What question did this study set out to answer?

To generalize earlier mathematical frameworks to the compressible Navier-Stokes equations with heat conduction by constructing a symmetric formulation based on entropy variables.

February 1, 1986Computer Methods in Applied Mechanics and EngineeringOpen Access

A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics

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Authors

THThomas J.R. HughesÉcole Centrale de Nantes LFL.P. FrancaIBM Research - Brazil MMM. MalletDassault Aviation (France)

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Implication

Computational study demonstrates a symmetric formulation for compressible fluid equations, indicating guaranteed numerical stability through the second law of thermodynamics.

Key Points

To generalize earlier mathematical frameworks to the compressible Navier-Stokes equations with heat conduction by constructing a symmetric formulation based on entropy variables.
Extended the mathematical formulations established by Harten and Tadmor to compressible Navier-Stokes equations incorporating heat conduction.
Derived a symmetric system of governing equations using entropy variables as the primary degrees of freedom.
Evaluated the mathematical properties of finite element discretizations constructed from this symmetric formulation.
Established a symmetric formulation of the compressible Navier-Stokes equations in terms of entropy variables.
Demonstrated that finite element methods utilizing this formulation automatically fulfill the second law of thermodynamics.
Proved that numerical stability of the discrete solution is fundamentally guaranteed ab initio.

Cite This Study

Hughes et al. (1986) studied this question.

synapsesocial.com/papers/6aa3d003aaaedccdac749c86 https://doi.org/10.1016/0045-7825(86)90127-1

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Implication

Computational study demonstrates a symmetric formulation for compressible fluid equations, indicating guaranteed numerical stability through the second law of thermodynamics.

A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics

Discussion

Member takes

Implication

Key Points

Cite This Study

A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics

Discussion

Member takes

Implication

Key Points

Cite This Study

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