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Internal Variables as a Tool for Extending Navier-Stokes Equations

  • Arkadi Berezovski EMAIL logo
Published/Copyright: April 5, 2022

Abstract

The formalism of the internal variable theory is applied to extend Navier-Stokes equations. The internal variable theory provides a thermodynamically consistent derivation of constitutive relations and equations of motion without a priori specifying the nature of internal variables. Both single and dual internal variables cases are thoroughly examined. The similarities and differences of the approaches are emphasized. In the single internal variable framework, the elimination of the internal variable results in Maxwell-type constitutive relations and hyperbolic equations of motion. The dual internal variable technique enables us to create even more sophisticated fluid flow models with coupled equations for fluid motion and internal variable evolution.

Funding source: Eesti Teadusagentuur

Award Identifier / Grant number: RPG1227

Award Identifier / Grant number: CZ.02.1.01/0.0/0.0/15_003/0000493

Funding statement: The work was supported by the Estonian Research Council under Research Project RPG1227 and by the Centre of Excellence for Nonlinear Dynamic Behaviour of Advanced Materials in Engineering CZ.02.1.01/0.0/0.0/15_003/0000493 (European Regional Development Fund) (Excellent Research Teams) in the framework of Operational Programme Research, Development and Education within institutional support Rijksdienst voor Ondernemend Nederland: 61388998.

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Received: 2021-11-25
Revised: 2022-01-31
Accepted: 2022-02-17
Published Online: 2022-04-05
Published in Print: 2022-07-31

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