A Kinetic Energy Preserving and Entropy Conserving Scheme for Stable Simulation of Fluid Flow
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Author(s)
Schau, Kyle Arthur
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Abstract
This work contributes to the non-linear stability of fluid flow simulation by indirectly enforcing entropy evolution through the numerical internal energy flux. Existing numerical methods are improved and extended to a fully discrete numerical method for solving the Euler equations. The presented scheme preserves the accurate evolution of kinetic energy and is entropy conservative. The developed scheme demonstrates improved stability and accuracy over existing methods by formulating the numerical internal energy flux as a temperature weighted average. The presented scheme is extended to multicomponent simulations and demonstrates improved entropy properties over existing methods; however, numerical mixing rules prevent desired entropy conservation. Finally, a shock capturing extension of the presented scheme is designed from kinetic energy preserving and entropy stability principles. The scheme demonstrates the ability to resolve shocks and provides a novel method for prescribing entropy dissipation through the internal energy dissipation.
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2023-10-31
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Dissertation