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We present a quantitative assessment of the impact of high-order mappings on the simulation of flows over complex orography. Curved boundaries were not used in early numerical methods, whereas they are employed to an increasing extent in…

Atmospheric and Oceanic Physics · Physics 2025-08-27 Giuseppe Orlando , Tommaso Benacchio , Luca Bonaventura

We formulate and implement the Euler equations with SGS dynamics and provide numerical tests of an SGS turbulence energy model that predicts the turbulent pressure of unresolved velocity fluctuations and the rate of dissipation for highly…

Astrophysics of Galaxies · Physics 2015-05-20 W. Schmidt , C. Federrath

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…

Computational Physics · Physics 2019-05-14 Matteo Franciolini , Lorenzo Botti , Alessandro Colombo , Andrea Crivellini

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Large eddy simulation (LES) is an alternative that is computationally less demanding, but is…

Fluid Dynamics · Physics 2021-09-09 Shengyu Chen , Shervin Sammak , Peyman Givi , Joseph P. Yurko1 , Xiaowei Jia

We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…

Numerical Analysis · Mathematics 2025-08-26 Spiros Zafeiris , Emmanuil H. Georgoulis , George Papadakis

In many engineering and industrial applications, the investigation of rotating turbulent flow is of great interest. In rotor-stator cavities, the centrifugal and Coriolis forces have a strong influence on the turbulence by producing a…

This article investigates matrix-free higher-order discontinuous Galerkin discretizations of the Navier--Stokes equations for incompressible flows with variable viscosity. The viscosity field may be prescribed analytically or governed by a…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Richard Schussnig , Niklas Fehn , Douglas Ramalho Queiroz Pacheco , Martin Kronbichler

The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…

Numerical Analysis · Mathematics 2021-04-27 Edward Laughton , Gavin Tabor , David Moxey

The trade-off among accuracy, robustness, and computational cost remains a key challenge in simulating complex flows. Second-order schemes are computationally efficient but lack the accuracy required for resolving intricate flow structures,…

Numerical Analysis · Mathematics 2025-08-28 Yaqing Yang , Fengxiang Zhao , Kun Xu

Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG…

Numerical Analysis · Mathematics 2013-01-01 Kolja Brix , Claudio Canuto , Wolfgang Dahmen

We investigate a hierarchy of eddy-viscosity terms in POD Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to Large Eddy Simulation data for a flow around the vehicle-like…

Fluid Dynamics · Physics 2015-06-17 Jan Östh , Bernd R. Noack , Siniša Krajnović , Diogo Barros , Jacques Borée

Discontinuous Galerkin (DG) methods are known to suffer from increasingly restrictive explicit time-step constraints as the polynomial order increases, limiting their efficiency at high orders for explicit time-stepping schemes. In this…

Numerical Analysis · Mathematics 2025-12-03 Kieran Ricardo , Kenneth Duru

The present work is concerned with a study of large eddy simulations (LES) of unsteady turbulent jet flows. In particular, the present analysis is focused on the effects of the subgrid-scale modeling used when a second-order spatial…

Fluid Dynamics · Physics 2022-12-26 Carlos Junqueira-Junior , Sami Yamouni , João Luiz F. Azevedo , William R. Wolf

We introduce CaLES, a GPU-accelerated finite-difference solver designed for large-eddy simulations (LES) of incompressible wall-bounded flows in massively parallel environments. Built upon the existing direct numerical simulation (DNS)…

Fluid Dynamics · Physics 2024-11-18 Maochao Xiao , Alessandro Ceci , Pedro Costa , Johan Larsson , Sergio Pirozzoli

Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…

Mathematical Software · Computer Science 2013-04-23 Andreas Klöckner , Timothy Warburton , Jan S. Hesthaven

Accurate representation of vertical turbulent fluxes is crucial for numerical ocean modelling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two…

Atmospheric and Oceanic Physics · Physics 2020-05-20 Tuomas Kärnä

With the continuing progress in large eddy simulations (LES), and ever increasing computational resources, it is currently possible to numerically solve the time-dependent and anisotropic large scales of turbulence in a large variety of…

Fluid Dynamics · Physics 2021-12-14 Ryan D. Hass , Aditya S. Ghate , Sanjiva K. Lele

We carry out a stability and convergence analysis of a fully discrete scheme for the time-dependent Navier-Stokes equations resulting from combining an $H(\mathrm{div}, \Omega)$-conforming discontinuous Galerkin spatial discretization, and…

Numerical Analysis · Mathematics 2025-10-22 L. Beirão da Veiga , F. Dassi , S. Gómez

The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at…

Fluid Dynamics · Physics 2009-11-13 C. Marchioli , M. V. Salvetti , A. Soldati

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…

Numerical Analysis · Mathematics 2017-05-24 Maurizio Tavelli , Michael Dumbser
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