Change search
ReferencesLink to record
Permanent link

Direct link
A new approach to computational turbulence modeling
Courant Institute, New York University.ORCID iD: 0000-0003-4256-0463
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2006 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 195, no 23-24, 2865-2880 p.Article in journal (Refereed) Published
Abstract [en]

We present a new approach to computational fluid dynamics (CFD) using adaptive stabilized Galerkin finite element methods with duality based a posteriori error control for chosen output quantities of interest. We address the basic question of computability in CFD: For a given flow, what quantity is computable to what tolerance to what cost? We focus on incompressible Newtonian flow with medium to large Reynolds numbers involving both laminar and turbulent flow features. We estimate a posteriori the output of the computed solution with the output based on the exact solution to the Navier–Stokes equations, thus circumventing introducing and modeling Reynolds stresses in averaged Navier–Stokes equations. Our basic tool is a representation formula for the error in the quantity of interest in terms of a space–time integral of the residual of a computed solution multiplied by weights related to derivatives of the solution of an associated dual problem with data connected to the output. We use the error representation formula to derive an a posteriori error estimate combining residuals with computed dual weights, which is used for mesh adaptivity in space–time with the objective of satisfying a given error tolerance with minimal computational effort. We show in a concrete example that outputs such as a mean value in time of drag of a turbulent flow around a bluff body are computable on a PC with a tolerance of a few percent using a few hundred thousand mesh points in space. We refer to our methodology as adaptive DNS/LES, where automatically by adaptivity certain features of the flow are resolved in a direct numerical simulation (DNS), while certain other small scale turbulent features are left unresolved in a large eddy simulation (LES). The stabilization of the Galerkin method giving a weighted least square control of the residual acts as the subgrid model in the LES. The a posteriori error estimate takes into account both the error from discretization and the error from the subgrid model. We pay particular attention to the stability of the dual solution from (i) perturbations replacing the exact convection velocity by a computed velocity, and (ii) computational solution of the dual problem, which are the crucial aspects entering by avoiding using averaged Navier–Stokes equations including Reynolds stresses. A crucial observation is that the contribution from subgrid modeling in the a posteriori error estimation is small, making it possible to simulate aspects of turbulent flow without accurate modeling of Reynolds stresses.

Place, publisher, year, edition, pages
2006. Vol. 195, no 23-24, 2865-2880 p.
Keyword [en]
Adaptive DNS/LES; Adaptivity; Computability; Adaptive finite element method; A posteriori error estimate; Turbulence; Incompressible flow; DNS; LES
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-40877DOI: 10.1016/j.cma.2004.09.015ISI: 000236783800002OAI: diva2:442609
QC 20110930Available from: 2011-09-22 Created: 2011-09-22 Last updated: 2011-11-17Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Hoffman, JohanJohnson, Claes
By organisation
Numerical Analysis, NA
In the same journal
Computer Methods in Applied Mechanics and Engineering
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 31 hits
ReferencesLink to record
Permanent link

Direct link