2 research outputs found
An explicit predictor/multicorrector time marching with automatic adaptivity for finite-strain elastodynamics
We propose a time-adaptive predictor/multi-corrector method to solve
hyperbolic partial differential equations, based on the generalized-
scheme that provides user-control on the numerical dissipation and second-order
accuracy in time. Our time adaptivity uses an error estimation that exploits
the recursive structure of the variable updates. The predictor/multicorrector
method explicitly updates the equation system but computes the residual of the
system implicitly. We analyze the method's stability and describe how to
determine the parameters that ensure high-frequency dissipation and accurate
low-frequency approximation. Subsequently, we solve a linear wave equation,
followed by non-linear finite strain deformation problems with different
boundary conditions. Thus, our method is a straightforward, stable and
computationally efficient approach to simulate real-world engineering problems.
Finally, to show the performance of our method, we provide several numerical
examples in two and three dimensions. These challenging tests demonstrate that
our predictor/multicorrector scheme dynamically adapts to sudden energy
releases in the system, capturing impacts and boundary shocks. The method
efficiently and stably solves dynamic equations with consistent and
under-integrated mass matrices conserving the linear and angular momenta as
well as the system's energy for long-integration times.Comment: Journal of Computational Physics (accepted
Dendrite formation in rechargeable lithium-metal batteries: Phase-field modeling using open-source finite element library
We describe a phase-field model for the electrodeposition process that forms
dendrites within metal-anode batteries. We derive the free energy functional
model, arriving at a system of partial differential equations that describe the
evolution of a phase field, the lithium-ion concentration, and an electric
potential. We formulate, discretize, and solve the set of partial differential
equations describing the coupled electrochemical interactions during a battery
charge cycle using an open-source finite element library. The open-source
library allows us to use parallel solvers and time-marching adaptivity. We
describe two- and three-dimensional simulations; these simulations agree with
experimentally-observed dendrite growth rates and morphologies reported in the
literature.Comment: Under Revie