Theoretical and Computational Aspects of Turbulence

Abstract

The computation of turbulent flows necessitate a better understanding of turbulence and the development of algorithms and computational tools which are well adapted to the handling of large numbers of data. Turbulent flows are due to the superposition of a range of small and large eddies which interact and the study of their interaction is an important part of understanding turbulence. An inertial manifold is an exact (quasi-static) interaction law between small and large eddies. In relation with the concept of approximate inertial manifolds (AIM), Foias-Manley-Temam have shown the existence of a simple finite- dimensional manifold lying close to the attractor. By projecting the Navier- Stokes equations on this manifold we obtain a new numerical algorithm called the Nonlinear Galerkin Method. This algorithm is well-adapted to the large time solution of the Navier-Stokes equations and this has been broadly confirmed by the numerical tests which has been performed during this contract. After further tests and studies, this algorithm will soon be available for industrial implementations. (jhd)

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Document Details

Document Type
Technical Report
Publication Date
Feb 27, 1990
Accession Number
ADA221795

Entities

People

  • Ciprian I. Foias
  • Roger Temam

Organizations

  • Indiana University Bloomington

Tags

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Algorithms
  • Applied Mathematics
  • Availability
  • Classification
  • Computational Fluid Dynamics
  • Differential Equations
  • Eigenvectors
  • Equations
  • Flow
  • Fourier Series
  • Galerkin Method
  • Mathematics
  • Navier Stokes Equations
  • Security
  • Turbulent Flow

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Linear Algebra