Monitoring unresolved scales in multiscale turbulence modeling

Collis, S. Scott

doi:10.1063/1.1367872

Cited by 118 publications

(133 citation statements)

References 13 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…For a detailed exposition on the VMS method, the reader is requested to consult the articles by Hughes et al [88] and Collis [42]. In VMS, the projection operation partitions the solution as U = U + U + U where U are the large scales, U are the small scales and U are the unresolved scales.…”

Section: Vms Formulationmentioning

confidence: 99%

“…Thus, reaffirming the well-known importance of spanwise resolution in wall-bounded turbulent flows [99,119]. Therefore, we first explore strategies to address the non-linear stability before proceeding to SGS modeling via VMS [42,43,88].…”

Section: Dg Spatial Discretizationmentioning

confidence: 99%

“…where B( W) Ω denotes a variational form of the Navier-Stokes equations with weighting functions W = W + W that correspond to the resolved scales (see Collis [42] for details) and M , M denote the model terms acting on the large and small scales, respectively. It is desirable that there be no direct modeling in the large scale equations (M = 0), while the small scales may have models such as a simple Smagorinsky closure, similar to classical LES.…”

Section: Vms Formulationmentioning

confidence: 99%

“…The variational formulation provides a solid mathematical foundation for turbulence modeling [42,88].…”

Section: Vms Formulationmentioning

confidence: 99%

“…Recently, the development of the Variational Multi-Scale (VMS) [42,88] method as a paradigm for LES has yielded promising results for a variety of applications [89,90,103,133]. VMS is attractive for LES as it addresses many of the limitations enumerated above.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Shadid¹,

Lehoucq²,

Christon³

et al. 2004

View full text Add to dashboard Cite

This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.

show abstract

Section: Vms Formulationmentioning

confidence: 99%

Section: Dg Spatial Discretizationmentioning

confidence: 99%

Section: Vms Formulationmentioning

confidence: 99%

“…The variational formulation provides a solid mathematical foundation for turbulence modeling [42,88].…”

Section: Vms Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Shadid¹,

Lehoucq²,

Christon³

et al. 2004

View full text Add to dashboard Cite

show abstract

Multiscale and Stabilized Methods

Hughes¹,

Scovazzi²,

Franca³

2004

Encyclopedia of Computational Mechanics

128

179

View full text Add to dashboard Cite

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 wave‐propagation problems in unbounded fluid domains governed by the Helmholtz equation. This leads to the well‐known Dirichlet‐to‐Neumann formulation. A general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is then presented, which is applicable to advective–diffusive processes and other processes of physical interest. It is shown how the exact theory represents a paradigm for subgrid‐scale models and a posteriori error estimation. Hierarchical p ‐methods and bubble function methods are examined in order to understand and ultimately approximate the ‘fine‐scale Green's function’ that appears in the theory. Relationships among so‐called residual‐free bubbles, element Green's functions, and stabilized methods are exhibited. These ideas are then generalized to a class of nonsymmetric, linear evolution operators formulated in space–time. The variational multiscale method also provides guidelines and inspiration for the development of stabilized methods (e.g. SUPG, GLS, etc.) that have attracted considerable interest and have been extensively utilized in engineering and the physical sciences. An overview of stabilized methods for advective–diffusive equations is presented. A variational multiscale treatment of incompressible viscous flows, including turbulence is also described. This represents an alternative formulation of Large Eddy Simulation, which provides a simplified theoretical framework of LES with potential for improved modeling.

show abstract

Multiscale and Stabilized Methods

Hughes

Scovazzi

Franca

2004

Encyclopedia of Computational Mechanics

View full text Add to dashboard Cite

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 wave‐propagation problems in unbounded fluid domains governed by the Helmholtz equation. This leads to the well‐known Dirichlet‐to‐Neumann formulation. A general treatment of the variational multiscale method in the context of an abstract Dirichlet problem is then presented, which is applicable to advective–diffusive processes and other processes of physical interest. It is shown how the exact theory represents a paradigm for subgrid‐scale models and a posteriori error estimation. Hierarchical p ‐methods and bubble function methods are examined in order to understand and ultimately approximate the ‘fine‐scale Green's function’ that appears in the theory. Relationships among so‐called residual‐free bubbles, element Green's functions, and stabilized methods are exhibited. These ideas are then generalized to a class of nonsymmetric, linear evolution operators formulated in space–time. The variational multiscale method also provides guidelines and inspiration for the development of stabilized methods (e.g. SUPG, GLS, etc.) that have attracted considerable interest and have been extensively utilized in engineering and the physical sciences. An overview of stabilized methods for advective–diffusive equations is presented. A variational multiscale treatment of incompressible viscous flows, including turbulence is also described. This represents an alternative formulation of large eddy simulation (LES), which provides a simplified theoretical framework of LES with potential for improved modeling.

show abstract

Monitoring unresolved scales in multiscale turbulence modeling

Cited by 118 publications

References 13 publications

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Multiscale and Stabilized Methods

Multiscale and Stabilized Methods

Contact Info

Product

Resources

About