11 papers · 1 filter
On the Role of Split Formulations on Aliasing Errors and Entropy Stability of Discontinuous Galerkin Schemes
Mathias Dufresne-Piché, Siva Nadarajah
In this work, we formally investigate the dealiasing properties of split form discontinuous Galerkin (DG) discretizations for the one-dimensional Burgers problem. By generalizing t…
A Space-time Approach to Entropy-Stable Discontinuous Galerkin and Flux Reconstruction
Carolyn M. V. Pethrick, Siva Nadarajah
We present a high-order space-time discretization equipped with fully-discrete entropy stability properties for general choices of volume and surface quadrature rules. The formulat…
An Adaptive Flux Reconstruction Scheme for Robust Shock Capturing
Sai Shruthi Srinivasan, Siva Nadarajah
In the case of hyperbolic conservation laws, high-order methods, such as the classical DG method, experience the phenomenon of unwanted high-frequency oscillations in the vicinity…
On the Superconvergence of ESFR Schemes
Mathias Dufresne-Piché, Siva Nadarajah
The energy stable flux reconstruction (ESFR) method provides an efficient and flexible framework to devise high-order linearly stable numerical schemes which can achieve high level…
Linearly Stable Generalizations of ESFR Schemes
Mathias Dufresne-Piché, Siva Nadarajah
The energy stable flux reconstruction (ESFR) method encompasses an infinite family of high-order, linearly stable schemes and thus provides a flex- ible and efficient framework for…
Investigation of Shock-Capturing with Bound-Preserving Limiters for the Nonlinearly Stable Flux Reconstruction Method
Sai Shruthi Srinivasan, Siva Nadarajah
Nonlinearly stable flux reconstruction (NSFR) combines the key properties of provable nonlinear stability with the increased time step from energy-stable flux reconstruction. The N…
A stabilized march approach to adjoint-based sensitivity analysis of chaotic flows
Pranshul Thakur, Siva Nadarajah
Adjoint-based sensitivity analysis is of interest in computational science due to its ability to compute sensitivities at a lower cost with respect to several design parameters. Ho…
Adjoint of Least Squares Shadowing: Existence, Uniqueness and Coarse Domain Discretization
Pranshul Thakur, Siva Nadarajah
Chaotic dynamical systems are characterized by the sensitive dependence of trajectories on initial conditions. Conventional sensitivity analysis of time-averaged functionals yields…
Fully-Discretely Nonlinearly-Stable Flux Reconstruction Methods for Compressible Flows
Carolyn M V Pethrick, Siva Nadarajah
A fully-discrete, nonlinearly-stable flux reconstruction (FD-NSFR) scheme is developed, which ensures robustness through entropy stability in both space and time for high-order flu…
Adjoint-based goal-oriented implicit shock tracking using full space mesh optimization
Pranshul Thakur, Siva Nadarajah
Solutions to the governing partial differential equations obtained from a discrete numerical scheme can have significant errors, especially near shocks when the discrete representa…
Discretely Nonlinearly Stable Weight-Adjusted Flux Reconstruction High-Order Method for Compressible Flows on Curvilinear Grids
Alexander Cicchino, Siva Nadarajah
Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entrop…