Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 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

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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