Abstract
High Peclet number, turbulent convection is a classic system with a large timescale separation between flow speeds and the thermal relaxation time. In this paper, we present a method of fast-forwarding through the long thermal relaxation of convective simulations, and we test the validity of this method. This accelerated evolution (AE) method involves measuring the dynamics of convection early in a simulation and using its characteristics to adjust the mean thermodynamic profile within the domain towards its evolved state. We study Rayleigh-B\'enard convection as a test case for AE. Evolved flow properties of AE solutions are measured to be within a few percent of solutions which are reached through standard evolution (SE) over a full thermal timescale. At the highest values of the Rayleigh number at which we compare SE and AE, we find that AE solutions require roughly an order of magnitude fewer computing hours to evolve than SE solutions.
Highlights
Astrophysical convection occurs in the presence of disparate timescales
We have studied a method of accelerated evolution (AE) which can be employed to achieve rapid thermal relaxation of convective simulations
We compared this technique to the standard evolution (SE) of convection through a full thermal diffusion timescale, and we showed that AE rapidly obtains solutions whose dynamics are statistically similar to SE solutions
Summary
Astrophysical convection occurs in the presence of disparate timescales. Studying realistic models of natural systems through direct numerical simulations is infeasible because of the large separation between various flow timescales and relaxation times. Initial value problems solved using explicit timestepping methods are bound by the Courant-Friedrich-Lewy (CFL) timestep limit corresponding to the fastest motions (sound waves), resulting in timesteps which are prohibitively small for studies of the deep, low-Ma motions. These systems are numerically stiff, and the difference between the sound crossing time and the convective overturn time has made studies of low-Ma stellar convection difficult. This stiffness can be avoided using approximations such as the anelastic approximation, in which sound waves are explicitly filtered out [1,2]. Advanced numerical techniques which use fully implicit [3,4,5] or mixed implicit-explicit [6,7,8] timestepping mechanisms have made it possible to study convection in the fully compressible equations at low Mach numbers, and careful studies of deep convection which would have been impossible a decade ago are widely accessible
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