A finite element analysis for a thermal convection problem with the infinite Prandtl number
نویسندگان
چکیده
منابع مشابه
Effects of vertical boundaries on infinite Prandtl number thermal convection
The physics of thermomechanical coupling of the continental lithosphere and its surrounding mantle is studied using a simple hydrodynamic model in which a fluid is heated from below and is bounded by rigid side walls. Rayleigh numbers up to 10 are considered. A series of finite-element stability analyses is employed to characterize systematically the nature of convective instability in such a s...
متن کاملInvestigations into the applicability of adaptive finite element methods to twodimensional infinite Prandtl number thermal and thermochemical convection
[1] An adaptive finite element procedure is presented for improving the quality of solutions to convectiondominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error e...
متن کاملBifurcation of Infinite Prandtl Number Rotating Convection
We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...
متن کاملLogarithmic bounds for infinite Prandtl number rotating convection
Convection refers to fluid motion that is induced by buoyancy. In thermal convection buoyancy is due to temperature differences and one of the interesting questions is how much of the total heat transfer is due to convection. The natural measure of this quantity is the Nusselt number, N , and many experiments and numerical simulations have been performed to discern the relationship between N an...
متن کاملInfinite Prandtl Number Limit of Rayleigh-Bénard Convection
We rigorously justify the infinite Prandtl number model of convection as the limit of the Boussinesq approximation to the Rayleigh-Bénard convection as the Prandtl number approaches infinity. This is a singular limit problem involving an initial layer.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hiroshima Mathematical Journal
سال: 1998
ISSN: 0018-2079
DOI: 10.32917/hmj/1206126684