| Isogeometric Analysis of the Cahn-Hilliard Phase-Field Model |
11 DEC 2007 |
47 pages |
| Authors:
Hector Gomez; Victor M. Calo; Yuri Bazilevs; Thomas J. Hughes; TEXAS UNIV AT AUSTIN
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 | The Cahn-Hilliard equation involves fourth-order spatial derivatives. Finite element solutions are not common because primal variational formulations of fourth-order operators are well defined and integrable only if the finite element basis functions are piecewise smooth and globally C1-continuous. There are a very limited number of two-dimensional finite elements possessing C1-continuity applicable to complex geometries, but none in three-dimensions. We propose Isogeometric Analysis as a technology that possesses a unique combination ... |
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| Conservation Properties for the Galerkin and Stabilised Forms of the Advection-Diffusion and Incompressible Navier-Stokes Equations |
2005 |
38 pages |
| Authors:
Thomas J. Hughes; Garth N. Wells; TEXAS UNIV AT AUSTIN
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| A common criticism of continuous Galerkin finite element methods is their perceived lack of conservation. This may in fact be true for incompressible flows when advective, rather than conservation, weak forms are employed. However, advective forms are often preferred on grounds of accuracy despite violation of conservation. It is shown here that this deficiency can be easily remedied, and conservative procedures for advective forms can be developed from multiscale concepts. ... |
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| Multiscale and Stabilized Methods |
2004 |
103 pages |
| Authors:
Thomas J. Hughes; Guglielmo Scovazzi; Leopoldo P. Franca; TEXAS UNIV AT AUSTIN DEPT OF AEROSPACE ENGINEERING AND ENGINEERING MECHANICS
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| This article presents an introduction to multiscale and stabilized methods, which represent unified approaches to modeling and numerical solution of fluid dynamic phenomena. Finite element applications are emphasized but the ideas are general and apply to other numerical methods as well. (They have been used in the development of finite difference, finite volume, and spectral methods, in addition to finite element methods.) The analytical ideas are first illustrated for time-harmonic ... |
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| Energy Transfers and Spectral Eddy Viscosity in Large-Eddy Simulations of Homogeneous Isotropic Turbulence: Comparison of Dynamic Smagorinsky and Multiscale Models Over a Range of Discretizations |
2004 |
28 pages |
| Authors:
Thomas J. Hughes; Garth N. Wells; Alan A. Wray; TEXAS UNIV AT AUSTIN
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| Energy transfers within LES and DNS grids are studied. The spectral eddy viscosity for conventional dynamic Smagorinsky and variational multiscale LES methods are compared with DNS results. Both models underestimate the DNS results for a very coarse LES, but the dynamic Smagorinsky model is significantly better. For moderately to well-refined LES, the dynamic Smagorinsky model overestimates the spectral eddy viscosity at low wave numbers. The multiscale model is in good ... |
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| LOCATING AN UNDERWATER SITE OF A NUCLEAR EXPLOSION DETECTED BY A HYDROACOUSTIC NETWORK. |
1962 |
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| Authors:
Thomas J. Hughes; NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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