共查询到20条相似文献,搜索用时 15 毫秒
1.
A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well. 相似文献
2.
In this paper,we present a Cole-Hopf transformation based lattice Boltzmann(LB) model for solving one-dimensional Burgers' equation,and compared to available LB models,the effect of nonlinear convection term can be eliminated.Through Chapman-Enskog analysis,it can be found that the converted diffusion equation based on the Cole-Hopf transformation can be recovered correctly from present LB model.Some numerical tests are also performed to validate the present LB model,and the numerical results show that,similar to previous LB models,the present model also has a second-order convergence rate in space,but it is more accurate than the previous ones. 相似文献
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A general propagation lattice Boltzmann model is used to solve Boussinesq equations. Different local equilibrium distribution functions are selected, and the macroscopic equation is recovered with second order accuracy by means of the Chapman–Enskog multi-scale analysis and the Taylor expansion technique. To verify the effectiveness of the present model, some Boussinesq equations with initial boundary value problems are simulated. It is shown that our model can remain stable and accurate, which is an effective algorithm worthy of promotion and application. 相似文献
5.
A new lattice Boltzmann model with amending-function for KdV-Burgers equation, ut + uux -αuxx + βuxxx = 0, is presented by using the single-relaxation form of the lattice Boltzmann equation. Applying the proposed model, we simulate the solutions of a kind of KdV-Burgers equations, and the numerical results agree with the analytical solutions quite well. 相似文献
6.
We coupled the lattice Boltzmann method with enhanced collisions for hydrodynamics with a model for the anisotropic liquid/solid phase transition. The model is based on a simple reaction model. As a test we have performed calculations for dendritic growth of a crystal into an undercooled melt. 相似文献
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New Solitary Wave Solutions to the KdV-Burgers Equation 总被引:12,自引:0,他引:12
Based on the analysis on the features of the Burgers equation and KdV equation as well as KdV-Burgers equation, a superposition method is proposed to construct the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and KdV equation, and then by using it we obtain many solitary wave solutions to the KdV-Burgers equation, some of which are new ones.PACS: 02.30.Jr; 03.65.Ge 相似文献
9.
Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow. 相似文献
10.
New Travelling Wave Solutions to Compound KdV-Burgers Equation 总被引:1,自引:0,他引:1
The compound KdV-Burgers equation and combined KdV-mKdV equation
are real physical models concerning many branches in
physics. In this paper, applying the improved trigonometric function
method to these equations, rich explicit and exact travelling
wave solutions, which contain solitary-wave solutions, periodic
solutions, and combined formal solitary-wave solutions, are
obtained. 相似文献
11.
A New Differential Lattice Boltzmann Equation and Its Application to Simulate Incompressible Flows on Non-Uniform Grids 总被引:1,自引:0,他引:1
A new differential lattice Boltzmann equation (LBE) is presented in this work, which is derived from the standard LBE by using Taylor series expansion only in spatial direction with truncation to the second-order derivatives. The obtained differential equation is not a wave-like equation. When a uniform grid is used, the new differential LBE can be exactly reduced to the standard LBE. The new differential LBE can be applied to solve irregular problems with the help of coordinate transformation. The present scheme inherits the merits of the standard LBE. The 2-D driven cavity flow is chosen as a test case to validate the present method. Favorable results are obtained and indicate that the present scheme has good prospects in practical applications. 相似文献
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In this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for
simulation of viscous compressible flows. In the solver, the finite volume method is
applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes
solvers, in this work, the inviscid flux across the cell interface is evaluated by
local reconstruction of solution using one-dimensional lattice Boltzmann model, while
the viscous flux is still approximated by conventional smooth function approximation.
The present work overcomes the two major drawbacks of existing LBFS [28–31], which
is used for simulation of inviscid flows. The first one is its ability to simulate viscous
flows by including evaluation of viscous flux. The second one is its ability to effectively
capture both strong shock waves and thin boundary layers through introduction of a
switch function for evaluation of inviscid flux, which takes a value close to zero in
the boundary layer and one around the strong shock wave. Numerical experiments
demonstrate that the present solver can accurately and effectively simulate hypersonic
viscous flows. 相似文献
14.
Alfonso Caiazzo 《Journal of statistical physics》2005,121(1-2):37-48
LB simulations can be affected by the arising of initial layers due to an inconsistent initialization of the discrete LB populations.
We present some previously proposed initialization routines built to overcome that problem; using the asymptotic expansion
technique, we show how their features can be analyzed and, in some cases, how accuracy and computational efficiency can be
improved 相似文献
15.
GONG Lun-Xun PAN Jun-Ting 《理论物理通讯》2008,50(7):51-52
Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f (ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献
16.
A coarse-grained Lattice Boltzmann equation is examined in which the effects of unresolved (subgrid) scales are formally incorporated within a renormalized relaxation time of the collision operator. Actual values of the renormalized relaxation time are analyzed for the practical case of high-Reynolds flows past slant bodies (airfoils). 相似文献
17.
DUAN WenShan 《理论物理通讯》2002,37(6):739-740
Korteweg, de Vries-Burges equation is obtained for an incompressible and viscous fluid which is flowing in one direction for the shallow water. We assume that the wave amplitude is small but finite, the viscosity of the fluid is also small enough. 相似文献
18.
A lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary. 相似文献
19.
In terms of the solutions of an auxiliary ordinary differential
equation, a new algebraic method, which contains the terms of first-order
derivative of functions f(ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献