Journal ArticleDOI
A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases
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This work presents spectral element and discontinuous Galerkin solutions of the Euler and compressible Navier-Stokes equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling and recommends the DG method due to its conservation properties.About:
This article is published in Journal of Computational Physics.The article was published on 2008-04-01. It has received 243 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Euler equations.read more
Citations
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Solving PDEs with radial basis functions
Bengt Fornberg,Natasha Flyer +1 more
TL;DR: During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems.
Journal ArticleDOI
On the accuracy of high-order discretizations for underresolved turbulence simulations
Gregor J. Gassner,Andrea Beck +1 more
TL;DR: It is shown that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing, so proper stabilization is necessary for a successful computation of underresolved turbulence.
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Explicit Discontinuous Galerkin methods for unsteady problems
Florian Hindenlang,Gregor J. Gassner,Christoph Altmann,Andrea Beck,Marc Staudenmaier,Claus-Dieter Munz +5 more
TL;DR: The DGSEM scheme is described and the efficiency of element-wise operations is highly improved compared to standard DG implementations, and the applicability of the scheme is shown with a direct numerical simulation of a weak turbulent flow past a sphere at Reynolds number 1000.
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Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)
TL;DR: An implicit-explicit IMEX formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale as well as global regimes, is derived.
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On the Quadrature and Weak Form Choices in Collocation Type Discontinuous Galerkin Spectral Element Methods
TL;DR: Two formulations of tensor product discontinuous Galerkin spectral element approximations are shown to be algebraically equivalent with either Gauss or Gauss-Lobatto quadratures when global polynomial interpolations are used to approximate the solutions and fluxes within the elements.
References
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Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
TL;DR: In this article, the generalized Riemann problem is used to solve the Euler Equation problem and the ADER approach is used for non-linear systems with finite forces in multiple dimensions.
A Description of the Advanced Research WRF Version 2
William C. Skamarock,Joseph B. Klemp,Jimy Dudhia,David O. Gill,Dale Barker,Wei Wang,Jordan G. Powers +6 more
TL;DR: The Weather Research and Forecasting (WRF) model as mentioned in this paper was developed as a collaborative effort among the NCAR Mesoscale and Microscale Meteorology (MMM) Division, the National Oceanic and Atmospheric Administration's (NOAA) National Centers for Environmental Prediction (NCEP) and Forecast System Laboratory (FSL), the Department of Defense's Air Force Weather Agency (AFWA) and Naval Research Laboratory (NRL), the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma, and the Federal Aviation Administration (F