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Journal ArticleDOI

A proposed modification of the Germano subgrid‐scale closure method

01 Mar 1992-Physics of Fluids (American Institute of Physics)-Vol. 4, Iss: 3, pp 633-635
TL;DR: In this paper, the subgrid-scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses.
Abstract: The subgrid‐scale closure method developed by Germano et al. is modified by use of a least squares technique to minimize the difference between the closure assumption and the resolved stresses. This modification removes a source of singularity and is believed to improve the method’s applicability.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a subgrid scale model is proposed for large eddy simulations in complex geometries, which accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations.
Abstract: A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y 3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

2,855 citations

Journal ArticleDOI
TL;DR: In this paper, a second-order accurate, highly efficient method is developed for simulating unsteady three-dimensional incompressible flows in complex geometries, which is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid.

1,643 citations

Journal ArticleDOI
TL;DR: In this article, a method for generating three-dimensional, time-dependent turbulent inflow data for simulations of complex spatially developing boundary layers is described, which is essentially a variant of the Spalart method, optimized so that an existing inflow?outflow code can be converted to an inflow-generation device through the addition of one simple subroutine.

1,462 citations

Journal ArticleDOI
TL;DR: In this article, a review of scale-invariance properties of high-Reynolds-number turbulence in the inertial range is presented, focusing on dynamic and similarity subgrid models and evaluating how well these models reproduce the true impact of the small scales on large scale physics and how they perform in numerical simulations.
Abstract: ▪ Abstract Relationships between small and large scales of motion in turbulent flows are of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-number turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on evaluating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Various criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simulation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compressible, and reacting flows are also mentioned. Other recent modeling approaches are briefly introduced.

1,395 citations

Book
01 Jan 2015
TL;DR: This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and code parallelization.
Abstract: Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques Will provide you with the knowledge required to develop and understand modern flow simulation codes Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

1,228 citations

References
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Journal ArticleDOI
TL;DR: In this article, an extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation, and the solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically.
Abstract: An extended period numerical integration of a baroclinic primitive equation model has been made for the simulation and the study of the dynamics of the atmosphere's general circulation. The solution corresponding to external gravitational propagation is filtered by requiring the vertically integrated divergence to vanish identically. The vertical structure permits as dependent variables the horizontal wind at two internal levels and a single temperature, with the static stability entering as a parameter. The incoming radiation is a function of latitude only corresponding to the annual mean, and the outgoing radiation is taken to be a function of the local temperature. With the requirement for thermal equilibrium, the domain mean temperature is specified as a parameter. The role of condensation is taken into account only as it effectively reduces the static stability. All other external sources and sinks of heat are assumed to balance each other locally, and are thus omitted. The kinematics are th...

12,952 citations

Journal ArticleDOI
TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

6,747 citations

Journal ArticleDOI
TL;DR: In this article, the three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers.
Abstract: The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

1,868 citations

Journal ArticleDOI
TL;DR: Germano et al. as discussed by the authors generalized the dynamic subgrid-scale (SGS) model for the large eddy simulation (LES) of compressible flows and transport of a scalar.
Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

1,588 citations

DOI
01 Jan 1966
TL;DR: In this paper, it was shown that an eddy diffusion hypothesis for use in numerical solutions of turbulent flow problems is consistent with the existence of an inertial subrange at the smallest resolvable scale of the numerical model.
Abstract: It is shown that an eddy diffusion hypothesis suggested by Smagorinsky for use in numerical solutions of turbulent flow problems is consistent with the existence of an inertial subrange at the smallest resolvable scale of the numerical model. The arbitrary constant, assumed by Smagorinsky to be of order unity, is shown to be a unique function of the constant of the Kolmogoroff energy spectrum function. An alternative hypothesis, involving an explicit turbulent intensity, is introduced as a possible improvement for flows with large space and time variations of turbulent stress. On the Application of the Eddy Viscosity Concept in the Inertial Sub-range of Turbulence Despite persistent efforts by fluid dynamicists and mathematicians the problem of obtaining useful analytic solutions of turbulent flow equations remains formidable. By comparison to the slow progress of analytic theory, the development of digital computers continues to proceed at a rapid pace. Thus the "brute force" methods of solution of fluid dynamics problems become more attractive, in spite of the difficulty of obtaining generalized results and the many annoying, purely numerical difficulties, Numerical methods have become virtually indispensible for solutions of non-linear two-dimensional or quasitwo-dimensional problems, such as occur in large-scale atmospheric and oceanic dynamics. Fully turbulent three-dimensional initialboundary value flow problems are now just beginning to be approachable for computer solutions. It is still totally inconceivable that a computer could resolve both the energy containing and dissipative scales in a high Reynolds number regime, but it is not at all unlikely that the limits of resolution could extend from the largest energy containing scale into the inertial sub-range. It is the purpose of this paper to describe and rationalize methods of simulating the turbulent energy exchange between the scales of motion explicitly computed and the dissipation scale, through an assumed idealized inertial sub-range. The methods are not entirely new, having been used previously, although somewhat inappropriately in two-dimensional computations, by Smagorinsky (1963, 1965) and 2 Lilly (1962). It is e not intended to present a complete theory, but only to partly rationalize some methods or recipes which have already been found moderately successful, but are believed to be most valid in computational models only now becomging accessible. For purposes of simplification we consider incompressible flow of a fluid of constant density. The continuous Eulerian equations of fluid motion and the continuity equation, in standard tensor subscript notation , are written as follows: -; •. ;• @( d ' -O (1)

341 citations