The Connection Between Upwind Dissipation, Entropy Production, Velocity-Space Resolution and Steady-States of Turbulence in GYRO Simulations

The connection between dissipation and steady states of turbulence in gyrokinetic simulations has been discussed by Krommes [1] who argued that nondissipative simulations cannot achieve a true turbulent steady state. The issue was revisited in the context of Eulerian simulations by Watanabe [2], providing a clear and precise confirmation of Krommes' analysis. In this presentation we show how the upwind advection schemes used in GYRO [3] provide the dissipation required for the achievement of steady states of turbulence. These steady states are grid-converged not only with respect to transport coefficients but also with respect to entropy. We put to rest the commonplace but ill-founded notions that Eulerian simulations (a) require velocity-space dissipation and (b) miss important velocity-space structure.\par \vspace{0.5em} \noindent [1]~J.A.\ Krommes and G.~Hu, Phys.\ Plasmas ${\bf 1}$, 3211 (1994).\par \noindent [2]~T.-H.\ Watanabe and H.~Sugama, Proc.\ of 20th IAEA Fusion Energy Conf., Vilamoura, 2004, Paper TH/8-3Rb.\par \noindent [3]~J.~Candy and R.E.\ Waltz, J.~Comput.\ Phys.\ ${\bf 186}$, 545 (2003).