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Parallel adaptive solution of coupled Rayleigh–Bénard–Marangoni problems with the Navier‐slip
Author(s) -
Peterson J. W.,
Carey G. F.
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2264
Subject(s) - marangoni effect , mechanics , slip (aerodynamics) , surface tension , buoyancy , nonlinear system , free surface , boundary value problem , materials science , physics , geometry , convection , mathematics , thermodynamics , mathematical analysis , quantum mechanics
This study deals with modeling certain nonlinear interactions that give rise to cellular flow in heated thin fluid layers with thermocapillary surface‐tension at the free surface. Of particular interest in these Rayleigh–Bénard–Marangoni (RBM) studies is the effect of varying roughness (stick and slip) on the base or sides of the fluid container. This stick‐slip behavior at container boundaries and thermocapillary shear stress at the free surface may lead to strongly varying local gradients in the solution that are addressed here using local adaptive mesh refinement. In turn, these local effects influence the global structure of cell patterns resulting from competing buoyancy, surface‐tension and stick‐slip effects. This behavior is illustrated by the results of numerical simulations of cellular flow structure in containers of varying aspect ratio and with spatially varying base boundary treatments. Details of the Navier‐slip approximation and the adaptive mesh refinement strategy are given, together with a brief description of the relevant features of the parallel adaptive software framework, LibMesh , and associated algorithms employed in the present simulations. Copyright © 2010 John Wiley & Sons, Ltd.