Numerical Stability Analysis of a Distributed Thermal Model for Pouch Cell Assemblies via Gershgorin Circle Theorem

Thermal simulation plays a key role in battery pack design, supporting cooling system sizing, temperature control and thermal failure prevention. However, accurate thermal models involving the numerical solution of a large number of partial differential equations (PDEs) can exhibit numerical instabilities that are difficult to diagnose and resolve. This letter applies the Gershgorin Circle Theory to evaluate the numerical stability of a distributed-parameter thermal model (DTM), which simulates the temperature distribution evolution of a multi-body assembly composed of a Li-ion pouch cell, its tabs, and a compression aluminum plate. A discrete state-space representation of the system is developed before calculating the Gershgorin circles. This method identifies the stability boundaries of the DTM as a function of the physical parameters of the system, e.g., thermal conductivities and thermal resistances, and simulation parameters, e.g., mesh size and sampling step. The proposed approach provides an efficient tool for optimizing simulation settings, ensuring convergence and reliability in thermal simulations of complex multi-element Li-ion pouch cell assembly.