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

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

A method of solution to solve the compressible unsteady 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 fl...

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Main Author: Terry E. Moschandreou
Format: Article
Language:English
Published: MDPI AG 2019-01-01
Series:Mathematics
Subjects:
compressible
Navier-Stokes
cylindrical
Hunter-Saxton
Geometric Algebra
Online Access:https://www.mdpi.com/2227-7390/7/2/126
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spelling doaj-ff52766bf48349e2b535c7d16a7ba59a2020-11-25T02:53:48ZengMDPI AGMathematics2227-73902019-01-017212610.3390/math7020126math7020126A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric AlgebraTerry E. Moschandreou0London International Academy, 365 Richmond Street, London, ON N6A 3C2, CanadaA method of solution to solve the compressible unsteady 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 tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force in the direction of gravity to obtain an integral form of the Hunter-Saxton equation.https://www.mdpi.com/2227-7390/7/2/126compressibleNavier-StokescylindricalHunter-SaxtonGeometric Algebra
collection DOAJ
language English
format Article
sources DOAJ
author Terry E. Moschandreou
spellingShingle Terry E. Moschandreou
A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
Mathematics
compressible
Navier-Stokes
cylindrical
Hunter-Saxton
Geometric Algebra
author_facet Terry E. Moschandreou
author_sort Terry E. Moschandreou
title A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
title_short A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
title_full A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
title_fullStr A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
title_full_unstemmed A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra
title_sort method of solving compressible navier stokes equations in cylindrical coordinates using geometric algebra
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-01-01
description A method of solution to solve the compressible unsteady 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 tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force in the direction of gravity to obtain an integral form of the Hunter-Saxton equation.
topic compressible
Navier-Stokes
cylindrical
Hunter-Saxton
Geometric Algebra
url https://www.mdpi.com/2227-7390/7/2/126
work_keys_str_mv AT terryemoschandreou amethodofsolvingcompressiblenavierstokesequationsincylindricalcoordinatesusinggeometricalgebra
AT terryemoschandreou methodofsolvingcompressiblenavierstokesequationsincylindricalcoordinatesusinggeometricalgebra
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