上的一维重构来取代有限体积法中网格单元上的二维重构,分别在一致矩形网格和非结构三角形网格上发展了基于网格边重构的求解二维Euler方程的新方法,称为降维重构算法.数值算例表明该算法可以计算有强激波的无黏流动问题,且有较高的计算效率. 相似文献
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计算二维静电场的非正交有限差分算法 总被引:1,自引:0,他引:1
讨论了计算二维维静电场的非正交有限差分算法,给出了数值计算公式,通过对一些实例的以及与理论解的比较,结果表明非正交有限差分算法具有数值网格的合的特点,只要较少用网格就可以达到较高的精度,是求解复杂边界情况下二维静电问题的一种有效方法。 相似文献
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应用直接边界元素法求解表征寄生电阻电容的混合边界条件拉普拉斯方程,处理角点法向电场间断是一个难点。作者曾提出了多重法向导数方法处理2-D角点处理,取得良好效果。 相似文献
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二维拉氏自适应流体动力学软件LAD2D,是采用建立在拉氏自适应结构和非结构网格上的有限体积格式,可以计算平面二维和柱对称二维多物质大变形弹塑性流体动力学问题。LAD2D软件系统主要由5部分组成:主控程序、数据模块、前处理模块、主体计算模块、网格模块和后处理模块。其中主体计算采用了结构网格与非结构网格联合使用的拉氏网格体系,计算格式采用了有限体积格式。网格模块包括网格生成、自适应网格加密(AMR技术)和网格重分技术,以及网格改变后物理量守恒重映技术。LAD2D软件系统由主体程序、二维网格生成程序(GRID2D)、二维自适应网格加密程序(AMR2D)、二维自适应程序(ADAPT2D)f[I-维物理量重映程序(REMAP2D)组成。 相似文献
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We present a novel dynamic approach for solid–fluid coupling by joining two different numerical methods: the boundary-element method (BEM) and the finite element method (FEM). The FEM results describe the thermomechanical evolution of the solid while the fluid is solved with the BEM. The bidirectional feedback between the two domains evolves along a Lagrangian interface where the FEM domain is embedded inside the BEM domain. The feedback between the two codes is based on the calculation of a specific drag tensor for each boundary on finite element. The approach is presented here to solve the complex problem of the descent of a cold subducting oceanic plate into a hot fluid-like mantle. The coupling technique is shown to maintain the proper energy dissipation caused by the important secondary induced mantle flow induced by the lateral migrating of the subducting plate. We show how the method can be successfully applied for modelling the feedback between deformation of the oceanic plate and the induced mantle flow. We find that the mantle flow drag is singular at the edge of the retreating plate causing a distinct hook shape. In nature, such hooks can be observed at the northern end of the Tonga trench and at the southern perimeter, of the South American trench. 相似文献
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《中国科学:物理学 力学 天文学(英文版)》2010,(8)
This paper deals with the computational simulation of both scalar wave and vector wave propagation problems in infinite domains. Due to its advantages in simulating complicated geometry and complex material properties, the finite element method is used to simulate the near field of a wave propagation problem involving an infinite domain. To avoid wave reflection and refraction at the common boundary between the near field and the far field of an infinite domain, we have to use some special treatments to this boundary. For a wave radiation problem, a wave absorbing boundary can be applied to the common boundary between the near field and the far field of an infinite domain, while for a wave scattering problem, the dynamic infinite element can be used to propagate the incident wave from the near field to the far field of the infinite domain. For the sake of illustrating how these two different approaches are used to simulate the effect of the far field, a mathematical expression for a wave absorbing boundary of high-order accuracy is derived from a two-dimensional scalar wave radiation problem in an infinite domain, while the detailed mathematical formulation of the dynamic infinite element is derived from a two-dimensional vector wave scattering problem in an infinite domain. Finally, the coupled method of finite elements and dynamic infinite elements is used to investigate the effects of topographical conditions on the free field motion along the surface of a canyon. 相似文献
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We present the direct formulation of the two-dimensional boundary element method (BEM) for time-harmonic dynamic problems in solids of general anisotropy. We split the fundamental solution, obtained by Radon transform, into static singular and dynamics regular parts. We evaluate the boundary integrals for the static singular part analytically and those for the dynamic regular part numerically over the unit circle.We apply the developed BEM to eigenvalue analysis. We determine eigenvalues of full non-symmetric complex-valued matrices, depending non-linearly on the frequency, by first reducing them to the generalized linear eigenvalue problem and then applying the QZ algorithm. We test the performance of the QZ algorithm thoroughly in comparison with the FEM solution. The proposed BEM is not only a strong candidate to replace the FEM for industrial eigenvalue problems, but it is also applicable to a wider class of two-dimensional time-harmonic problems. 相似文献
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Analysis of Two-Dimensional Thin Structures (from Micro- to Nano-Scales) Using the Singular Boundary Method 下载免费PDF全文
Dejian Shen & Yan Gu 《advances in applied mathematics and mechanics.》2015,7(5):597-609
This study investigates the applicability of the singular boundary method
(SBM), a recent developed meshless boundary collocation method, for the analysis
of two-dimensional (2D) thin structural problems. The troublesome nearly-singular
kernels, which are crucial in the applications of SBM to thin shapes, are dealt with
efficiently by using a non-linear transformation technique. Promising SBM results
with only a small number of boundary nodes are obtained for thin structures with
the thickness-to-length ratio is as small as 1E-9, which is sufficient for modeling most
thin layered coating systems as used in smart materials and micro-electro-mechanical
systems. The advantages, disadvantages and potential applications of the proposed
method, as compared with the finite element (FEM) and boundary element methods
(BEM), are also discussed. 相似文献
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Tadatoshi Tanifuji 《Optical Review》2009,16(3):283-289
Alternative boundary conditions for solving optical diffusion equations in three-dimensional (3-D) scattering medium by a
finite difference time domain (FDTD) analysis formulated by the author are proposed. The previous boundary conditions were
defined only by fluence rate, which, although essential, is only one factor needed to solve approximated diffusion equations
for fluence rate. In this paper, alternative boundary conditions defined both by fluence rate and radiant flux have been proposed
for use in the FDTD analysis, which is derived from the two coupled differential equations for fluence rate and radiant flux.
It has been become clear that these boundary conditions are almost equivalent to the previous boundary conditions in the FDTD
analysis for sufficiently fine grid spacing. For the analysis with coarser grid spacing, the proposed boundary conditions
suppress analytical errors, especially in intensity of time-resolved reflectance and transmittance. 相似文献
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A two-dimensional boundary element model for sound propagation in a homogeneous atmosphere above non-flat terrain has been constructed. An infinite impedance plane is taken into account in the Green's function in the underlying integral equation, so that only the non-flat parts of the terrain need to be discretised in the boundary element model. This Green's function is undefined for points below the impedance plane, and therefore valleys and hollows are taken into account by coupling the exterior domain above the ground with one or several interior domains below the ground, as suggested in a recent paper [J. Sound Vibrat. 223 (1999) 355]. The resulting BEM model, which can handle arbitrary combinations of barriers and hollows, has been used for validating a ray model for various difficult configurations, including combinations of valleys and barriers. 相似文献
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In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of our new PML approach, which we call as locally-conformal PML, using Monte Carlo simulations. The locally-conformal PML method is an easily implementable conformal PML implementation, to the problem of mesh truncation in the FEM. The most distinguished feature of the method is its simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. The method is based on a special complex coordinate transformation which is ‘locally-defined’ for each point inside the PML region. The method can be implemented in an existing FEM software by just replacing the nodal coordinates inside the PML region by their complex counterparts obtained via complex coordinate transformation. We first introduce the analytical derivation of the locally-conformal PML method for the FEM solution of the two-dimensional scalar Helmholtz equation arising in the mathematical modeling of various steady-state (or, time-harmonic) wave phenomena. Then, we carry out its numerical performance analysis by means of some Monte Carlo simulations which consider both the problem of constructing the two-dimensional Green’s function, and some specific cases of electromagnetic scattering. 相似文献
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《Journal of computational physics》2008,227(2):1225-1245
In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of our new PML approach, which we call as locally-conformal PML, using Monte Carlo simulations. The locally-conformal PML method is an easily implementable conformal PML implementation, to the problem of mesh truncation in the FEM. The most distinguished feature of the method is its simplicity and flexibility to design conformal PMLs over challenging geometries, especially those with curvature discontinuities, in a straightforward way without using artificial absorbers. The method is based on a special complex coordinate transformation which is ‘locally-defined’ for each point inside the PML region. The method can be implemented in an existing FEM software by just replacing the nodal coordinates inside the PML region by their complex counterparts obtained via complex coordinate transformation. We first introduce the analytical derivation of the locally-conformal PML method for the FEM solution of the two-dimensional scalar Helmholtz equation arising in the mathematical modeling of various steady-state (or, time-harmonic) wave phenomena. Then, we carry out its numerical performance analysis by means of some Monte Carlo simulations which consider both the problem of constructing the two-dimensional Green’s function, and some specific cases of electromagnetic scattering. 相似文献
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《Revue Generale de Thermique》1996,35(410):83-94
Application of the discrete method to the radiative heat transfer in a two-dimensional grey medium of complex geometry. This paper describes a new approach in determining the radiative intensity and the temperature fields in a semi-transparent medium enclosed in a two-dimensional cavity the boundary surfaces of which are uniformly grey and purely isotropic diffuse reflectors, with the help of a new combination of ray tracing, finite volumes and discrete ordinates method. Since the grid used can be unstructured, the technique is applicable to the calculation of radiative transfer in enclosures of complex geometry. The basic equations are given, followed by results for cases of simple geometry compared with the exact solutions and the treatment of other cases of more complex geometry. The method eliminates oscillations in the intensity field and yields accurate results. 相似文献
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密度矩阵重正化群方法(DMRG)在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器(CPU)和图形处理器(GPU)的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到104,使用的GPU显存小于12 GB. 相似文献