Relaxation Time and Dissipation Interaction in Hot Planet Atmospheric Flow Simulations

TL;DR

This paper investigates how the choice of relaxation times and numerical dissipation methods affect the accuracy and stability of hot exoplanet atmosphere simulations, highlighting the risks of unphysical oscillations and over-dissipation.

Contribution

It demonstrates the impact of relaxation time scales on simulation stability and accuracy, providing diagnostics for optimal parameter selection in atmospheric modeling.

Findings

Short relaxation times cause unphysical oscillations.

Excessive artificial viscosity is used to control oscillations.

Optimal diagnostics can improve simulation reliability.

Abstract

We elucidate the interplay between Newtonian thermal relaxation and numerical dissipation, of several different origins, in flow simulations of hot extrasolar planet atmospheres. Currently, a large range of Newtonian relaxation, or "cooling", times (~10 days to ~1 hour) is used among different models and within a single model over the model domain. In this study we demonstrate that a short relaxation time (much less than the planetary rotation time) leads to a large amount of unphysical, grid-scale oscillations that contaminate the flow field. These oscillations force the use of an excessive amount of artificial viscosity to quench them and prevent the simulation from "blowing up". Even if the blow-up is prevented, such simulations can be highly inaccurate because they are either severely over-dissipated or under-dissipated, and are best discarded in these cases. Other numerical stability and timestep size enhancers (e.g., Robert-Asselin filter or semi-implicit time-marching schemes) also produce similar, but less excessive, damping. We present diagnostics procedures to choose the "optimal" simulation and discuss implications of our findings for modeling hot extrasolar planet atmospheres.