An immersed interface Adaptive Mesh Refinement algorithm for Li-ion battery simulations. I. Development of a fast P2D solver

Abstract

We present a Cartesian immersed interface solver for the P2D model that integrates seamlessly with hierarchical Adaptive Mesh Refinement (AMR), providing marked improvements in computational efficiency while preserving solution accuracy. Governing equations are discretized using the finite volume method and solved implicitly using a multigrid linear solver, via a sequential approach. The hierarchical AMR enables the use of a coarse mesh covering the entire domain, with local grid refinement applied where required, such as at the electrode–separator interfaces, effectively reducing the computational burden of the solver while preserving solution accuracy. To facilitate the integration of our method with the AMR, we introduce an immersed interface technique to model material interfaces, allowing for the discretization of the electrode-pair domain on a single mesh without the need to mesh the anode, separator, and cathode regions separately. The solver was validated against numerical results across a wide range of discharge/charge rates and various operating conditions, including constant discharge rate tests and tests under the New European Driving Cycle. In all cases, our solver accurately solves the P2D model with a computational efficiency that demonstrates its suitability for use in real-time applications. The numerical techniques introduced in this work can naturally extend to multi-dimensional simulations, and this capability will be demonstrated in Part II of the paper.