Analysis of Model Variance for Ensemble Based Turbulence Modeling

Jiang, Nan
Kaya Merdan, Songül
Layton, William
This report develops an ensemble or statistical eddy viscosity model. The model is parameterized by an ensemble of solutions of an ensemble-Leray regularization. The combined approach of ensemble time stepping and ensemble eddy viscosity modeling allows direct parametrization of the turbulent viscosity co-efficient. We prove unconditional stability and that the model's solution approaches statistical equilibrium as t -> infinity; the model's variance converges to zero as t -> infinity. The ensemble method is used to interrogate a rotating flow, testing its predictability by computing effiective averaged Lyapunov exponents.


An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows
Demir, Medine (Elsevier BV, 2020-10-01)
This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, includin...
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Yilmaz, Yidiz E.; Akkaya, Ayşen (Elsevier BV, 2008-07-01)
We consider one-way classification model in experimental design when the errors have generalized secant hyperbolic distribution. We obtain efficient and robust estimators for block effects by using the modified maximum likelihood estimation (MML) methodology. A test statistic analogous to the normal-theory F statistic is defined to test block effects. We also define a test statistic for testing linear contrasts. It is shown that test statistics based on MML estimators are efficient and robust. The methodolo...
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Taşeli, Hasan (Elsevier BV, 2004-03-01)
The eigenvalues of singular Sturm-Liouville problems defined over the semi-infinite positive real axis are examined on a truncated interval 0<x<l as functions of the boundary point l. As a basic theoretical result, it is shown that the eigenvalues of the truncated interval problems satisfying Dirichlet and Neumann boundary conditions provide, respectively, upper and lower bounds to the eigenvalues of the original problem. Moreover, the unperturbed system in a perturbation problem, where l remains sufficient...
On the smoothness of solutions of impulsive autonomous systems
Akhmet, Marat (Elsevier BV, 2005-01-01)
The aim of this paper is to investigate dependence of solutions on parameters for nonlinear autonomous impulsive differential equations. We will specify what continuous, differentiable and analytic dependence of solutions on parameters is, define higher order derivatives of solutions with respect to parameters and determine conditions for existence of such derivatives. The theorem of analytic dependence of solutions on parameters is proved.
Modeling of dislocation-grain boundary interactions in a strain gradient crystal plasticity framework
ÖZDEMİR, İZZET; Yalçınkaya, Tuncay (Springer Science and Business Media LLC, 2014-08-01)
This paper focuses on the continuum scale modeling of dislocation-grain boundary interactions and enriches a particular strain gradient crystal plasticity formulation (convex counter-part of Yal double dagger inkaya et al., J Mech Phys Solids 59:1-17, 2011; Int J Solids Struct 49:2625-2636, 2012) by incorporating explicitly the effect of grain boundaries on the plastic slip evolution. Within the framework of continuum thermodynamics, a consistent extension of the model is presented and a potential type non-...
Citation Formats
N. Jiang, S. Kaya Merdan, and W. Layton, “Analysis of Model Variance for Ensemble Based Turbulence Modeling,” COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, pp. 173–188, 2015, Accessed: 00, 2020. [Online]. Available: