This paper proposes a hierarchy of numerical fluxes for the compressible flow
equations which are kinetic-energy and pressure equilibrium preserving and
asymptotically entropy conservative, i.e., they are able to arbitrarily reduce
the numerical error on entropy production due to the spatial discretization.
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. The use of the
geometric mean is also explored and identified to be well-suited to reduce
errors on entropy evolution. Results of numerical tests confirmed the
theoretical predictions and the entropy-conserving capabilities of a selection
of schemes have been compared.Comment: 9 pages, 4 figure