# Instability of natural convection in a laterally heated cube with perfectly conducting horizontal boundaries

## TL;DR

This paper investigates the oscillatory instability in buoyancy-driven convection within a laterally heated cube with perfect horizontal boundaries, using advanced numerical methods to analyze the onset and underlying process.

## Contribution

It introduces a novel Krylov-subspace-iteration approach combined with SIMPLE iteration for analyzing stability in convection problems with complex boundary conditions.

## Key findings

- Identified the self-sustaining oscillatory process causing instability
- Analyzed the effect of spanwise boundaries on instability onset
- Refined finite volume grid improves accuracy of results

## Abstract

Oscillatory instability of buoyancy convection in a laterally heated cube with perfectly thermally conducting horizontal boundaries is studied. The effect of the spanwise boundaries on the oscillatory instability onset is studied. The problem is treated by Krylov-subspace-iteration based Newton and Arnoldi methods. The Krylov basis vectors are calculated by a novel approach that involves the SIMPLE iteration and a projection onto a space of functions satisfying all linearized and homogeneous boundary conditions. The finite volume grid is gradually refined from 1003 to 2563 finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.

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Source: https://tomesphere.com/paper/1905.11601