电池系统建模中Butler-Volmer方程的同伦分析求解  

Analytical Solution of Butler-Volmer Equation in Battery System Modeling

作　　者：宋辉[1] 李芬[1] 徐献芝[1] 

机构地区：[1]中国科技大学近代力学系,合肥230027

出　　处：《应用数学和力学》2013年第4期373-382,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10872193)

摘　　要：Butler-Volmer方程是电化学系统中描述电极动力学过程的本构方程,具有强非线性.为了对这一方程(耦合两个Ohm方程)进行解析求解,在同伦分析方法的框架下,发展了满足简单条件的广义非线性算子的算法,以取代原同伦分析中的非线性算子.该广义非线性算子的构造保证了高阶形变方程的线性特征.这一方法的有效性通过一些算例得到了验证.最后通过同伦分析方法对Butler-Volmer方程进行了求解,结果显示过电位和电流密度的级数解析解与数值解吻合很好,并有很好的收敛效率.Butler-Volmer equation is the constitutive equation to describe the dynamic process of electrode reaction in electrochemical systems. Due to its strong nonlinearity in the mathe- matical form, the computing efficiency by numerical methods was frequently limited. Aiming at solving this equation （ coupled with two Ohm equations） more efficiently, an improved homotopy analysis method（HAM） was presented, in which a generalized nonlinear operator satisfying simple conditions was developed to replace the nonlinear operator in the original homotopy. The construction of generalized nonlinear operator guaranteed the linear property of higher-order deformation equations. The validity of this method was verified through some examples. Furthermore, this method was successfully applied in solving Butler-Volmer equation. The analytical solutions of overpotential and current density agree very well with the numerical solutions and the high efficiency is shown in the computing process.

关 键 词：Butler-Volmer方程 同伦分析方法 复合函数 强非线性项 广义非线性算子 

分 类 号：O29[理学—应用数学] O175.8[理学—数学]