A novel robust strategy for discontinuous Galerkin methods in computational fluid mechanics: Why? When? What? Where?
GJ Gassner, AR Winters - Frontiers in Physics, 2021 - frontiersin.org
In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
Arbitrary L agrangian–E ulerian Methods
J Donea, A Huerta, JP Ponthot… - Encyclopedia of …, 2004 - Wiley Online Library
The aim of the present chapter is to provide an in‐depth survey of arbitrary Lagrangian–
Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical …
Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical …
Facilitating the adoption of unstructured high-order methods amongst a wider community of fluid dynamicists
PE Vincent, A Jameson - Mathematical Modelling of Natural …, 2011 - cambridge.org
Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …
methods can provide solutions to otherwise intractable fluid flow problems within complex …
A registration method for model order reduction: data compression and geometry reduction
T Taddei - SIAM Journal on Scientific Computing, 2020 - SIAM
We propose a general---ie, independent of the underlying equation---registration method for
parameterized model order reduction. Given the spatial domain Ω⊂R^d and the manifold …
parameterized model order reduction. Given the spatial domain Ω⊂R^d and the manifold …
Hybridizable discontinuous Galerkin methods for partial differential equations in continuum mechanics
We present hybridizable discontinuous Galerkin methods for solving steady and time-
dependent partial differential equations (PDEs) in continuum mechanics. The essential …
dependent partial differential equations (PDEs) in continuum mechanics. The essential …
Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking
MA Mirhoseini, MJ Zahr - Journal of Computational Physics, 2023 - Elsevier
This work introduces a new approach to reduce the computational cost of solving partial
differential equations (PDEs) with convection-dominated solutions: model reduction with …
differential equations (PDEs) with convection-dominated solutions: model reduction with …
Insights from von Neumann analysis of high-order flux reconstruction schemes
The flux reconstruction (FR) approach unifies various high-order schemes, including
collocation based nodal discontinuous Galerkin methods, and all spectral difference …
collocation based nodal discontinuous Galerkin methods, and all spectral difference …
A moving discontinuous Galerkin finite element method for flows with interfaces
A Corrigan, AD Kercher… - International Journal for …, 2019 - Wiley Online Library
A moving discontinuous Galerkin finite element method with interface condition enforcement
is formulated for flows with discontinuous interfaces. The underlying weak formulation …
is formulated for flows with discontinuous interfaces. The underlying weak formulation …
An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
MJ Zahr, PO Persson - Journal of Computational Physics, 2018 - Elsevier
This work introduces a novel discontinuity-tracking framework for resolving discontinuous
solutions of conservation laws with high-order numerical discretizations that support inter …
solutions of conservation laws with high-order numerical discretizations that support inter …
High-order, finite-volume methods in mapped coordinates
We present an approach for constructing finite-volume methods for flux-divergence forms to
any order of accuracy defined as the image of a smooth mapping from a rectangular …
any order of accuracy defined as the image of a smooth mapping from a rectangular …