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ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554
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STUDY OF NATURAL CONVECTION WITH A STABILIZED FINITE ELEMENT FORMULATION
ABSTRAKT
In this work we study two cases of natural convection using a second-order finite element formulation stabilized by local time-steps. The pressure, velocity, and temperature fields are determined from procedures that use the mass conservation law, the Navier-Stokes equations, and the convection-diffusion energy equation, employing a second-order scheme. A Taylor-Galerkin methodology is first applied to determine the pressure field at each time step, in a process that combines the continuity equation and the Navier-Stokes equations. Once the pressure field has been determined, the velocity and temperature fields are solved by another second-order time-accurate procedure on momentum and energy equations. A least-squares minimization procedure from the previous residuals leads to a set of discretized equations for temperature and velocity fields. The finite element method is naturally stabilized by the process, where local time-steps, chosen according to the time scales of convection-diffusion of momentum and energy, play the role of stabilization parameters. Results are given for quasi-incompressible viscous flows and heat transfer for transient and steady states for two-dimensional free convection in a square cavity and from a hot horizontal cylinder utilizing the described method. Numerical investigations were carried out for the Rayleigh number range 104 ≤ Ra ≤ 108. Excellent agreement with previously published experimental and computational results has been obtained.
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