Algorithm for the synthesis of equations of thermal conductivity of lithium-ion accumulator for finite volumes during division

The current level of technology development makes it possible to improve the volumes of on-board equipment significantly, the same applies to backup power supply systems, in which the use of lithium-ion batteries is promising, which, if there are significant advantages, have a number of disadvantages that must be taken into account when using them. First of all, this is thermal acceleration, which is caused by internal physico-chemical processes and improper operation. To prevent thermal overclocking, it is proposed to use a digital twin, the basis of which is a mathematical model of thermal processes of a lithium-ion battery, obtained by mathematical prototyping of energy processes. For the numerical implementation of the mathematical prototyping method, it is proposed to use a modified finite volume method with the implementation of the division procedure until the required accuracy of the model is obtained. The presented article discusses the procedure for the formation of thermal conductivity equations when modeling the dynamic distribution of the thermal field in a lithium-ion battery in a three-plane formulation of the problem. This procedure is necessary when implementing the modified finite element method using the method of mathematical prototyping of energy processes, which involves dividing finite volumes to achieve the required calculation accuracy. A special feature of the division procedure is the change in volumes, areas of contact of interacting elements, and the change in elements that are sources of heat. In the simulation cycle, it is necessary to re-form the system of differential equations, taking into account the changes that occurred after the division. For clarity, the article discusses the procedures for dividing volumes into two equal parts according to one of the coordinates, and the Cartesian coordinate system is also considered to obtain a model. The proposed procedure for forming a system of differential equations is implemented in Python, the simulation results have shown the adequacy of the model and the efficiency of the proposed method.