| 格子Boltzmann方法求解Burgers方程 |
| |
| 引用本文： | 沈智军,袁光伟,沈隆钧. 格子Boltzmann方法求解Burgers方程[J]. 计算物理, 2000, 17(1): 166-172 |
| |
| 作者姓名： | 沈智军 袁光伟 沈隆钧 |
| |
| 作者单位： | 北京应用物理与计算数学研究所计算物理实验室,北京,100088 |
| |
| 基金项目： | Subsided by the Special Funds for Major State Basic Research Project (G1999032801), the National Natural Science Foundation of China(19932010) and the Foundation of LCP. |
| |
| 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。
|
| 关 键 词： | 格子Boltzmann Burgers方程 稳定性 |
| 文章编号： | 1001-246X(2000)01-0166-07 |
| 修稿时间： | 1999-09-06 |
LATTICE BOLTZMANN METHOD FOR BURGERS EQUATION |
| |
| SHEN Zhi-jun,YUAN Guang-wei,SHEN Long-jun. LATTICE BOLTZMANN METHOD FOR BURGERS EQUATION[J]. Chinese Journal of Computational Physics, 2000, 17(1): 166-172 |
| |
| Authors: | SHEN Zhi-jun YUAN Guang-wei SHEN Long-jun |
| |
| Abstract: | 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. |
| |
| Keywords: | lattice Boltzmann Burgers equation stability |
| 本文献已被 维普 万方数据 等数据库收录！ |
