arXiv subjects

Nicholas R. Cross

Publications and source records attributed to Nicholas R. Cross.

3 recordsLinked to original sources

arXiv2026

Scalable Preconditioners for the Pseudo-4D DFN Lithium-ion Battery Model

The pseudo-4D Doyle-Fuller-Newman (DFN) model enables predictive simulation of lithium-ion batteries with three-dimensional electrode architectures and particle-scale diffusion, extending the standard pseudo-2D (P2D) formulation to fully resolve cell geometry. This leads to large, nonlinear systems with strong coupling across multiple physical scales, posing significant challenges for scalable numerical solution. We introduce block-structured preconditioning strategies that exploit the mathematical properties of the coupled system, employing multigrid techniques for electrode-level operators and localized solvers for particle-scale diffusion. Comprehensive scalability studies are performed across a range of geometries, including homogeneous and heterogeneous cubic cells, flattened jelly-roll configurations, and triply periodic minimal surface electrodes, to assess solver robustness and parallel scalability. The proposed methods consistently deliver efficient convergence and enable the solution of battery models with hundreds of millions of degrees of freedom on large-scale parallel hardware.

math.NA↗

arXiv2024

Shape matters: Understanding the effect of electrode geometry on cell resistance and chemo-mechanical stress

Rechargeable batteries that incorporate shaped three-dimensional electrodes have been shown to have increased power and energy densities for a given footprint area when compared to a conventional geometry, i.e., a planar cathode and anode that sandwich an electrolyte. Electrodes can be shaped to enable a higher loading of active material, while keeping the ion transport distance small, however, the relationship between electrical and mechanical performance remains poorly understood. A variety of electrode shapes have been explored, where the electrodes are individually shaped or intertwined with one another. Advances in manufacturing and shape and topology optimization have made such designs a reality. In this paper, we explore sinusoidal half cells and interdigitated full cells. First, we use a simple electrostatics model to understand the cell resistance as a function of shape. We focus on low-temperature conditions, where the electrolyte conductivity decreases and the governing dimensionless parameters change. Next, we use a chemo-mechanics model to examine the stress concentrations that arise due to intercalation-driven volume expansion. We show that shaped electrodes provide a significant reduction in resistance, however, they result in unfavorable stress concentrations. Overall, we find that the fully interdigitated electrodes may provide the best balance with respect to this trade-off.

physics.chem-ph↗

arXiv2024

Topology Optimization for the Full-Cell Design of Porous Electrodes in Electrochemical Energy Storage Devices

In this paper, we introduce a density-based topology optimization framework to design porous electrodes for maximum energy storage. We simulate the full cell with a model that incorporates electronic potential, ionic potential, and electrolyte concentration. The system consists of three materials, namely pure liquid electrolyte and the porous solids of the anode and cathode, for which we determine the optimal placement. We use separate electronic potentials to model each electrode, which allows interdigitated designs. As a result, a penalization is required to ensure that the anode and cathode do not touch, i.e., causing a short circuit. We compare multiple 2D designs generated for different fixed conditions, e.g. material properties. A 3D design with complex channel and interlocked structure is also created. All optimized designs are far superior to the traditional monolithic electrode design with respect to energy storage metrics. We observe up to a 750% increase in energy storage for cases with slow effective ionic diffusion within the porous electrode.

physics.app-ph↗