@Article{CiCP-5-273,
author = {Tormod Bjøntegaard and Einar M. Rønquist},
title = {Simulation of Three-Dimensional Bénard-Marangoni Flows Including Deformed Surfaces},
journal = {Communications in Computational Physics},
year = {2009},
volume = {5},
number = {2-4},
pages = {273--295},
abstract = {<p style="text-align: justify;">We present a coupled thermal-fluid model for Bénard-Marangoni convection in a three-dimensional fluid layer. The governing equations are derived in detail
for two reasons: first, we do not assume a flat free surface as commonly done; and
second, we prepare for the use of flexible discretizations. The governing equations
are discretized using spectral elements in space and an operator splitting approach in
time. Since we are here primarily interested in steady state solutions, the focus is on
the spatial discretization. The overall computational approach is very attractive to use
for several reasons: (i) the solution can be expected to have a high degree of regularity,
and rapid convergence can be expected; (ii) the spectral element decomposition automatically gives a convenient parameterization of the free surface that allows powerful
results from differential geometry to easily be exploited; (iii) free surface deformation can readily be included; (iv) both normal and tangential stresses are conveniently
accounted for through a single surface integral; (v) no differentiation of the surface
tension is necessary in order to include thermocapillary effects (due to integration-by-parts twice); (vi) the geometry representation of the free surface need only be C<sup>0</sup> across
element boundaries even though curvature effects are included. Three-dimensional
simulation results are presented, including the free surface deflection due to buoyancy
and thermocapillary effects.</p>},
issn = {1991-7120},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cicp/7733.html}
}