Neil N. Carlson

Nonlinear Krylov acceleration applied to a discrete ordinates formulation of the k-eigenvalue problem

We compare a variant of Anderson Mixing with the Jacobian-Free Newton-Krylov and Broyden methods applied to an instance of the k-eigenvalue formulation of the linear Boltzmann transport equation. We present evidence that one variant of Anderson Mixing finds solutions in the fewest number of iterations. We examine and strengthen theoretical results of Anderson Mixing applied to linear problems.

The balanced-force volume tracking algorithm and global embedded interface formulation for droplet dynamics with mass transfer

Understanding the complex interaction of droplet dynamics with mass transfer and chemical reactions is of fundamental importance in liquid-liquid extraction. High-fidelity numerical simulation of droplet dynamics with interfacial mass transfer is particularly challenging because the position of the interface between the fluids and the interface physics need to be predicted as part of the solution of the flow equations. In addition, the discontinuity in fluid density, viscosity and species concentration at the interface present additional numerical challenges. In this work, we extend our balanced-force volume-tracking algorithm for modeling surface tension force (Francois et al., 2006) and we propose a global embedded interface formulation to model the interfacial conditions of an interface in thermodynamic equilibrium. To validate our formulation, we perform simulations of pure diffusion problems in one- and two-dimensions. Then we present two and three-dimensional simulations of a single droplet dynamics rising by buoyancy with mass transfer.Copyright