Insights from a pseudospectral approach to the Elder problem
File(s)
Published version
Author(s)
van Reeuwijk, M
Mathias, SA
Simmons, CT
Ward, JD
Type
Journal Article
Abstract
The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem. A pseudospectral method is used to avoid numerical error associated with spatial discretization. The pseudospectral method is verified by comparison to an analytical solution at Rayleigh number, Ra = 0, and by reproducing the three stable steady state solutions that are known to exist at Ra = 400. A bifurcation diagram for 0 < Ra < 400 which is free of discretization error, confirms that multiple steady states are indeed an intrinsic characteristic of the Elder problem. The existence of multiple steady states makes the Ra = 400 Elder problem less suitable for benchmarking numerical models. To avoid the multiple steady states, we propose a benchmark at Ra = 60. The results for this Low Rayleigh Number Elder Problem are presented and compared to simulations with the commercial groundwater modeling package FEFLOW. Correspondence between the pseudospectral model and FEFLOW is excellent.
Date Issued
2009
Citation
WATER RESOUR RES, 2009, 45, W0441
ISSN
0043-1397
Publisher
AMER GEOPHYSICAL UNION
Journal / Book Title
WATER RESOUR RES
Volume
45, W0441
Copyright Statement
Copyright 2009 by the American Geophysical Union. This is the peer reviewed version of the following article: van Reeuwijk, M., S. A. Mathias, C. T. Simmons, and J. D. Ward (2009), Insights from a pseudospectral approach to the Elder problem, Water Resour. Res., 45, W04416, which has been published in final form at http://dx.doi.org/10.1029/2008WR007421. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=000265333100001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
ARTN W04416
Publication Status
Published