TY - JOUR
T1 - h‐adaptive finite element solution of unsteady thermally driven cavity problem
AU - Mayne, David
AU - Usmani, Asif
AU - Crapper, Martin
PY - 2001
Y1 - 2001
N2 - An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem for Rayleigh numbers at which no steady state exists (greater than 1.9 × 108). This problem is characterised by sharp thermal and flow boundary layers and highly advection dominated transport, which normally requires special algorithms, such as streamline upwinding, to achieve stable and smooth solutions. It will be shown that h‐adaptivity provides a suitable solution to both of these problems (sharp gradients and advection dominated transport). Adaptivity is also very effective in resolving the flow physics, characterised by unsteady internal waves, are calculated for three Rayleigh numbers; 2 × 108, 3 × 108 and 4 × 108 using a Prandtl number of 0.71 and results are compared with other published results.
AB - An h‐adaptive finite element code for solving coupled Navier‐Stokes and energy equations is used to solve the thermally driven cavity problem for Rayleigh numbers at which no steady state exists (greater than 1.9 × 108). This problem is characterised by sharp thermal and flow boundary layers and highly advection dominated transport, which normally requires special algorithms, such as streamline upwinding, to achieve stable and smooth solutions. It will be shown that h‐adaptivity provides a suitable solution to both of these problems (sharp gradients and advection dominated transport). Adaptivity is also very effective in resolving the flow physics, characterised by unsteady internal waves, are calculated for three Rayleigh numbers; 2 × 108, 3 × 108 and 4 × 108 using a Prandtl number of 0.71 and results are compared with other published results.
KW - Natural convection
KW - Finite element method
U2 - 10.1108/09615530110381584
DO - 10.1108/09615530110381584
M3 - Article
VL - 11
SP - 172
EP - 195
JO - International Journal of Numerical Methods for Heat and Fluid Flow
JF - International Journal of Numerical Methods for Heat and Fluid Flow
SN - 0961-5539
IS - 2
ER -