Finite-difference lattice Boltzmann model for nonlinear convection-diffusion equations

Huili Wang, Baochang Shi, Hong Liang and Zhenhua Chai

Applied Mathematics and Computation, 2017, vol. 309, issue C, 334-349

Abstract: In this paper, a finite-difference lattice Boltzmann (LB) model for nonlinear isotropic and anisotropic convection-diffusion equations is proposed. In this model, the equilibrium distribution function is delicately designed in order to recover the convection-diffusion equation exactly. Different from the standard LB model, the temporal and spatial steps in this model are decoupled such that it is convenient to study convection-diffusion problem with the non-uniform grid. In addition, it also preserves the advantage of standard LB model that the complex-valued convection-diffusion equation can be solved directly. The von Neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model. To test the performance of the model, a series of numerical simulations of some classical problems, including the diffusion equation, the nonlinear heat conduction equation, the Sine-Gordon equation, the Gaussian hill problem, the Burgers–Fisher equation, and the nonlinear Schrödinger equation, have also been carried out. The results show that the present model has a second-order convergence rate in space, and generally it is also more accurate than the standard LB model.

Keywords: Finite-difference lattice Boltzmann model; Nonlinear convection-diffusion equation; Non-uniform grid (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:309:y:2017:i:c:p:334-349

DOI: 10.1016/j.amc.2017.04.015

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