9 papers
SAILOR: Solver-Assisted Interactive LLM-based Optimization Recovery
Shaghayegh Sadeghi, Stephen L. Smith, David C. Del Rey Fern'andez
Natural-language descriptions of optimization problems may be incomplete or vague about numerical information that a solver requires, including costs, capacities, demands, bounds,…
Oblique projection for scalable rank-adaptive reduced-order modeling of nonlinear stochastic PDEs with time-dependent bases
M. Donello, G. Palkar, M. H. Naderi +2
Time-dependent basis reduced order models (TDB ROMs) have successfully been used for approximating the solution to nonlinear stochastic partial differential equations (PDEs). For m…
Provably Stable Flux Reconstruction High-Order Methods on Curvilinear Elements
Alexander Cicchino, David C. Del Rey Fernández, Siva Nadarajah +2
Provably stable flux reconstruction (FR) schemes are derived for partial differential equations cast in curvilinear coordinates. Specifically, energy stable flux reconstruction (ES…
Nonlinearly Stable Flux Reconstruction High-Order Methods in Split Form
Alexander Cicchino, Siva Nadarajah, David C. Del Rey Fernández
The flux reconstruction (FR) method has gained popularity in the research community as it recovers promising high-order methods through modally filtered correction fields, such as…
Entropy stable spectral collocation schemes for the 3-D Navier-Stokes equations on dynamic unstructured grids
Nail K. Yamaleev, David C. Del Rey Fernandez, Jialin Lou +1
New entropy stable spectral collocations schemes of arbitrary order of accuracy are developed for the unsteady 3-D Euler and Navier-Stokes equations on dynamic unstructured grids.…
Entropy Stable Space-Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws
Lucas Friedrich, Gero Schnücke, Andrew R. Winters +3
This work examines the development of an entropy conservative (for smooth solutions) or entropy stable (for discontinuous solutions) space-time discontinuous Galerkin (DG) method f…