KdV方程的格子Boltzmann模型求解  

Solution Method for KDV Equation by Lattice Boltzmann Model

作　　者：陈梦涵 王希胤 李金 CHEN Meng-han;WANG Xi-yin;LI Jin(College of Science,North China University of Science and Technology,Tangshan Hebei 063210,China)

机构地区：[1]华北理工大学理学院,河北唐山063210

出　　处：《华北理工大学学报（自然科学版）》2024年第1期103-110,共8页Journal of North China University of Science and Technology：Natural Science Edition

基　　金：国家自然科学基金项目(32070669)。

摘　　要：浅水波模型被广泛地用于模拟水波传播的动力学行为。很多问题,如强非线性问题、非平衡问题、实际应用中发生的问题等,使得传统的理论研究手段通常无能为力。文章首先给出了格子Boltzmann方法(LBM)的基本理论,然后利用经典的一维五速度(D1Q5)的离散速度模型,给出Korteweg-de Vries(KdV)方程中含有修正项的格子Boltzmann(LB)模型推导公式,最后进行数值模拟,将KdV方程的精确解和模拟解进行比较,然后验证修正模型的精确性。实验结果表明,用格子Boltzmann方法对KdV方程进行求解,其模拟解和精确解吻合度较高。Shallow water wave model is widely used to simulate the dynamic behavior of water wave propagation in ocean and atmosphere field.Many problems,such as strong nonlinear problems,non-equilibrium problems,problems in practical applications,make the traditional theoretical research methods are usually powerless.In this paper,the basic theory of lattice Boltzmann method(LBM) was firstly given.Then,the formula of lattice Boltzmann(LB) model with correction term in Korteweg-de Vries(KdV) equation was given by using the classical one-dimensional five-velocity(D1Q5) discrete velocity model.Finally,the accurate solution of the KdV equation was compared with the simulated solution,and then the accuracy of the modified model is verified.The experimental results show that the lattice Boltzmann method is used to solve the KdV equation,and the simulation solution is in good agreement with the exact solution.

关 键 词：KDV方程 D1Q5模型 格子BOLTZMANN方法 

分 类 号：O212.1[理学—概率论与数理统计]