20 citations · 56 across the 9 of their papers we have counts for
13 papers
Targeted Entropy-Stable Nonlinear Artificial Dissipation for High-Order Spectral-Element Summation-By-Parts Discretizations
Zelalem Arega Worku, Alex Bercik, David C. Del Rey Fernández +1
Artificial dissipation improves the robustness of high-order methods for under-resolved flows, but can compromise accuracy and suppress physically relevant structures if its streng…
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…
SBP-SAT finite difference discretization of acoustic wave equations on staggered block-wise uniform grids
Longfei Gao, David C. Del Rey Fernandez, Mark Carpenter +1
We consider the numerical simulation of the acoustic wave equations arising from seismic applications, for which staggered grid finite difference methods are popular choices due to…
An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property
Lucas Friedrich, Andrew R. Winters, David C. Del Rey Fernández +3
This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomia…
Conservative and Stable Degree Preserving SBP Operators for Non-Conforming Meshes
Lucas Friedrich, David C. Del Rey Fernandez, Andrew R. Winters +3
Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex ge…
Simultaneous Approximation Terms for Multi-Dimensional Summation-by-Parts Operators
David C. Del Rey Fernández, Jason E. Hicken, David W. Zingg
This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) fini…
Multidimensional Summation-By-Parts Operators: General Theory and Application to Simplex Elements
Jason E. Hicken, David C. Del Rey Fernández, David W. Zingg
Summation-by-parts (SBP) finite-difference discretizations share many attractive properties with Galerkin finite-element methods (FEMs), including time stability and superconvergen…
Generalized Summation-by-Parts Operators for the Second Derivative with Variable Coefficients
David C. Del Rey Fernández, David W. Zingg
The comprehensive generalization of summation-by-parts of Del Rey Fernández et al.\ (J. Comput. Phys., 266, 2014) is extended to approximations of second derivatives with variable…