用于预测超级电容器可逆与不可逆发热的熵增数值方法
Entropy Increasing Numerical Methods for Prediction of Reversible and Irreversible Heating in Supercapacitors
AI总结：
针对超级电容器熵变化数值捕捉方法缺失的问题，本研究开发一阶与二阶熵增有限体积格式，证明其守恒性与熵增特性，揭示温度与电压扫描速率的二次标度律，为超级电容器发热预测提供有效工具。
摘要：
熵的准确表征对于捕捉超级电容器充放电循环过程中的可逆与不可逆发热至关重要。然而，目前仍缺乏能够如实捕捉超级电容器中熵变化的数值方法。本研究开发了用于预测超级电容器非等温电动特性的一阶与二阶有限体积格式。将温度与离子浓度、电势解耦的半隐式离散化方法，得到了一种高效的一阶精度格式。其数值分析从理论上证明了该非线性格式的唯一可解性，且离散层面存在正的离子浓度与温度。为获得熵增的二阶格式，本研究提出一种改进的Crank-Nicolson方法，对温度和离子浓度的对数进行离散化，用于保证数值正性。此外，数值分析严格证明，对于封闭、绝热的超级电容器，一阶与二阶格式均能无条件保持离子质量守恒和原始熵增特性。大量数值模拟表明，所提出的格式具有预期的精度，且在保持所需特性方面性能稳健。研究成功预测了充放电过程中的温度振荡，揭示了温度上升斜率与电压扫描速率之间的二次标度律。研究还证明，作为可逆发热潜在机制的离子熵贡献变化得到了如实捕捉。本研究为预测超级电容器的可逆与不可逆发热提供了一种有前景的工具。
英文摘要：
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in supercapacitors are still in lack. This work develops first-order and second-order finite-volume schemes for the prediction of non-isothermal electrokinetics in supercapacitors. Semi-implicit discretization that decouples temperature from ionic concentrations and electric potential results in an efficient first-order accurate scheme. Its numerical analysis theoretically establishes the unique solvability of the nonlinear scheme with the existence of positive ionic concentrations and temperature at discrete level. To obtain an entropy-increasing second-order scheme, a modified Crank-Nicolson approach is proposed for discretization of the logarithm of both temperature and ionic concentrations, which is employed to enforce numerical positivity. Moreover, numerical analysis rigorously demonstrates that both first-order and second-order schemes are able to unconditionally preserve ionic mass conservation and original entropy increase for a closed, thermally insulated supercapacitor. Extensive numerical simulations show that the proposed schemes have expected accuracy and robust performance in preserving the desired properties. Temperature oscillation in the charging/discharging processes is successfully predicted, unraveling a quadratic scaling law of temperature rising slope against voltage scanning rate. It is also demonstrated that the variation of ionic entropy contribution, which is the underlying mechanism responsible for reversible heating, is faithfully captured. Our work provides a promising tool in predicting reversible and irreversible heating in supercapacitors.
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