Solitary wave of the Korteweg-de Vries equation based on lattice Boltzmann model with three conservation laws

详细信息    查看全文

• 作者：Huimin Wang ^{whm780921@sina.com whm20110605@126.com}
• 关键词：Lattice Boltzmann model ; KdV equation ; Conservation law ; Solitary wave
• 刊名：Advances in Space Research
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：59
• 期：1
• 页码：283-292
• 全文大小：1110 K
• 卷排序：59

文摘

In this paper, a new lattice Boltzmann model for the Korteweg-de Vries (KdV) equation is proposed. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher- order moments of equilibrium distribution functions are obtained. In order to make the scheme obey the three conservation laws of the KdV equation, two equilibrium distribution functions are used and a correlation between the first conservation law and the second conservation law is constructed. In numerical examples, the numerical results of the KdV equation obtained by this scheme are compared with those results obtained by the previous lattice Boltzmann model. Numerical experiments demonstrate this scheme can be used to reduce the truncation error of the lattice Boltzmann scheme and preserve the three conservation laws.