A MIXED DISCRETE FOURIER TRANSFORM-FINITE DIFFERENCE ALGORITHM FOR THE SOLUTION OF THE NAVIER-STOKES EQUATIONS

ANDREA RINALDO, Purdue University

Abstract

A mixed Discrete Fourier Transform-Finite Difference algorithm for the solution of the Navier-Stokes equations has been presented. The objective of the work is the calculation of the scalar and vectorial fields for the time dependent two dimensional viscous flow past a circular cylinder of infinite width for a variety of flow conditions. The computational procedure makes use of fast numerical methods for the evaluation of the nonlinear convolution sums which portray the convective terms of the ruling equations in Fourier space. The finite difference schemes implemented are in the overall third order accurate. Time integration has been chosen as fourth order accurate, according to a suitable Runge-Kutta scheme, because of accuracy-stability requirements of the procedure proposed. The calculated time dependent fields have been compared with theoretical, experimental and numerical results in analogous conditions from the extensive related literature. The accuracy of the results and limits and validity of the proposed approach are discussed. Some new phenomena indicated in the flow patterns are revealed, and several different regimes are studied by detailed analyses of the evolution of flow characteristics. A correlation with experimental and numerical results is established for Reynolds number regimes ranging from 20 to 9500.

Degree

Ph.D.

Subject Area

Mechanical engineering

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