Arman Khoubani, Jan-Bert Flor and I will present our numerical work on instabilities in vertical convection in a 2D rectangular cavity at the workshop Convection naturelle : aspects fondamentaux et applications .

My slides are available here .

We plan to divide the presentation in two short talks:

# Prandtl and aspect ratio effects in vertical convection in a 2D rectangular cavity ¶

## Abstract ¶

In this presentation we consider numerical stability results on the motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity. In particular the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O( \(10^8\) ) is considered [1]. This flow consists of two plume motions near the boundaries and a linear stable temperature stratification in the interior. As a function of the Prandtl number, \(Pr\) , and the height-to-width aspect ratio of the domain, \(A\) , the base flow of each case is computed and linear simulations are used to obtain the properties of the leading linear mode of the instability.

The flow regimes show a rich variation with Prandtl number and aspect ratio. These regimes depend on whether the plumes generate a circulation in the entire cavity, detach from the horizontal boundaries or the corner regions, and further on whether the oscillation frequency of the instability is slower (or faster) than the buoyancy frequency of the stratification in the interior, and allows for the presence of internal waves (or not), Accordingly, the regime is called slow or fast, respectively. Internal wave allow for the coupling between the top and bottom plumes, and their absence implies asymmetry in part of the regimes.

Six essentially different flow regimes are found in the range of \(0.1 \leq Pr \leq 4\) and \(0.5 \leq A \leq 2\) . For small \(Pr \leq 0.4 \) the plume thickness is large and the base flow is driven by a large circulation in the entire cavity. The aspect ratio has an effect on the cell patterns, the plume detachment, and the oscillation frequency of the instability, which is slow for wide cavities and fast for tall cavities. For large \(Pr \geq 0.7\) the wall plumes are thin and the instability is driven by the motion at the wall and the detached plume. A transition between these regimes is marked by a dramatic change in oscillation frequency at \(Pr = 0.55\) .

# Numerical simulations of natural convection flows with Snek5000 and Fluidsimfoam ¶

## Authors ¶

Pierre Augier, Ashwin Vishnu Mohanan, Arman Khoubani, Pooria Danaeifar and Jan-Bert Flor

## Abstract ¶

We will present two twin projects, Snek5000 and Fluidsimfoam, designed to improve the user experience of the very popular CFD codes Nek5000 and OpenFOAM, respectively. These packages builds upon the functionality of Nek5000 and OpenFOAM by providing a user-friendly interface for launching and restarting simulations, loading simulation data, and generating figures and movies. Snek5000 and Fluidsimfoam are based on the CFD framework FluidSim, which introduces the concept of “FluidSim solvers”. A FluidSim solver consists of few files describing a set of potential and similar simulations. A concrete simulation can be created and run via a simple and generic Python API. We will show how these tools can be used to study different types of natural convection problems. We will see how Snek5000 helped us greatly for a recent study on linear instabilities in vertical convection.