共查询到20条相似文献,搜索用时 31 毫秒
1.
《Physics letters. A》2006,359(6):564-572
In this Letter an incompressible MRT-LB model has been proposed. The equilibria in momentum space are derived from an earlier incompressible LBGK model by Guo et al. Through the Chapman–Enskog expansion the incompressible Navier–Stokes equations can be recovered without artificial compressible effects. The steady Poiseuille flow, the driven cavity flow and the double shear flow have been carried on by the incompressible MRT-LB model. The numerical simulation results agree well with the analytical solutions or the existing results. It is found that the incompressible MRT-LB model shows better numerical stability. 相似文献
2.
Jie Sha Lixiang Zhang & Chuijie Wu 《advances in applied mathematics and mechanics.》2015,7(6):754-779
This paper is concerned with a low-dimensional dynamical system model
for analytically solving partial differential equations (PDEs). The model proposed is
based on a posterior optimal truncated weighted residue (POT-WR) method, by which
an infinite dimensional PDE is optimally truncated and analytically solved in required
condition of accuracy. To end that, a POT-WR condition for PDE under consideration
is used as a dynamically optimal control criterion with the solving process. A set of
bases needs to be constructed without any reference database in order to establish a
space to describe low-dimensional dynamical system that is required. The Lagrangian
multiplier is introduced to release the constraints due to the Galerkin projection, and
a penalty function is also employed to remove the orthogonal constraints. According
to the extreme principle, a set of ordinary differential equations is thus obtained
by taking the variational operation of the generalized optimal function. A conjugate
gradient algorithm by FORTRAN code is developed to solve the ordinary differential
equations. The two examples of one-dimensional heat transfer equation and nonlinear
Burgers’ equation show that the analytical results on the method proposed are good
agreement with the numerical simulations and analytical solutions in references, and
the dominant characteristics of the dynamics are well captured in case of few bases
used only. 相似文献
3.
A general theory for nonlinear propagation of one dimensional modified ion-acoustic waves in an unmagnetized electron-positron-ion (e-p-i) degenerate plasma is investigated. This plasma system is assumed to contain relativistic electron and positron fluids, non-degenerate viscous positive ions, and negatively charged static heavy ions. The modified Burgers and Gardner equations have been derived by employing the reductive perturbation method and analyzed in order to identify the basic features (polarity, width, speed, etc.) of shock and double layer (DL) structures. It is observed that the basic features of these shock and DL structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers equations. The implications of these results in space and interstellar compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are also briefly mentioned. 相似文献
4.
Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2– and 3– dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrödinger (NLS) equation in 2– and 3– dimensional Euclidean space, respectively. In 2–dimensional Minkowski space, timelike/spacelike inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers’ equation and its symmetry integrability structure. In 3–dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers. 相似文献
5.
A symmetry-preserving difference scheme for high dimensional nonlinear evolution equations 下载免费PDF全文
In this paper, a procedure for constructing discrete models of the high dimensional nonlinear evolution equanons is presented. In order to construct the difference model, with the aid of the potential system of the original equation and compatibility condition, the difference equations which preserve all Lie point symmetries can be obtained. As an example, invariant difference models of the (2+1)-dimensional Burgers equation are presented. 相似文献
6.
Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results. 相似文献
7.
MA Chang-Feng SHI Bao-Chang CHEN Xing-Wang 《理论物理通讯》2005,44(5):917-920
Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice.Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results. 相似文献
8.
9.
A. M. Balonishnikov 《Technical Physics》2005,50(10):1251-1254
A model of parallel noninteracting cascades in the spectral space is suggested in terms of which the turbulent flow of an
incompressible fluid subject to arbitrary large-scale velocity gradients is described. The linear parts of model equations
for two polarization components of the velocity are derived from the Navier-Stokes equations, and their nonlinear parts correspond
to the 1D Burgers model. Using the model suggested, explicit expressions for subgrid Reynolds stresses without empiric parameters
are obtained. 相似文献
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12.
Density waves are investigated analytically and numerically in the optimal velocity model with reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. The results show that the decrease of reaction-time delay of drivers leads to the stabilization of traffic flow. The Burgers, Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions respectively. The triangular shock waves, soliton waves and kink-antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams. The numerical simulations are given. 相似文献
13.
Minimal stencil width discretizations of combined mixed and non-mixed second-order derivatives are analyzed with respect to accuracy and stability. We show that these discretizations lead to stability for Cauchy problems. With a careful boundary treatment, we also show that the stability holds for initial-boundary value problems. The analysis is verified by numerical simulations of Burgers’ and Navier–Stokes equations in two and three space dimensions. 相似文献
14.
《Waves in Random and Complex Media》2013,23(2):142-151
In this paper, exponential rational function method is applied to obtain analytical solutions of the space–time fractional Fokas equation, the space–time fractional Zakharov Kuznetsov Benjamin Bona Mahony, and the space–time fractional coupled Burgers’ equations. As a result, some exact solutions for them are successfully established. These solutions are constructed in fractional complex transform to convert fractional differential equations into ordinary differential equations. The fractional derivatives are described in Jumarie’s modified Riemann–Liouville sense. The exact solutions obtained by the proposed method indicate that the approach is easy to implement and effective. 相似文献
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16.
研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。 相似文献
17.
研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。 相似文献
18.
Burgers vortices are explicit stationary solutions of the Navier-Stokes equations which are often used to describe the vortex
tubes observed in numerical simulations of three-dimensional turbulence. In this model, the velocity field is a two-dimensional
perturbation of a linear straining flow with axial symmetry. The only free parameter is the Reynolds number Re = Γ/ν, where Γ is the total circulation of the vortex and ν is the kinematic viscosity. The purpose of this paper is to show that Burgers vortices are asymptotically stable with respect
to small three-dimensional perturbations, for all values of the Reynolds number. This general result subsumes earlier studies
by various authors, which were either restricted to small Reynolds numbers or to two-dimensional perturbations. Our proof
relies on the fact that the linearized operator at Burgers vortex has a simple and very specific dependence upon the axial
variable. This allows to reduce the full linearized equations to a vectorial two-dimensional problem, which can be treated
using an extension of the techniques developed in earlier works. Although Burgers vortices are found to be stable for all
Reynolds numbers, the proof indicates that perturbations may undergo an important transient amplification if Re is large,
a phenomenon that was indeed observed in numerical simulations. 相似文献
19.
We study shock reflection for the two 2D Burgers equation. This model equation is an asymptotic limit of the Euler equations, and retains many of the features of the full equations. A von Neumann type analysis shows that the 2D Burgers equation has detachment, sonic, and Crocco points in complete analogy with gas dynamics. Numerical solutions support the detachment/sonic criterion for transition from regular to Mach reflection. There is also strong numerical evidence that the reflected shock in the 2D Burgers Mach reflection forms a smooth wave near the Mach stem, as proposed by Colella and Henderson in their study of the Euler equations. 相似文献
20.
Local discontinuous Galerkin method for solving Burgers and coupled Burgers equations 总被引:1,自引:0,他引:1 下载免费PDF全文
In the current work, we extend the local discontinuous Galerkin method to a more general application system. The Burgers and coupled Burgers equations are solved by the local discontinuous Galerkin method. Numerical experiments are given to verify the efficiency and accuracy of our method. Moreover the numerical results show that the method can approximate sharp fronts accurately with minimal oscillation. 相似文献