On entropy stable temporal fluxes
This work provides a new perspective for improving nonlinear stability in high-order methods for computational fluid dynamics, though it is an incremental extension of existing spatial ES flux ideas to temporal discretizations.
The authors identify that entropy-stable (ES) schemes for turbulent flow simulations can be improved by tuning ES interface fluxes in the temporal direction, not just spatial, to control entropy production. They demonstrate this concept theoretically and through numerical examples.
Entropy-stable (ES) schemes have gained considerable attention over the last decade, especially in the context of turbulent flow simulations using high-order methods. While promising because of their nonlinear stability properties, ES schemes have to address a number of issues to become practical. One of them is how much entropy should be produced by the scheme at a certain level of under-resolution. This problem has been so far studied by considering different ES interfaces fluxes in the spatial discretization only because they can be tuned to generate a certain amount of entropy. In this note, we point out that, in the context of space-time discretizations, the same applies to ES interface fluxes in the temporal direction.