摘要
众所周知 ,格子方法 (包括格子气和格子Boltzmann方法 )在计算物理领域取得巨大进展。与之形成鲜明对比 ,格子方法的数学理论始终处于停滞不前的状况。为求解Burgers方程 ,一类带有BGK模型格子方法被构造出来 ,经过变量替换 ,发现他们属于三层非线性差分方法。使用极值原理 ,给出此类格式稳定性的严格证明。最后 ,从数值实验中可以看出 ,使用LBM得到的结果 ,与经典二阶守恒差分方法的结果符合得非常好。
It is well known that lattice Boltzmann methods(LBM) make great success in many computational physics fields,expecially in fluid mechanics.A lattice Boltzmann method with BGK model is developed to solve Burgers equation.Detailed analysis shows that the calculating scheme is a three level nonlinear finite difference one.The maximum value principle has been proved and the existence,uniqueness and stability are also discussed.The computational results agree with second order finite difference solutions very well. [
出处
《计算物理》
CSCD
北大核心
2000年第1期166-172,共7页
Chinese Journal of Computational Physics
基金
SubsidedbytheSpecialFundsforMajorStateBasicResearchProject!(G19990 3 2 80 1)
theNationalNaturalScienceFoundationofChina!(
