A review of element-based Galerkin methods for numerical weather prediction: Finite elements, spectral elements, and discontinuous Galerkin
Numerical weather prediction (NWP) is in a period of transition. As resolutions increase,
global models are moving towards fully nonhydrostatic dynamical cores, with the local and …
global models are moving towards fully nonhydrostatic dynamical cores, with the local and …
Entropy viscosity method for nonlinear conservation laws
A new class of high-order numerical methods for approximating nonlinear conservation laws
is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on …
is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on …
A splitting method for incompressible flows with variable density based on a pressure Poisson equation
JL Guermond, A Salgado - Journal of Computational Physics, 2009 - Elsevier
A new fractional time-stepping technique for solving incompressible flows with variable
density is proposed. The main feature of this method is that, as opposed to other known …
density is proposed. The main feature of this method is that, as opposed to other known …
Viscous shock capturing in a time-explicit discontinuous Galerkin method
A Klöckner, T Warburton… - Mathematical Modelling of …, 2011 - cambridge.org
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)
methods. The output of this detector is a reliably scaled, element-wise smoothness estimate …
methods. The output of this detector is a reliably scaled, element-wise smoothness estimate …
Bridging Large Eddy Simulation and Reduced Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives
Reduced order models (ROMs) have achieved a lot of success in reducing the
computational cost of traditional numerical methods across many disciplines. For convection …
computational cost of traditional numerical methods across many disciplines. For convection …
A second-order maximum principle preserving Lagrange finite element technique for nonlinear scalar conservation equations
This paper proposes an explicit,(at least) second-order, maximum principle satisfying,
Lagrange finite element method for solving nonlinear scalar conservation equations. The …
Lagrange finite element method for solving nonlinear scalar conservation equations. The …
On some implicit and semi-implicit staggered schemes for the shallow water and Euler equations
R Herbin, W Kheriji, JC Latché - ESAIM: Mathematical Modelling and …, 2014 - cambridge.org
In this paper, we propose implicit and semi-implicit in time finite volume schemes for the
barotropic Euler equations (hence, as a particular case, for the shallow water equations) and …
barotropic Euler equations (hence, as a particular case, for the shallow water equations) and …
Implementation of the entropy viscosity method with the discontinuous Galerkin method
Implementation of the entropy viscosity method with the discontinuous Galerkin method -
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Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid–structure interaction for deforming domains and complex geometry
We present a framework for adaptive finite element computation of turbulent flow and fluid–
structure interaction, with focus on general algorithms that allow for complex geometry and …
structure interaction, with focus on general algorithms that allow for complex geometry and …
New adaptive artificial viscosity method for hyperbolic systems of conservation laws
A Kurganov, Y Liu - Journal of Computational Physics, 2012 - Elsevier
We propose a new finite volume method for solving general multidimensional hyperbolic
systems of conservation laws. Our method is based on an appropriate numerical flux and a …
systems of conservation laws. Our method is based on an appropriate numerical flux and a …