3 papers
physics.comp-ph2025
Phase-Field/Discontinuity Capturing operator for direct van der Waals simulation (DVS)
Tianyi Hu, Thomas J. R. Hughes, Guglielmo Scovazzi +1
Discontinuity capturing (DC) operators are commonly employed to numerically solve problems involving sharp gradients in the solution. Despite their success, the application of DC o…
physics.flu-dyn2025
Extensions to the Navier-Stokes-Fourier Equations for Rarefied Transport: Variational Multiscale Moment Methods for the Boltzmann Equation
F. A. Baidoo, I. M. Gamba, T. J. R. Hughes +1
We derive a fourth order entropy stable extension of the Navier-Stokes-Fourier equations into the transition regime of rarefied gases. We do this through a novel reformulation of t…
math.NA2025
An optimal Petrov-Galerkin framework for operator networks
Philip Charles, Deep Ray, Yue Yu +7
The optimal Petrov-Galerkin formulation to solve partial differential equations (PDEs) recovers the best approximation in a specified finite-dimensional (trial) space with respect…