Estudo dos mecanismos de troca de calor e dos efeitos da resolução numérica em simulações de convecção turbulenta - Hugo Demattos Nogueira (2020)
Convection is a heat transport mechanism observed in several instances in nature, especially on Earth’s atmosphere and on the outer third of the Sun’s radius, playing a role in matters such as climate and stellar evolution. An analytical time dependent theory capable of completely describing the properties of convection does not yet exist, and laboratory experiments allow the probing of a limited region of parameter space. Therefore, the investigation of this phenomenon with numerical simulations is paramount. There exist several issues associated with the simulation of turbulent convective systems. One of these issues regards the heat exchange mechanism. Most of the simulations of turbulent convection use a heat conduction mechanism. However, the relaxation time of these simulations is long, prompting several authors to use an artificially high value of the heat conduction coefficient. A way around this problem is to replace the heat conduction by an energy forcing-dissipation mechanism. Another issue refers to the numerical discretization of the computational domain and the integration time needed to reach the final state of the system. If the discretization is excessively fine, the code is able to capture small scale features of the flow, however, the time needed to numerically integrate the Navier-Stokes equations would be too long, precluding timely attainment of solutions. On the other hand, a very coarse descretization would miss important details of the flow and would not be useful either. On this work we present two-dimensional ILES (implicit large-eddy simulation) simulations of stratified convection using several numerical resolutions and two heat exchange mecha- nisms. Our goals are to compare both heat exchange mechanisms and study convergence of simulations for different resolutions. The forcing-dissipation mechanism reduces the relaxation time, allowing for efficient use of higher resolutions than the heat conduction. Therefore, we can study how the smallest structures resolved by high resolution simulations contribute to the general solution. We found that, while the effective viscosity decreases with the numerical resolution, from a certain resolution of approximately 512^2 grid points, some physical quantities converge to the same values and vertical profiles. Likewise, the turbulent viscosity converges assimptoticaly with the increase of grid points.