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

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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 examined. 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 \(100^{3}\) to \(256^{3}\) finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.

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Acknowledgements

This research was supported by Israel Science Foundation (ISF) grant No 415/18 and was enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada (www.computecanada.ca).

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  1. School of Mechanical Engineering, Faculty of Engineering, Tel-Aviv University, Ramat Aviv, 69978, Tel-Aviv, Israel

    Alexander Yu. Gelfgat

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  1. Alexander Yu. Gelfgat
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Correspondence to Alexander Yu. Gelfgat.

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Communicated by Vassilios Theofilis.

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Gelfgat, A.Y. Instability of natural convection in a laterally heated cube with perfectly conducting horizontal boundaries. Theor. Comput. Fluid Dyn. 34, 693–711 (2020). https://doi.org/10.1007/s00162-020-00541-z

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