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Physical Sciences › Engineering › Computational Mechanics
Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
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Conflicts of Interest
Identified Weaknesses
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Paper Summary
Paperzilla title
Chill, RK Methods Got Your Entropy Back! (But Don't Ask About Big Problems Yet)
This paper extends the framework of relaxation Runge-Kutta methods to ensure conservation or dissipation of general convex quantities, such as entropy. It enforces stability through a relaxation parameter, modifying existing Runge-Kutta implementations with minimal cost and maintaining accuracy and other desirable properties.
Possible Conflicts of Interest
None identified
Identified Weaknesses
Limited Practical Application
The study lacks practical applications to real-world scenarios. While the methods presented may be useful in other applications, their applicability needs further exploration.
Lack of Comparison
The paper doesn't offer comprehensive comparison or analysis with other existing projection schemes. Such an analysis is crucial to assess the superiority of the proposed method.
Implementation limited to smaller ODE problems
The study doesn't offer concrete implementations for larger PDE problems. The focus remains primarily on smaller ODE problems, which limits the practicality of the method.
Rating Explanation
This paper presents a novel and potentially valuable method for ensuring entropy stability in Runge-Kutta methods, applicable across various functionals and retaining key properties. The detailed analyses and proofs showcase a strong methodology. However, limitations in practical application and comparison with other schemes prevent a perfect score.
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File Information
Original Title:
Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
File Name:
1905.09129.pdf
[download]
File Size:
3.03 MB
Uploaded:
July 14, 2025 at 06:54 AM
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