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Mathematics 2019, 7(2), 126; https://doi.org/10.3390/math7020126

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

1
London International Academy, 365 Richmond Street, London, ON N6A 3C2, Canada
2
Department of Applied Mathematics, Faculty of Science, Western University, London, ON N6A 5C1, Canada
Received: 5 December 2018 / Revised: 18 January 2019 / Accepted: 23 January 2019 / Published: 27 January 2019
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Abstract

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. View Full-Text
Keywords: compressible; Navier-Stokes; cylindrical; Hunter-Saxton; Geometric Algebra compressible; Navier-Stokes; cylindrical; Hunter-Saxton; Geometric Algebra
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Moschandreou, T.E. A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra. Mathematics 2019, 7, 126.

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