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

Author

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  • Terry E. Moschandreou

    (London International Academy, 365 Richmond Street, London, ON N6A 3C2, Canada
    Department of Applied Mathematics, Faculty of Science, Western University, London, ON N6A 5C1, Canada)

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.

Suggested Citation

  • Terry E. Moschandreou, 2019. "A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra," Mathematics, MDPI, vol. 7(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:126-:d:201166
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