Kinetic energy fix for low internal energy flows

Authors:
X. Y. Hu;B. C. Khoo
Affiliations:
Singapore-MIT Alliance, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore;Singapore-MIT Alliance, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore and Department of Mechanical Engineering, National University of Singapore, Singapore 1 ...
Venue:
Journal of Computational Physics
Year:
2004

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Abstract

When the kinetic energy of a flow is dominant, numerical schemes employed can encounter difficulties due to negative internal energy. A case study with several commonly used conservative schemes (MUSCL, ENO, WENO and CE/SE) shows that high order schemes may have less ability to preserve positive internal energy (MUSCL and CE/SE), or present less accurate results (WENO and ENO) when the internal energy to kinetic energy ratio is low. By analyzing the positivity property for second-order conservative schemes with large fixed CFL number conditions for time step restriction, this paper proposes the energy consistency conditions for second-order Riemann-solver type schemes and CE/SE method. According to the said energy consistency conditions, a kinetic energy fix method which limits the magnitude of kinetic energy relative to the total energy is introduced. The numerical examples show that the kinetic energy fixed CE/SE method produces reasonable results and keeps positive internal energy for flows with very low internal energy even when a vacuum occurs.