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Fluids 2017, 2(1), 11; doi:10.3390/fluids2010011

The Elder Problem

1
Emeritus Professor, University of Manchester, Manchester M13 9PL, UK (Retired)
2
National Centre for Groundwater Research and Training, Flinders University, GPO Box 2100, Adelaide, SA 5001, Australia
3
DHI WASY GmbH, 12489 Berlin, Germany
4
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05 Bratislava, Slovakia
5
Department of Applied Geosciences, German University of Technology in Oman (GUtech), P.O. Box 1816, Athaibah, 130 Muscat, Oman
6
Uni Research Computing, Center for Big Data Analysis, University Research AS, 5008 Bergen, Norway
*
Author to whom correspondence should be addressed.
Academic Editors: D. Andrew S. Rees and Antonio Barletta
Received: 12 February 2017 / Revised: 14 March 2017 / Accepted: 14 March 2017 / Published: 21 March 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
View Full-Text   |   Download PDF [5804 KB, uploaded 21 March 2017]   |  

Abstract

This paper presents an autobiographical and biographical historical account of the genesis, evolution and resolution of the Elder Problem. It begins with John W. Elder and his autobiographical story leading to his groundbreaking work on natural convection at Cambridge in the 1960’s. His seminal work published in the Journal of Fluid Mechanics in 1967 became the basis for the modern benchmark of variable density flow simulators that we know today as “The Elder Problem”. There have been well known and major challenges with the Elder Problem model benchmark—notably the multiple solutions that were ultimately uncovered using different numerical models. Most recently, it has been shown that the multiple solutions are indeed physically realistic bifurcation solutions to the Elder Problem and not numerically spurious artefacts. The quandary of the Elder Problem has now been solved—a major scientific breakthrough for fluid mechanics and for numerical modelling. This paper—records, reflections, reminiscences, stories and anecdotes—is an historical autobiographical and biographical memoir. It is the personal story of the Elder Problem told by some of the key scientists who established and solved the Elder Problem. 2017 marks the 50 year anniversary of the classical work by John W. Elder published in Journal of Fluid Mechanics in 1967. This set the stage for this scientific story over some five decades. This paper is a celebration and commemoration of the life and times of John W. Elder, the problem named in his honour, and some of the key scientists who worked on, and ultimately solved, it. View Full-Text
Keywords: Elder Problem; John W. Elder; free convection; natural convection; variable density flow; modelling; simulation; history of fluid mechanics; autobiography; memoir Elder Problem; John W. Elder; free convection; natural convection; variable density flow; modelling; simulation; history of fluid mechanics; autobiography; memoir
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Elder, J.W.; Simmons, C.T.; Diersch, H.-J.; Frolkovič, P.; Holzbecher, E.; Johannsen, K. The Elder Problem. Fluids 2017, 2, 11.

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