Abstract
In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon.
Highlights
Nonlinear dynamic phenomenon, which exists in many fields of science and engineering, such as hydrodynamic, nonlinear optics, biology, plasma physics, and so on, can be modeled by many systems of nonlinear partial differential equations (NPDEs) [1,2]
Based on the mesoscopic lattice BGK method, we have investigated the numerical solution of
With the help of the Chapman-Enskog multiscale expansion, the macroscopic dynamical evolution equation can be precisely obtained from the present mesoscopic scheme in the continuity system without appending any amending term
Summary
Nonlinear dynamic phenomenon, which exists in many fields of science and engineering, such as hydrodynamic, nonlinear optics, biology, plasma physics, and so on, can be modeled by many systems of nonlinear partial differential equations (NPDEs) [1,2]. The mesoscopic lattice Boltzmann method (LBM) has made significant progress in the research nonlinear dynamical equations and evolving process of complexity micro-mesoscopic systems [9], especially in fluid mechanics [10,11,12]. Inspired by the successful promotion and application of the mesoscopic LBM in modeling nonlinear convection-diffusion system [45,46], the aim of this work is to further develop and apply the lattice Boltzmann Bhatnagar-Gross-Krook (BGK) method to solve (2 + 1)-dimensional wave equation with nonlinear damping and source terms. In the process of linking the mesoscopic Boltzmann equation to the nonlinear damped evolution system, we should choose suitable local equilibrium distribution functions to meet some constraints. A summary of the research is given in the last section
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