Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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

Version 1 : Received: 5 December 2018 / Approved: 6 December 2018 / Online: 6 December 2018 (08:57:24 CET)
Version 2 : Received: 27 December 2018 / Approved: 28 December 2018 / Online: 28 December 2018 (04:53:26 CET)

A peer-reviewed article of this Preprint also exists.

Moschandreou, T.E. A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra. Mathematics 2019, 7, 126. Moschandreou, T.E. A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra. Mathematics 2019, 7, 126.

Journal reference: Mathematics 2019, 7, 126
DOI: 10.3390/math7020126

## 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 boundary layer of 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 directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

## Keywords

cylindrical; geometric algebra; boundary layer; compressible flow; Hunter-Saxton

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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