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Hyperbolic model for the classical Navier‐Stokes equations
Author(s) -
Abohadima Samir,
Guaily Amr
Publication year - 2016
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.22482
Subject(s) - mathematics , hyperbolic partial differential equation , mathematical analysis , consistency (knowledge bases) , compressibility , constitutive equation , shock (circulatory) , boundary value problem , navier–stokes equations , partial differential equation , mechanics , geometry , physics , finite element method , medicine , thermodynamics
A new formulation of the classical Navier‐Stokes equations is presented, which overcomes the equations' main disadvantage: being a mixed parabolic‐hyperbolic system. The new model is achieved by adopting the compressible codeformational time derivative in the stress‐strain constitutive relation, resulting in a consistency with the principle of material frame indifference. The main advantage of the new formulation is that the resulting system of equations is purely hyperbolic. The proposed formulation is used to model the benchmark problem of the shock/boundary layer/expansion fan interaction with an apparent degree of success.