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The thermoconvective instability of plane poiseuille flow heated from below: A proposed benchmark solution for open boundary flows
Author(s) -
Evans G.,
Paolucci S.
Publication year - 1990
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.1650110707
Subject(s) - mechanics , open channel flow , instability , boussinesq approximation (buoyancy) , richardson extrapolation , flow (mathematics) , vorticity , physics , hagen–poiseuille equation , buoyancy , extrapolation , mathematics , convection , mathematical analysis , vortex , natural convection , rayleigh number
The transient two‐dimensional Navier‐Stokes and energy equations have been solved numerically for flow in a horizontal channel heated from below in the Boussinesq limit. For the set of dimensionless parameters chosen, the flow consists of periodic transverse travelling waves resulting from a convective instability. The solution is proposed as a benchmark for the application of outflow boundary conditions (OBC) in time‐dependent flows with strong buoyancy effects. Richardson extrapolation in both time and space is used in obtaining the solution. Field plots and profiles of velocity, temperature, vorticity and streamfunction at selected axial positions and times are also presented from the finest grid and smallest time step calculation. The calculations have been made on an extended domain so that the effects of OBC used in the present study would be negligible in the test region.