电池系统建模中Butler-Volmer方程的同伦分析求解

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．

Analytical Solution of Butler-Volmer Equation in Battery System Modeling

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 mathematical 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.