共查询到20条相似文献,搜索用时 15 毫秒
1.
M. Lagha P. Manneville 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(4):433-447
The Galerkin method is used to derive a realistic model of
plane Couette flow in terms of partial differential equations governing
the space-time dependence of the amplitude of a few cross-stream modes.
Numerical simulations show that it reproduces the globally sub-critical
behavior typical of this flow. In particular, the statistics of turbulent
transients at decay from turbulent to laminar flow displays striking
similarities with experimental findings. 相似文献
2.
A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids 下载免费PDF全文
A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook
(BGK) formulation is presented for the solution of the compressible
Navier-Stokes equations on arbitrary grids. The idea behind this
approach is to combine the robustness of the BGK scheme with the
accuracy of the DG methods in an effort to develop a more accurate,
efficient, and robust method for numerical simulations of viscous
flows in a wide range of flow regimes. Unlike the traditional
discontinuous Galerkin methods, where a Local Discontinuous Galerkin
(LDG) formulation is usually used to discretize the viscous fluxes
in the Navier-Stokes equations, this DG method uses a BGK scheme to
compute the fluxes which not only couples the convective and
dissipative terms together, but also includes both discontinuous and
continuous representation in the flux evaluation at a cell interface
through a simple hybrid gas distribution function. The developed
method is used to compute a variety of viscous flow problems on
arbitrary grids. The numerical results obtained by this BGKDG method
are extremely promising and encouraging in terms of both accuracy
and robustness, indicating its ability and potential to become not
just a competitive but simply a superior approach than the current
available numerical methods. 相似文献
3.
M. Makar 《Il Nuovo Cimento D》1996,18(5):565-569
Summary Using the Laplace transform, an analytical solution of the Navier-Stokes equation is obtained for a two-dimensional incompressible
elasto-viscous fluid past between two infinite parallel walls. It is assumed that the lower wall is moving with velocity which
is a function of any given free stream velocity. As an application of the solution, two cases for the stream velocity are
studied. 相似文献
4.
Clayton Bjorland 《Physica D: Nonlinear Phenomena》2011,240(7):670-674
Infinite energy solutions to the Navier-Stokes equations in R2 may be constructed by decomposing the initial data into a finite energy piece and an infinite energy piece, which are then treated separately. We prove that the finite energy part of such solutions is bounded for all time and decays algebraically in time when the same can be said of heat energy starting from the same data. As a consequence, we describe the asymptotic behavior of the infinite energy solutions. Specifically, we consider the solutions of Gallagher and Planchon (2002) [2] as well as solutions constructed from a “radial energy decomposition”. Our proof uses the Fourier Splitting technique of M.E. Schonbek. 相似文献
5.
Direct numerical simulation of rotating plane Couette flow(RPCF) at Re_w= 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with ?x~+=8.51, ?z~+= 4.26, ?y~+|_(min)= 0.0873 and ?y~+|_(max)= 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length Lxand spanwise length Lzof the computational box have different impacts on the flow statistics, where the statistics were converged if Lxis longer than 8πh, while no converged results were obtained for different Lz. More importantly,our results with very long simulation time showed that a state transition would happen if L_x≥ 8πh, from a state with four pairs of roll cells to a state with three pairs of roll cells with L_z= 6πh. Each state could survive for more than 1500 h/U_w, and the flow statistics were different. 相似文献
6.
Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases. The results suggest a scenario for weakly turbulent viscoelastic flow which is similar to the one for Newtonian fluids as a function of Reynolds number. 相似文献
7.
In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266–281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question. 相似文献
8.
S. Bottin H. Chaté 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,6(1):143-155
We argue on general grounds that the transition to turbulence in plane Couette flow is best studied experimentally at a statistical
level. We present such a statistical analysis of experimental data guided by a parallel investigation of a simple coupled
map lattice model for spatiotemporal intermittency. We confirm that this generic type of spatiotemporal chaos is relevant
in the context of plane Couette flow, where the linear stability of the laminar regime at all Reynolds numbers insures the
necessary local subcriticality. Using large ensembles of similar experiments, we show the existence of a well-defined threshold
Reynolds number above which a unique, turbulent, intermittent attractor coexists with the laminar flow. Furthermore, our data
reveals that this transition to spatiotemporal intermittency is discontinuous, i.e. akin to a first-order phase transition.
Received: 10 April 1998 / Revised: 22 June 1998 / Accepted: 24 June 1998 相似文献
9.
《中国物理 B》2015,(10)
A series of direct numerical simulations of the fully developed plane Couette flow at a Reynolds number of 6000(based on the relative wall speed and half the channel height h) with different streamwise and spanwise lengths are conducted to investigate the effects of the computational box sizes on the secondary flow(SF). Our focuses are the number of counter-rotating vortex pairs and its relationship to the statistics of the mean flow and the SF in the small and moderate computational box sizes. Our results show that the number of vortex pairs is sensitive to the computational box size, and so are the slope parameter, the rate of the turbulent kinetic energy contributed by the SF, and the ratio of the kinetic energy of the SF to the total kinetic energy. However, the averaged spanwise width of each counter-rotating vortex pair in the plane Couette flow is found, for the first time, within 4(1 ± 0.25)h despite the domain sizes. 相似文献
10.
《Physics letters. A》2020,384(14):126287
Time evolution of pertinent operators in the Rabi Hamiltonian and its rotating wave approximation (RWA) version, the Jaynes-Cummings model (JCM), in the Heisenberg picture, gives systems of nonlinear differential equations (NDEs). Considering well localized atom, the mean field theory (MFT) was applied to replace the operators by equivalent expectation values. The Rabi model was reduced to a fourth orders NDE describing atoms position. Solution by the harmonic balance method (HBM) showed good accuracy and consistency to the numerical results, which introduces it as a useful tool in the quantum dynamics studies. The NDEs describing the JCM in the Heisenberg picture structurally prevent applying the MFT and shows inconsistency to the Ehrenfest's theorem, contrary to the Rabi model. 相似文献
11.
构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强. 相似文献
12.
Based on the complex variable moving least-square (CVMLS) approximation, the complex variable element-free Galerkin (CVEFG) method for two-dimensional viscoelasticity problems under the creep condition is presented in this paper. The Galerkin weak form is employed to obtain the equation system, and the penalty method is used to apply the essential boundary conditions, then the corresponding formulae of the CVEFG method for two-dimensional viscoelasticity problems under the creep condition are obtained. Compared with the element-free Galerkin (EFG) method, with the same node distribution, the CVEFG method has higher precision, and to obtain the similar precision, the CVEFG method has greater computational efficiency. Some numerical examples are given to demonstrate the validity and the efficiency of the method. 相似文献
13.
In this paper, we present a mathematical and numerical studies of the three-dimensional time-harmonic Maxwell equations. The problem is solved by a discontinuous Galerkin DG method coupled with an integral representation. This study was completed by some numerical tests to justify the effectiveness of the proposed approach. The numerical simulation was done by an iterative solver implemented in FORTRAN. 相似文献
14.
The improved element-free Galerkin(IEFG) method of elasticity is used to solve the topology optimization problems.In this method, the improved moving least-squares approximation is used to form the shape function. In a topology optimization process, the entire structure volume is considered as the constraint. From the solid isotropic microstructures with penalization, we select relative node density as a design variable. Then we choose the minimization of compliance to be an objective function, and compute its sensitivity with the adjoint method. The IEFG method in this paper can overcome the disadvantages of the singular matrices that sometimes appear in conventional element-free Galerkin(EFG) method. The central processing unit(CPU) time of each example is given to show that the IEFG method is more efficient than the EFG method under the same precision, and the advantage that the IEFG method does not form singular matrices is also shown. 相似文献
15.
In this paper we study the Navier-Stokes flow on the two-dimensional torusS
1
×S
1 excited by the external force (k
2 sinky, 0) and find the long-time behavior for the flow starting from some states, whereS
1=[0,2](mod 2). Especially for the casek=2, it follows from an analysis and computation that the Navier-Stokes flow with the initial state cos(mx+ny) or sin(mx+ny) will likely evolve through at most one step bifurcation to either a steady-state solution or a time-dependent periodic solution for any Reynolds number and integersm andn. 相似文献
16.
G. Adomian 《Foundations of Physics Letters》1995,8(4):389-400
An analytical procedure is proposed to study the flow of viscous compressible continuous fluids. 相似文献
17.
Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems 下载免费PDF全文
We first give a stabilized improved moving least squares(IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. 相似文献
18.
基于高阶的间断有限元方法, 数值模拟低马赫数下并列圆柱的可压缩层流流动, 捕捉并列圆柱流场中的漩涡结构, 以便分析并列圆柱尾流的流动特性. 针对二维圆柱的边界形式, 采用曲边三角形单元构造二维圆柱的曲面边界, 以适应高阶离散格式的精度. 在验证方法合理性的基础上, 分析圆柱间距及雷诺数对漩涡脱落及受力特性的影响规律. 研究结果表明: 并列圆柱的间距是影响流场流动特性的一个主要因素, 它会改变圆柱漩涡脱落的形式. 随着圆柱间距的增加, 上下圆柱的平均阻力系数及平均升力系数的绝对值随之显著下降. 雷诺数对于平均阻力系数的影响相对较小. 但随着雷诺数的增加, 上下圆柱的平均升力系数会随之降低, 而漩涡的脱落频率会随之增大. 相似文献
19.
20.
Christian Matyssek Jens Niegemann Wolfram Hergert Kurt Busch 《Photonics and Nanostructures》2011,9(4):367-373
In this work, we demonstrate how to extract electron energy loss spectra of metallic nano-particles from time-domain computations. Specifically, we employ the Discontinuous Galerkin Time-Domain (DGTD) method in order to model the excitation of individual metallic nano-spheres and dimers of spheres by a tightly focussed electron beam. The resulting electromagnetic fields that emanate from the particles act back on the electrons and the accumulated effect determines the electrons’ total energy loss. We validate this approach by comparing with analytical results for single spheres. For dimers, we find that the electron beam allows for an efficient excitation of dark modes that are inaccessible for optical spectroscopy. In addition, our time-domain approach provides a basis for dealing with materials that exhibit a significant nonlinear response. 相似文献