A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations

Hughes, Thomas J.R.; Franca, Leopoldo P.; Hulbert, Gregory M.

doi:10.1016/0045-7825(89)90111-4

Cited by 1,302 publications

(744 citation statements)

References 13 publications

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“…Scott King (VT) uses a grid of quadrilateral elements with streamline upwind Petrov-Galerkin (SUPG), which is a form of the Galerkin-least-squares approach (Hughes et al, 1989) for the heat equation. A Q1-P0 quadrilateral element is used for the Stokes equation.…”

Section: Contributing Codesmentioning

confidence: 99%

“…Nine-node isoparametric elements are used for temperature and velocity, with compatible four-node elements for pressure. Galerkin-least squares (Hughes et al, 1989) is used to stabilize the solution of the heat equation for advection dominated flows. The Stokes and heat equations are solved simultaneously and a non-linear iteration is performed using a multi-corrector fixed point algorithm.…”

Section: Contributing Codesmentioning

confidence: 99%

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A community benchmark for subduction zone modeling

Keken

Currie

King

et al. 2008

Physics of the Earth and Planetary Interiors

197

144

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Section: Contributing Codesmentioning

confidence: 99%

Section: Contributing Codesmentioning

confidence: 99%

A community benchmark for subduction zone modeling

Keken

Currie

King

et al. 2008

Physics of the Earth and Planetary Interiors

197

144

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“…First, it is designed for time-stepping mode, although it allows for stationary inversion as an option. Second, it uses Galerkin least-squares (GLS) stabilization (Hughes et al, 1989) modified for transient problems which ensures stable performance with time steps up to 12 h. Finally, it pays special attention to the accuracy of volume conservation.…”

Section: Introductionmentioning

confidence: 99%

“…Another problem comes from the fact that given low order polynomials on elements one cannot use biharmonic viscosity and diffusion to stabilize the momentum and tracer equations, as is becoming common with current eddy-permitting or eddy-resolving FD models. A set of residual-free stabilization techniques is known for FEM (see, e.g., Hughes et al, 1989;Hughes, 1995;Franca and Russo, 1996;Codina and Soto, 1997), which stabilize the equations without introducing excessive dissipation. The implementation of stabilization in primitive equations is also discussed in some detail below.…”

Section: Introductionmentioning

confidence: 99%

A finite-element ocean model: principles and evaluation

2004

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We describe a three-dimensional (3D) finite-element ocean model designed for investigating the largescale ocean circulation on time scales from years to decades. The model solves the primitive equations in the dynamical part and the advection-diffusion equations for temperature and salinity in the thermodynamical part. The time-stepping is implicit. The 3D mesh is composed of tetrahedra and has a variable resolution. It is based on an unstructured 2D surface mesh and is stratified in the vertical direction. The model uses linear functions for horizontal velocity and tracers on tetrahedra, and for surface elevation on surface triangles. The vertical velocity field is elementwise constant. An important ingredient of the model is the Galerkin least-squares stabilization used to minimize effects of unresolved boundary layers and make the matrices to be inverted in time-stepping better conditioned. The model performance was tested in a 16-year simulation of the North Atlantic using a mesh covering the area between 7°and 80°N and providing variable horizontal resolution from 0.3°to 1.5°.

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“…Numerical convergence can be difficult to achieve for the UCM and Oldroyd B models, especially for high Weissenberg numbers in the presence of large velocity gradients. Here we make use of the Galerkin least squares (GLS) method to stabilize the equations as originally proposed by Hughes et al [33]. The scheme used here follows the procedure of Behr et al [34] which was implemented in COMSOL by Craven et al [32].…”

Section: Governing Equationsmentioning

confidence: 99%

Viscoelastic Hele-Shaw flow in a cross-slot geometry

Chaffin

Rees

2018

European Journal of Mechanics - B/Fluids

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a b s t r a c tIn this paper a cross-slot geometry for which the height of the channel is small compared to the other channel dimensions is considered. The normal components of the viscoelastic stresses are found analytically for a second order fluid up to numerical inversion. The validity of the theoretical analysis was corroborated by comparison with numerical simulations based on a stabilized Galerkin least squares finite element method using an Oldroyd B fluid. Close agreement was found between numerical predictions and analytical results for Weissenberg numbers up to 0.2. An explicit expression is formulated for viscoelastic parameters in terms of the variation and strength of the first normal stress difference around the stagnation point. The analysis is generalized for the case where the inlet channel width is different from the outlet channel width. For such configurations it was found that uniformity of the elongation rate was reduced.

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A new finite element formulation for computational fluid dynamics: VIII. The galerkin/least-squares method for advective-diffusive equations

Cited by 1,302 publications

References 13 publications

A community benchmark for subduction zone modeling

A community benchmark for subduction zone modeling

A finite-element ocean model: principles and evaluation

Viscoelastic Hele-Shaw flow in a cross-slot geometry

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