Journal ArticleDOI
Numerical solution of Burgers' equation by lattice Boltzmann method
Yun Gao,Li-Hua Le,Baochang Shi +2 more
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TLDR
A lattice Boltzmann model for Burgers' equation is proposed through selecting equilibrium distribution function properly and the model has been verified by three test examples, so it is very easy to implement and deal with more complex problems.About:
This article is published in Applied Mathematics and Computation.The article was published on 2013-03-01. It has received 25 citations till now. The article focuses on the topics: Burgers' equation & Lattice Boltzmann methods.read more
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Lattice Methods and Their Applications To Reacting Systems
TL;DR: In this paper, the basic principles of the lattice gas automata and lattice Boltzmann automata were introduced and their applications to pattern formation in chemical reaction-diffusion systems, multiphase fluid flows and polymeric dynamics were discussed.
Journal ArticleDOI
A systematic literature review of Burgers’ equation with recent advances
TL;DR: The objectives of this paper are to discuss the recent developments in mathematical modelling of Burgers’ equation, and throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.
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Efficient numerical techniques for Burgers' equation
Vijitha Mukundan,Ashish Awasthi +1 more
TL;DR: New efficient numerical techniques for solving one dimensional quasi-linear Burgers' equation used in the study of turbulence, boundary layer behavior, shock waves, convection dominated diffusion phenomena, gas dynamics, acoustic attenuation in fog and continuum traffic simulation are presented.
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Wavelet solutions of Burgers’ equation with high Reynolds numbers
TL;DR: In this paper, a wavelet method is proposed to solve the Burgers' equation, which has a much better accuracy and efficiency than many other existing numerical methods, and whose order of convergence can go up to 5.
Journal ArticleDOI
Appropriate stabilized Galerkin approaches for solving two-dimensional coupled Burgers’ equations at high Reynolds numbers
Yong Chai,Jie Ouyang +1 more
TL;DR: Numerical experiments reveal that the SUPG method is optimal for the former problem, and the SOLD method is more appropriate for the latter one, which indicates the potential of this class of methods to solve nonlinear unsteady convection-dominated problems.
References
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Book
The Finite Difference Method in Partial Differential Equations
TL;DR: The authors created Reference Record created on 2005-11-18, modified on 2016-08-08, and used it to build a reference record for mathematical calculiques and differentielles.
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Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
TL;DR: In this paper, a general fourth order differencing scheme was developed and applied to three viscous test problems to verify the accuracy and applicability of the technique, which is atypical since only three nodes are necessary to obtain the desired fourth order accuracy.
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An efficient numerical scheme for Burgers' equation
TL;DR: This paper applies the multiquadric (MQ) as a spatial approximation scheme for solving the nonlinear Burgers' equation using a low order explicit finite difference approximation of the time derivative.