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1.
Multiresolution analysis based on the reproducing kernel particle method (RKPM) is developed for computational fluid dynamics. An algorithm incorporating multiple-scale adaptive refinement is introduced. The concept of using a wavelet solution as an error indicator is also presented. A few representative numerical examples are solved to illustrate the performance of this new meshless method. Results show that the RKPM is a good candidate for tackling the widespread large-scale problems in fluid dynamics. © 1997 John Wiley & Sons, Ltd. 相似文献
2.
An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non-similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely. 相似文献
3.
基于核重构思想的最小二乘配点型无网格方法 总被引:4,自引:3,他引:4
介绍重构核点法的基本原理和近似函数的构造方法,并基于核重构思想,应用配点法和最小二乘原理,离散微分方程,建立求解的代数方程,提出了一种基于核重构思想的最小二乘配点型无网格方法.与一般配点法相比,该方法的系数矩阵是有对称正定的,计算精度高,稳定性好.该方法的实施不需要背景网格,不需要进行高斯积分,与Galerkin法相比,具有计算量小、边界条件处理简单的特点,是一种真正的无网格法.对该方法构造过程中的近似函数及其导数的计算、修正函数的计算及方法的实现等问题进行了探讨.文中结合若干典型算例,检验了该方法的有效性. 相似文献
4.
插值型重构核粒子法的形函数具有离散点插值特性和不低于核函数的高阶光滑性,因而不仅可以直接施加本质边界条件,同时也保证了较高的计算精度.本文将弹性动力学方程作拉氏变换后,在变换域内用插值型重构核粒子法求解,最后再借助Durbin数值反演方法求得时间域的解.针对典型的弹性动力学问题,给出了插值型重构核粒子法的数值算例,并验证了本文方法的有效性. 相似文献
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Chih-Ping Wu Shih-Wei YangYung-Ming Wang Hsuan-Teh Hu 《Mechanics Research Communications》2011,38(6):471-476
A meshless collocation method is developed for the static analysis of plane problems of functionally graded (FG) elastic beams and plates under transverse mechanical loads using the differential reproducing kernel (DRK) interpolation, in which the DRK interpolant is constructed by the randomly distributed nodes. A point collocation method based on this DRK interpolation is developed for the plane stress and strain problems of homogeneous and FG elastic beams and plates. It is shown that the present DRK interpolation-based collocation method is indeed a truly meshless approach with excellent accuracy and has a fast convergence rate. 相似文献
7.
分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于
某个临界值方能使算法稳定. 然而在高黏性流动模拟中,已有的显式和半隐式分步算法由于
其显式本质,必须采用小时间步长计算,不但降低了计算效率,同时也常与为使分步算法稳
分步算法已被广泛应用于数值求解不可压缩N-S方程. Guermond等认为时间步长必须大于
某个临界值方能使算法稳定. 然而在高黏性流动模拟中,已有的显式和半隐式分步算法由于
其显式本质,必须采用小时间步长计算,不但降低了计算效率,同时也常与为使分步算法稳
定必须满足的最小时间步长要求冲突. 本文目的是构造一种含迭代格式的分步算法,它能在
保证精度的前提下大幅度地增大时间步长. 方腔流和平面Poisseuille流数值计算结果证实
了此特点,该方法被有效应用于充填流动过程的数值模拟. 相似文献
8.
采用一般质点近似和再生核质点近似表示系统响应量,给出了动力系统响应量的一般表达式。在此基础上,发展了一类求解广义概率密度演化方程的再生核质点加密算法,给出了详细求解步骤。以单自由度系统为例,从响应概率密度的角度考察了再生核质点加密算法的精度。以多自由度框架结构为例,验证了再生核质点加密算法求取非线性随机动力系统响应概率密度的正确性。 相似文献
9.
Amit Shaw 《International Journal of Non》2009,44(4):417-431
Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM. 相似文献
10.
基于核重构思想的配点型无网格方法的研究--一维问题 总被引:1,自引:0,他引:1
无网格方法按其离散原理可分为Galerkin型、配点型等。其中Galerkin型无网格方法的实施需要背景网格,不属于真正的无网格法;配点型无网格方法的实施不需要背景网格,是真正的无网格法。本文首先介绍了重构核点法的基本原理,然后基于核重构思想,与配点法相结合,以一维问题为例,研究了配点型无网格方法,对该方法构造过程中的近似函数及其导数的计算、修正函数的计算及方法的实现等问题进行了探讨。并结合若干典型算例,检验了其计算精度与收敛姓。 相似文献
11.
The stability of flow in a lid‐driven cavity is investigated using an accurate numerical technique based on a hybrid scheme with spectral collocation and high‐order finite differences. A global stability analysis is carried out and critical parameters are identified for various aspect ratios. It is found that while there is reasonable agreement with the literature for the critical parameters leading to loss of stability for the square cavity, there are significant discrepancies for cavities of aspect ratios 1.5 and 2. Simulations of the linearized unsteady equations confirm the results from the global stability analysis for aspect ratios A = 1, 1.5 and A = 2. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
12.
Yung-Chao Wu 《国际流体数值方法杂志》1988,8(7):803-811
This paper describes the characteristics of small-amplitude waves generated by a sinusoidally oscillating, inclined paddle-type wavemaker operating in a constant-depth channel. Two-dimensional, linearized potential flow is assumed. A semi-analytical method, the boundary collocation method, is used to establish the relationship between wave amplitude and paddle stroke. The numerical results are compared with the numerical results of the boundary integral equation method. It is found that the boundary collocation method is simpler and more flexible to implement and faster to compute. In addition, the numerical results are in reasonably good agreement with the laboratory experimental data. For the vertical wavemaker, which is a special case of the inclined wavemaker, an analytical series solution can be found. By using the boundary collocation method and the boundary integral equation method to solve the vertical wavemaker problem and comparing the results with the analytical series solution, it is found that the boundary collocation method yields a solution which is much more accurate than that from the boundary integral equation method. Finally, the relationships between wave amplitude and paddle stroke are established for different inclinations of the paddle-type wavemaker, based on the boundary collocation method. 相似文献
13.
The effects of mean flame radius and turbulence on self-sustained combustion of turbulent premixed spherical flames in decaying
turbulence have been investigated using three-dimensional direct numerical simulations (DNS) with single step Arrhenius chemistry.
Several flame kernels with different initial radius or initial turbulent field have been studied for identical conditions
of thermo-chemistry. It has been found that for very small kernel radius the mean displacement speed may become negative leading
ultimately to extinction of the flame kernel. A mean negative displacement speed is shown to signify a physical situation
where heat transfer from the kernel overcomes the heat release due to combustion. This mechanism is further enhanced by turbulent
transport and, based on simulations with different initial turbulent velocity fields, it has been found that self-sustained
combustion is adversely affected by higher turbulent velocity fluctuation magnitude and integral length scale. A scaling analysis
is performed to estimate the critical radius for self-sustained combustion in premixed flame kernels in a turbulent environment.
The scaling analysis is found to be in good agreement with the results of the simulations. 相似文献
14.
The present paper discusses the crack problem in the linear porous elastic plane using the model developed by Nunziato and Cowin. With the help of Fourier transform the problem is reduced to an integral equation over the boundary of the crack. Some analytical transformations are applied to calculate the kernel of the integral equation in its explicit form. We perform a numerical collocation technique to solve the derived hyper-singular integral equation. Due to convolution type of the kernel, we apply, at each iteration step, the classical iterative conjugate gradient method in combination with the Fast Fourier technique to solve the problem in almost linear time. There are presented some numerical examples for materials of various values of porosity. 相似文献
15.
将重构核粒子法和势问题的边界积分方程方法结合,提出了势问题的重构核粒子边界无单元法. 推导了势问题的重构核粒子边界无单元法的公式,研究其数值积分方案,建立了重构核粒子边界无单元法的离散化边界积分方程,并推导了重构核粒子边界无单元法的内点位势的积分公式. 重构核粒子法形成的形函数具有重构核函数的光滑性,且能再现多项式在插值点的精确值,所以该方法具有更高的精度. 最后给出了数值算例,验证了所提方法的有效性和正确性. } 相似文献
16.
A free-surface-tracking algorithm based on the SOLA-VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break-up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW-3D. One- and three-dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface. 相似文献
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18.
This study investigates a fictitious domain model for the numerical solution of various incompressible viscous flows. It is based on the so‐called Navier–Stokes/Brinkman and energy equations with discontinuous coefficients all over an auxiliary embedding domain. The solid obstacles or walls are taken into account by a penalty technique. Some volumic control terms are directly introduced in the governing equations in order to prescribe immersed boundary conditions. The implicit numerical scheme, which uses an upwind finite volume method on staggered Cartesian grids, is of second‐order accuracy in time and space. A multigrid local mesh refinement is also implemented, using the multi‐level Zoom Flux Interface Correction (FIC) method, in order to increase the precision where it is needed in the domain. At each time step, some iterations of the augmented Lagrangian method combined with a preconditioned Krylov algorithm allow the divergence‐free velocity and pressure fields be solved for. The tested cases concern external steady or unsteady flows around a circular cylinder, heated or not, and the channel flow behind a backward‐facing step. The numerical results are shown in good agreement with other published numerical or experimental data. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
ZHANG Zhi-qian 《应用数学和力学(英文版)》2005,26(8):1064-1071
IntroductionAs one of the meshfree methods, multiple scale reproducing kernel particle method(RKPM)[1,2]bears, besides the common features of all meshfree methods, a uniqueinherent feature of multiresolution analysis by which the structural response can b… 相似文献
20.
众所周知,LBB条件排除了在不可压缩流动N-S方程空间离散中采用速度u和压力p同阶线性插值的简单单元。基于压力泊松(Poisson)方程的分步算法曾被认为可以绕开LBB条件限制,然而近年来研究表明,并非各种类型的分步算法都能有效地避开LBB条件。本文针对不同雷诺数下的平面Poiseuille流动问题模拟,分析对比了当采用不同类型的u-p单元空间插值时增量与非增量迭代分步算法的稳定性与精度,为合理选择分步算法和u-p插值类型提供了依据和参考。 相似文献