1,665 research outputs found
A Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann model for the coupled Burgers' equations
In this work, a Cole-Hopf transformation based fourth-order
multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional
coupled Burgers' equations is developed. We first adopt the Cole-Hopf
transformation where an intermediate variable \theta is introduced to eliminate
the nonlinear convection terms in the Burgers' equations on the velocity
u=(u_1,u_2,...,u_d). In this case, a diffusion equation on the variable \theta
can be obtained, and particularly, the velocity u in the coupled Burgers'
equations is determined by the variable \theta and its gradient term
\nabla\theta. Then we develop a general MRT-LB model with the natural moments
for the d-dimensional transformed diffusion equation and present the
corresponding macroscopic finite-difference scheme. At the diffusive scaling,
the fourth-order modified equation of the developed MRT-LB model is derived
through the Maxwell iteration method. With the aid of the free parameters in
the MRT-LB model, we find that not only the consistent fourth-order modified
equation can be obtained, but also the gradient term can be
calculated locally by the non-equilibrium distribution function with a
fourth-order accuracy, this indicates that theoretically, the MRT-LB model for
-dimensional coupled Burgers' equations can achieve a fourth-order accuracy
in space. Finally, some simulations are conducted to test the MRT-LB model, and
the numerical results show that the proposed MRT-LB model has a fourth-order
convergence rate, which is consistent with our theoretical analysis
A 8-neighbor model lattice Boltzmann method applied to mathematical-physical equations
© 2016. This version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/A lattice Boltzmann method (LBM) 9-bit model is presented to solve mathematical-physical equations, such as, Laplace equation, Poisson equation, Wave equation and Burgers equation. The 9-bit model has been verified by several test cases. Numerical simulations, including 1D and 2D cases, of each problem are shown respectively. Comparisons are made between numerical predictions and analytic solutions or available numerical results from previous researchers. It turned out that the 9-bit model is computationally effective and accurate for all different mathematical-physical equations studied. The main benefits of the new model proposed is that it is faster than the previous existing models and has a better accuracy.Peer ReviewedPostprint (author's final draft
Investigation of a lattice Boltzmann model with a variable speed of sound
A lattice Boltzmann model is considered in which the speed of sound can be
varied independently of the other parameters. The range over which the speed of
sound can be varied is investigated and good agreement is found between
simulations and theory. The onset of nonlinear effects due to variations in the
speed of sound is also investigated and good agreement is again found with
theory. It is also shown that the fluid viscosity is not altered by changing
the speed of sound
Application of Lattice Boltzmann Method for Surface Runoff in Watershed
Derived from simplifications of the Saint-Venant equations, the kinematic wave model has the ability to describe the behavior of surface runoff in watersheds. This paper aims to obtain the numerical simulation of the flow routing in a natural watershed, by using lattice Boltzmann method. In the computational model, the surface of the basin will be represented by a V-shaped segmented in two lateral planes and one main channel. The simulation considers the effective precipitation flowing on the watershed per unit of width at the exit of each of the planes that represent the surface of the basin. The water flowing from the planes enters the main channel in the form of lateral contribution. Hydrograms of two rain events are obtained, which present the volume drained in the outlet corresponding to the whole basin in each event. Two equilibrium distribution functions were developed by Chapmann-Enskog expansion at time scales and model D1Q3, one suitable for flow on the basin surface and another for the main channel, in order to obtain the variables of interest in each case. The numerical results obtained were compared with the KINEROS2 hydrological model.Peer Reviewe
Type-II Quantum Algorithms
We review and analyze the hybrid quantum-classical NMR computing methodology
referred to as Type-II quantum computing. We show that all such algorithms
considered so far within this paradigm are equivalent to some classical
lattice-Boltzmann scheme. We derive a sufficient and necessary constraint on
the unitary operator representing the quantum mechanical part of the
computation which ensures that the model reproduces the Boltzmann approximation
of a lattice-gas model satisfying semi-detailed balance. Models which do not
satisfy this constraint represent new lattice-Boltzmann schemes which cannot be
formulated as the average over some underlying lattice gas. We close the paper
with some discussion of the strengths, weaknesses and possible future direction
of Type-II quantum computing.Comment: To appear in Physica
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