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1.
快速多极子展开技术在高阶边界元方法中的实现   总被引:1,自引:0,他引:1  
高阶边界元法以较常数元方法计算精度高存储低而在工程计算中得到了广泛的应用,但由于其平方存储和计算量的本质,无法应用于大型工程问题中。本文将快速多极子方法(FMM)应用于高阶边界元中从而使其计算量和存储量分别降为O(Nlog N)和O(N)。通过无限区域中水流绕射算例的数值计算,对FMM高阶边界元法与传统高阶边界元法的运算速度和内存消耗进行了分析对比,结果表明对于大型计算问题FMM高阶边界元算法更加有效。  相似文献   

2.
pFFT快速边界元方法模拟三维声散射   总被引:1,自引:1,他引:0  
研究了用pFFT快速边界元方法模拟声散射问题的关键技术。采用Burton—Miller方程消除了声学边界元方法中外问题解的不唯一现象。为此,文中研究了采用常量元时该方程中超奇异积分的计算方法。最后,通过对平面声波的刚性圆球声散射的数值模拟,验证了建立的声学pFFT快速边界元方法。  相似文献   

3.
港口非线性波浪耦合计算模型研究   总被引:5,自引:1,他引:4  
建立了外域用差分法求解高阶Boussinesq方程、内域用边界元法求解Laplace方程的二维船 非线性波浪力时域计算的耦合模型. 研究了该类耦合模型的匹配条件、耦合求解过程和内域、 外域公共区域长度的确定. 该耦合模型计算结果与只用边界元求解Laplace方程模型的计算 结果和实验结果对比表明,该耦合模型不仅计算精度高,而且计算效率快,适用于研究较大 区域内波浪对物体的非线性作用.  相似文献   

4.
针对双色波浪与均匀流相互作用问题,采用时域高阶边界元方法建立自由水面满足完全非线性边界条件的数学模型。求解中采用混合欧拉-拉格朗日方法追踪流体瞬时水面,运用四阶龙格库塔方法更新下一时间步的波面和速度势。通过与已发表试验结果对比,验证了本模型的准确性。通过数值计算研究了水流参数对各组成波及衍生的高阶波幅值、波浪和水流间能量交换的影响规律。  相似文献   

5.
王本龙  刘桦 《力学季刊》2005,26(3):346-353
本文讨论了采用高阶Boussinesq方程模拟波浪散射时对基本速度变量位置的局部光滑处理方法。通过光滑局部基本速度变量的取值深度,减小其高阶导数项的量值、加快级数收敛速度进而改善模型方程求解深水波浪散射问题的能力。对于底部边界具有一阶导数不连续的情况,通过局部光滑.可以将基本速度变量取值深度尖角转化为圆角过渡,从而改善速度分布。对于其它任意变化的底部边界,为了减少高阶底坡导数项的影响,在曲率和高阶底坡导数项与斜率具有相同量级的情况下亦需要对基本速度变量的取值深度局部光滑。数值计算结果表明本文提出的光滑技术可以很好地改善Boussinesq方程模拟浅水波和深水波在斜坡地形上散射问题的能力。  相似文献   

6.
为了分析不同参数对波浪型辐板车轮声辐射特性的影响,根据列车波浪型辐板的建模方法,建立了不同波浪个数、不同波浪幅度的波浪型辐板车轮。首先,利用分块Lanzos法计算出不同波浪个数、不同波浪幅度的波浪型辐板车轮的固有模态;然后运用模态叠加法计算出简谐力作用下车轮的动态响应,并进行了对比分析;最后利用有限元-边界元方法,将车轮外表面的位移响应处理成声学边界元输入,得到不同波浪个数、不同波浪幅度车轮的声辐射功率大小。计算结果表明:波浪型辐板车轮在2波浪和6波浪时具有较低的声辐射功率;6波浪辐板车轮在波浪幅度约为30mm时,具有较低的声辐射功率。此结果为国内波浪型辐板车轮的研究提供了一定的参考。  相似文献   

7.
针对边界元法中高阶单元中几乎奇异积分计算难题,解剖了二维边界元法高阶单元的几何特征,定义源点相对高阶单元的接近度。将高阶单元上奇异积分核函数用近似奇异函数逼近,从而分离出积分核中主导的奇异函数部分,其奇异积分核分解为规则核函 数和奇异核函数两项积分之和。规则核函数用常规高斯数值积分,再对奇异核函数积分导出解析公式,从而建立了一种新的半解析法,用于高阶边界单元上几乎强奇异和超奇异积分计算。给出3个算例,采用边界元法高阶单元的半解析法计算了弹性力学薄体结构和近边界点位移/应力,并与线性边界元正则化算法结果作了比较,结果表明提出的二次元的半解析算法更加有效。特别是分析薄体结构,采用正则化算法的线性边界元分析比有限元有显著优势,而用提出的二次边界元半解析算法分析比其线性元的有效接近度又减小了4个量级。  相似文献   

8.
波流与结构物相互作用的数值模拟   总被引:2,自引:2,他引:0  
采用高阶边界元法建立波流与任意形状结构物相互作用的时域数学模型。在小流速假设下,将速度势进行摄动展开,边界条件分解为双物体假设下的零阶波陡稳定问题和一阶波陡下的不稳定波浪问题。物面速度势及自由水面速度势的法向导数等未知量通过求解高阶边界元积分方程得到,而积分方程的求解则通过一个数值程序来实现。在每个时间步上采用四阶Runge-Kutta法更新下一时刻自由水面波面和速度势,自由水面上采用人工阻尼层消除散射波。通过波流与直立圆柱相互作用的数值计算研究了一阶激振力和二阶慢漂力随波数的变化关系以及圆柱周围波幅的分布曲线,并与已有频域结果和时域结果对比验证了所建模型的准确性,进而应用本文模型研究了波流与实际工程结构物相互作用的问题。  相似文献   

9.
李俊  冯伟哲  高效伟 《力学学报》2016,48(2):387-398
相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果.  相似文献   

10.
提出了一种精确计算任意高阶奇异曲线积分的直接计算法.首先将曲线单元上的各种几何量用投影线上的几何量来表示,然后通过幂级数展开和解析的方法显式地消除了积分的奇异性.还导出了计算等参坐标对局部直角坐标偏导数的表达式.由于这种方法涉及到的是总体尺度间的坐标变换,操作起来直观明了,可以处理二维问题边界元分析中出现的任意高阶奇异边界积分.最后用具体算例验证该方法的正确性.  相似文献   

11.
A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered.This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h = O(H 2),which can still maintain the asymptotically optimal accuracy.It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution,which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h.Hence,the two-level stabilized finite element method can save a large amount of computational time.Moreover,numerical tests confirm the theoretical results of the present method.  相似文献   

12.
A numerical algorithm to determine the impingement of an axisymmetric free jet upon a curved deflector is presented. The problem is considered within the potential flow theory with the allowance of gravity and surface tension effects. The primary dependent variable is the Stokes streamfunction, which is approximated through finite elements using the isoparametric Hermite Zienkiewicz element. To find the correct position of the free boundaries, a trial-and-error method is employed which amounts to solving a boundary value problem (BVP) for the Stokes streamfunction at each iteration step. An efficient method is proposed to solve this BVP. The algorithm to find the correct position of the free boundaries is tested by computing the impingement upon an infinite disc and a hemispherical deflector. To confirm the correctness of the solution, each problem has been solved using several different mesh gradings. A comparison between the Zienkiewicz and the other standard C0 finite elements is also given.  相似文献   

13.
OPS算法中目标函数以及如何获取目标函数最优解是决定算法优劣的重要因素。对比分析了4种目标函数和10种求最优解方法在网格数、初始点位置、迭代次数以及需求精度等因素变化时对OPS算法优化效果的影响。结果表明,在顶点移动过程中目标函数f1和f4变化较为光滑。采用不同目标函数时,随着网格数的增加优化时间随之增加,但优化后最差单元质量并无此规律;随着需求精度的增加,网格中最差单元质量和优化时间都有所增加,迭代次数变化对于优化时间和优化效果的影响可以忽略不计。采用变尺度法求解目标函数下降方向以及二次插值法进行一维搜索的第6种方法,在耗费时间、优化效果以及收敛速度等方面都显示出了较好的优势。  相似文献   

14.
There are many challenges in the numerical simulation of liquid sloshing in horizontal cylinders and spherical containers using the finite element method of arbitrary Lagrangian–Eulerian (ALE) formulation: tracking the motion of the free surface with the contact points, defining the mesh velocity on the curved wall boundary and updating the computational mesh. In order to keep the contact points slipping along the curved side wall, the shape vector in each time advancement is defined to modify the kinematical boundary conditions on the free surface. A special function is introduced to automatically smooth the nodal velocities on the curved wall boundary based on the liquid nodal velocities. The elliptic partial differential equation with Dirichlet boundary conditions can directly rezone the inner nodal velocities in more than a single freedom. The incremental fractional step method is introduced to solve the finite element liquid equations. The numerical results that stemmed from the algorithm show good agreement with experimental phenomena, which demonstrates that the ALE method provides an efficient computing scheme in moving curved wall boundaries. This method can be extended to 3D cases by improving the technique to compute the shape vector. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

15.
This study presents an improved ghost‐cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work, ghost cells are mirrored through the boundary described using a level‐set method to farther image points, incorporating a higher‐order extra/interpolation scheme for the ghost‐cell values. A sensor is introduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement is used to improve the representation of the geometry efficiently in the Cartesian grid system. The improved ghost‐cell method is validated against four test cases: (a) double Mach reflections on a ramp, (b) smooth Prandtl–Meyer expansion flows, (c) supersonic flows in a wind tunnel with a forward‐facing step, and (d) supersonic flows over a circular cylinder. It is demonstrated that the improved ghost‐cell method can reach the accuracy of second order in L1 norm and higher than first order in L norm. Direct comparisons against the cut‐cell method demonstrate that the improved ghost‐cell method is almost equally accurate with better efficiency for boundary representation in high‐fidelity compressible flow simulations. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

16.
An efficient computing framework, namely PFlows, for fully resolved-direct numerical simulations of particle-laden flows was accelerated on NVIDIA General Processing Units (GPUs) and GPU-like accelerator (DCU) cards. The framework is featured as coupling the lattice Boltzmann method for fluid flow with the immersed boundary method for fluid-particle interaction, and the discrete element method for particle collision, using two fixed Eulerian meshes and one moved Lagrangian point mesh, respectively. All the parts are accelerated by a fine-grained parallelism technique using CUDA on GPUs, and further using HIP on DCU cards, i.e., the calculation on each fluid grid, each immersed boundary point, each particle motion, and each pair-particle collision is responsible by one computer thread, respectively. Coalesced memory accesses to LBM distribution functions with the data layout of Structure of Arrays are used to maximize utilization of hardware bandwidth. Parallel reduction with shared memory for data of immersed boundary points is adopted for the sake of reducing access to global memory when integrate particle hydrodynamic force. MPI computing is further used for computing on heterogeneous architectures with multiple CPUs-GPUs/DCUs. The communications between adjacent processors are hidden by overlapping with calculations. Two benchmark cases were conducted for code validation, including a pure fluid flow and a particle-laden flow. The performances on a single accelerator show that a GPU V100 can achieve 7.1–11.1 times speed up, while a single DCU can achieve 5.6–8.8 times speed up compared to a single Xeon CPU chip (32 cores). The performances on multi-accelerators show that parallel efficiency is 0.5–0.8 for weak scaling and 0.68–0.9 for strong scaling on up to 64 DCU cards even for the dense flow (φ = 20%). The peak performance reaches 179 giga lattice updates per second (GLUPS) on 256 DCU cards by using 1 billion grids and 1 million particles. At last, a large-scale simulation of a gas-solid flow with 1.6 billion grids and 1.6 million particles was conducted using only 32 DCU cards. This simulation shows that the present framework is prospective for simulations of large-scale particle-laden flows in the upcoming exascale computing era.  相似文献   

17.
A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.  相似文献   

18.
A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional problems does not require any numerical integration at all. In another development, a boundary contour implementation of a regularized hypersingular boundary integral equation (HBIE) using quadratic elements and end-node collocation was proposed and the technique is termed the hypersingular boundary contour method (HBCM). As reported in that work, the approach requires highly refined meshes in order to numerically enforce the stress continuity across boundary contour elements. This continuity requirement is very crucial since the regularized HBIE is only valid at collocation points where the stress tensor is continuous, while the computed stress at the endpoints of a boundary contour element, which is a non-conforming element, is generally not. This paper presents a new implementation of the HBCM for which the regularized HBIE is collocated at the mid-node of a boundary contour element. As the computed stress tensor is continuous at these mid-nodes, there is no need for unusually refined meshes. Some numerical tests herein show that, for the same mesh density, the HBCM using mid-node collocation has a comparable accuracy as the BCM.  相似文献   

19.
A new boundary element method is described for calculation of the steady incompressible laminar flows. The method is based on the well-known SIMPLE algorithm. The new boundary element method allows one to find the fields of the pressure and velocity corrections without inner iterations, thus reducing the computational time drastically. This makes it different from the method developed by Patankar and Spalding.32 However, the new method demands a much larger computer strorage. The boundary integral equations are discretized with the help of constant boundary elements and constant cells. The values of the integrals along the boundary elements and the cells for the two-dimensional domain are found analytically. To preserve the stability in the iteration process, under-relaxation for the convection terms is used. This paper gives the results of calculations of the flows between two plane parallel plates at Re = 20 and Re = 200, the flows in a square cavity with a moving upper lid at Re = 1 and Re = 100 and the flow in a plane channel with sudden symmetric expansion at Re =46·6.  相似文献   

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