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It has been demonstrated in the past that it is advantageous to write the set of fluid dynamic equations in Vector notationvector or Vector-matrix notationvector-matrix form. Any transformation of the coordinates (Chap. 6 ) or diagonalization of the corresponding Jacobi matrices (Chap. 14 ) can be executed in a homogeneous way. This is also true for statistical two equation turbulence models (Chap. 8 ) and for the conservation equation of species and species energy (Chap. 9 ) if the gas is in a non-equilibrium state (vibrational excitation, dissociation, ionisation). Therefore, in this and the following chapters the vector or vector-matrix representation is presented.

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The Navier-Stokes Equations in Cartesian Coordinates for Laminar and Turbulent Flow

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  • 发表日期：

    2025年

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  • Louise Elisabeth King

摘要

It has been demonstrated in the past that it is advantageous to write the set of fluid dynamic equations in Vector notationvector or Vector-matrix notationvector-matrix form. Any transformation of the coordinates (Chap. 6 ) or diagonalization of the corresponding Jacobi matrices (Chap. 14 ) can be executed in a homogeneous way. This is also true for statistical two equation turbulence models (Chap. 8 ) and for the conservation equation of species and species energy (Chap. 9 ) if the gas is in a non-equilibrium state (vibrational excitation, dissociation, ionisation). Therefore, in this and the following chapters the vector or vector-matrix representation is presented.