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A non-conventional discontinuous Lagrangian for viscous flow
1Heilbronn University , Institute for Automotive Technology and Mechatronics , 74081 Heilbronn, Germany.
Royal Society Open Science
|April 8, 2017
Summary
A novel discontinuous Lagrangian formulation for the Navier-Stokes equations is introduced, enabling variational analysis and extending thermodynamic principles beyond local equilibrium for fluid dynamics. This approach addresses complex discontinuous phenomena in physics.
Area of Science:
- Fluid Dynamics
- Quantum Mechanics Analogy
- Thermodynamics
Background:
- Variational formulation of Navier-Stokes equations has been challenging.
- Existing models struggle with discontinuous fluid behaviors.
Purpose of the Study:
- To propose a new Lagrangian for variational formulation of Navier-Stokes equations.
- To extend the framework to discontinuous physical phenomena.
- To interpret fluid dynamics within thermodynamics beyond local equilibrium.
Main Methods:
- Utilizing an analogy with quantum mechanics to develop a new Lagrangian.
- Employing variational principles for discontinuous behavior.
- Applying thermodynamic frameworks beyond local equilibrium.
Main Results:
- A discontinuous Lagrangian for the Navier-Stokes equations is successfully formulated.
- The mathematical challenges of the discontinuous variational problem are resolved.
- The equations of motion are consistently interpreted within non-equilibrium thermodynamics.
Conclusions:
- The new formalism provides a unified approach to fluid dynamics and thermodynamics.
- It offers a powerful tool for analyzing discontinuous phenomena like phase boundaries and shock waves.
- This work extends Lagrange's formalism to discontinuous systems.
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