Thermal convection simulation in three dimensions by a modified finite element method

Conference · Tue Jul 21 04:00:00 EDT 1981

OSTI ID:6125030

Upson, C D; Gresho, P M; Sani, R L; Chan, S T; Lee, R L

In the effort to model the advection and dispersion of pollutants in the planetary boundary layer over complex terrain, a relatively simple computer code was developed for solving the three-dimensional Navier-Stokes equations, or variants thereof. The program, which began as an implementation of the Galerkin Finite Element Methoda (GFEM), now incorporates some of the insights and experiences of the finite difference community and has become an eclectic approach to simulating the motion of fluids governed by these equations. In this study, the computer code was applied to the simulation of a Boussinesq fluid contained in a three-dimensional rectangular box which is heated below and cooled above. The temperature difference between these two isothermal surfaces (parameterized by the Rayleigh number, Ra) determines, to a large extent, the complex spatial and temporal thermoconvection patterns. Problems of this sort have received substantial attention recently due to their relevance to natural convection in solar energy collectors, crystal growth in liquids, radioactive waste storage, and more importantly because studying systems of this sort can provide insight into the onset of phase-chaotic-induced turbulence. Presented in the final section are numerical simulations of the two flow configurations observed experimentally, the three and two-roll cell patterns. These results are, to the best of our knowledge, the first calculations of truly time-dependent three-dimensional confined Benard convection at elevated Rayleigh numbers, and they appear to agree well with experiments.

• Research Organization: Lawrence Livermore National Lab., CA (USA)
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 6125030
• Report Number(s): UCRL-85555; CONF-810935-1; ON: DE81028847
• Country of Publication: United States
• Language: English

Related Subjects

500100* -- Environment
Atmospheric-- Basic Studies-- (-1989)
54 ENVIRONMENTAL SCIENCES
AIR POLLUTION
BOUNDARY LAYERS
COMPUTER CODES
CONVECTION
DIFFERENTIAL EQUATIONS
ENVIRONMENTAL TRANSPORT
EQUATIONS
FINITE ELEMENT METHOD
FLUID FLOW
LAYERS
MASS TRANSFER
MATHEMATICAL MODELS
NATURAL CONVECTION
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POLLUTION
TEMPERATURE EFFECTS
TURBULENCE
TURBULENT FLOW
VELOCITY