NUMERICAL STUDY OF THE NAVIER STOKES EQUATIONS IN THREE DIMENSIONS.

Abstract

To investigate the process of energy transfer from large eddies to smaller ones at high Reynolds Numbers, a finite difference method is used to obtain the periodic solutions of the Navier-Stokes equations in three dimensions when the initial motion is assumed to be v sub 1 = cos x sin y sin z, v sub 2 = -sin x cos y sin z, v sub 3 = 0. A numerical technique for the solution of Poisson's equation for the three dimensional problem is described and used for the solution of the problem. Mean kinetic energy and mean square vorticity are calculated and it is found that the numerical method provides estimates of these quantities up to a time of the order of 2. The structure of the turbulent flow is investigated by a study of the velocity correlation function R sub ij. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1967
Accession Number
AD0666604

Entities

People

  • Padam Jain

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Energy
  • Energy Transfer
  • Equations
  • Flow
  • Kinetic Energy
  • Mathematics
  • Navier Stokes Equations
  • Reynolds Number
  • Three Dimensional
  • Turbulent Flow

Fields of Study

  • Mathematics
  • Physics

Readers

  • Analytical Mechanics
  • Fluid Dynamics.