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Article

A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra

This version is not peer-reviewed.

Submitted:

05 December 2018

Posted:

06 December 2018

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Abstract
A method of solution to solve the compressible 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. It is concluded that the total divergence of the flow can be expressed as the integral with respect to time of the line integral of the dot product of inertial and azimuthal velocity. The line integral is evaluated on a contour that is annular and traces the boundary layer as time increases in the flow. Finally it's explicit dependence on the gradient of a density function and Laplacian of pressure is shown with complete dependence on the vorticity and it's rate of change for a flow associated with the Navier Stokes equations.
Keywords: 
cylindrical; geometric algebra; boundary layer; compressible flow; Hunter-Saxton
Subject: 
Computer Science and Mathematics  -   Applied Mathematics
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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