Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session A13: Compressible Flows: General
8:00 AM–9:31 AM,
Sunday, November 19, 2023
Room: 143C
Chair: Kenneth Granlund, North Carolina State University
Abstract: A13.00002 : Asymptotically entropy conservative and kinetic-energy and pressure-equilibrium preserving schemes based on economical algebraic fluxes
8:13 AM–8:26 AM
Presenter:
Gennaro Coppola
(Università di Napoli 'Federico II')
Authors:
Gennaro Coppola
(Università di Napoli 'Federico II')
Carlo De Michele
(Università di Napoli 'Federico II')
Existing KEP, PEP and EC schemes require the specification of nonlinear fluxes involving the evaluation of costly transcendental functions, which are more expensive than the classical algebraic fluxes associated with FD formulations. In this contribution, we propose a hierarchy of numerical fluxes for the compressible flow equations which are KEP, PEP and Asymptotically Entropy Conservative, i.e., they are able to arbitrarily reduce the numerical error on entropy production due to the spatial discretization. The main feature is that the fluxes are based on the use of the harmonic mean for internal energy and only use algebraic operations, making them less computationally expensive than the entropy-conserving fluxes based on the logarithmic mean. Numerical tests on benchmark 1D problems as well as on turbulent flows confirm the theoretical predictions and the favorable properties in terms of robustness and low computational cost of the proposed schemes.
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