Nathaniel Trask

Abstract:

Generalized moving least squares (GMLS) is a discretization that generates numerical solution of partial differential equations using only particle degrees of freedom and requires no underlying mesh. This makes the method ideal for problems involving complex multiphysics whose boundaries evolve over time. In particular, we are interested in developing techniques allowing the coupling of surface physics on an evolving manifold together with transport phenomena in a bulk domain. Such processes are representative of a range of mesoscale devices, and we consider a toy problem representing the mechanical degradation of a lithium ion battery which requires concurrent coupling of many physics – a deposition process where mass transport of lithium ions leads to an evolving interface between active lithium particles and a surrounding carbon matrix. In turn, this swelling of the interface imparts compressive stresses on the surrounding matrix and eventually leads to fracture. We use this simplified model as a driver for the development of a new method that is able to concurrently couple bulk-manifold diffusion, manifold evolution, and linear elasticity solvers while maintaining high-order accuracy.