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.

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.