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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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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