7 papers
Finite element methods for electroneutral multicomponent electrolyte flows
Aaron Baier-Reinio, Patrick E. Farrell, Charles W. Monroe
We present a broad family of high-order finite element algorithms for simulating the flow of electroneutral electrolytes. The governing partial differential equations that we solve…
A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect
Jakub Cach, Patrick E. Farrell, Josef Málek +1
Viscoelastic rate-type fluids represent a popular class of non-Newtonian fluid models due to their ability to describe phenomena such as stress relaxation, non-linear creep, and no…
Conservative and dissipative discretisations of multi-conservative ODEs and GENERIC systems
Boris D. Andrews, Patrick E. Farrell
Ordinary and partial differential equations describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated qu…
Helicity-preserving finite element discretization for magnetic relaxation
Mingdong He, Patrick E. Farrell, Kaibo Hu +1
The Parker conjecture, which explores whether magnetic fields in perfectly conducting plasmas can develop tangential discontinuities during magnetic relaxation, remains an open que…
Enforcing conservation laws and dissipation inequalities numerically via auxiliary variables
Boris D. Andrews, Patrick E. Farrell
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represen…
High-order finite element methods for three-dimensional multicomponent convection-diffusion
Aaron Baier-Reinio, Patrick E. Farrell
We derive and analyze a broad class of finite element methods for numerically simulating the stationary, low Reynolds number flow of concentrated mixtures of several distinct chemi…