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An analytical solution method for the unsteady, unbounded, incompressible three-dimensional Navier-Stokes equations in Cartesian coordinates using coordinate axis symmetry degeneracy

Abrecht, David G. (2011) An analytical solution method for the unsteady, unbounded, incompressible three-dimensional Navier-Stokes equations in Cartesian coordinates using coordinate axis symmetry degeneracy. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20111225-210446344

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Abstract

Analytical solutions are developed for the unsteady Navier-Stokes equations for incompressible fluids in unbounded flow systems with external, time-dependent driving pressure gradients using the degeneracy of the (1 1 1) axis to reduce the inherent non-linearity of the coupled partial differential equations, which is normally performed with boundary conditions. These solutions are then extended to all directions through rotation of the reference axis, yielding a general solution set. While the solutions are self-consistent and developed from a physical understanding of flow systems, they have not been proven unique or applied to experimental data.


Item Type:Report or Paper (Working Paper)
Additional Information:Addendum, February 17, 2012 - This document provides some additional derivations and clarifications as an extension of the discussion of the derivation of the uniaxial solution found in the last section of the article “An analytical solution method for the unsteady, unbounded, incompressible three-dimensional Navier-Stoke equations in Cartesian coordinates,” available at http://resolver.caltech.edu/CaltechAUTHORS:20111225-210446344. While this material may provide valuable additional information about the Navier-Stokes solutions, no attempt has been made to develop the contents as a stand-alone document. The information contained herein makes significant reference to the major work, and should be read in the same manner as supporting information for an article in a major journal would be.
Record Number:CaltechAUTHORS:20111225-210446344
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111225-210446344
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28596
Collection:CaltechAUTHORS
Deposited By: David Abrecht
Deposited On:03 Jan 2012 15:41
Last Modified:26 Dec 2012 14:39

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