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Spectral/hp element methods: Recent developments, applications, and perspectives

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Title: Spectral/hp element methods: Recent developments, applications, and perspectives
Authors: Xu, H
Cantwell, C
Monteserin, C
Eskilsson, C
Engsig-Karup, AP
Sherwin, SJ
Item Type: Journal Article
Abstract: The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
Issue Date: 1-Feb-2018
Date of Acceptance: 28-Dec-2017
URI: http://hdl.handle.net/10044/1/57126
DOI: https://dx.doi.org/10.1007/s42241-018-0001-1
ISSN: 1001-6058
Publisher: Elsevier
Start Page: 1
End Page: 22
Journal / Book Title: Journal of Hydrodynamics
Volume: 30
Issue: 1
Copyright Statement: © The Authors 2018 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/L000407/1
Keywords: Science & Technology
Technology
Mechanics
High-precision spectral/hp elements
continuous Galerkin method
discontinuous Galerkin method
implicit large eddy simulation
DISCONTINUOUS GALERKIN METHOD
SHALLOW-WATER EQUATIONS
NAVIER-STOKES EQUATIONS
BOUSSINESQ-TYPE EQUATIONS
LARGE-EDDY SIMULATION
FLUID-STRUCTURE INTERACTION
VANISHING VISCOSITY METHOD
FREE-SURFACE FLOWS
DIRECT NUMERICAL SIMULATIONS
NONLINEAR CONSERVATION-LAWS
09 Engineering
Mechanical Engineering & Transports
Publication Status: Published
Open Access location: https://link.springer.com/article/10.1007/s42241-018-0001-1
Online Publication Date: 2018-04-11
Appears in Collections:Faculty of Engineering
Aeronautics



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