2 citations · 2 across the 7 of their papers we have counts for
8 papers
Strongly enstrophy-stable integrators for the incompressible Navier-Stokes equations
Boris D. Andrews, Matin Shams, Patrick E. Farrell
We propose a mixed finite element discretisation for the incompressible Navier-Stokes equations that preserves the evolution laws of both energy and enstrophy, in a stronger sense…
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…
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…
The latent variable proximal point algorithm for variational problems with inequality constraints
Jørgen S. Dokken, Patrick E. Farrell, Brendan Keith +2
The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a s…
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…
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…
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…