Title: Natural convection for anomalous density variation of water: numerical benchmark

Authors: T. Michalek, T.A. Kowalewski, B. Sarler

Addresses: Department of Mechanics and Physics of Fluids, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw 00-049, Swietokrzyska 21, Poland. ' Department of Mechanics and Physics of Fluids, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw 00-049, Swietokrzyska 21, Poland. ' Nova Gorica Polytechnic, Laboratory for Multiphase Processes, SI-5000 Nova Gorica, Vipavska 13, Slovenia

Abstract: A steady-state natural convection in a differentially heated cavity for temperatures in a vicinity of the freezing point is used to investigate and compare performance of four different numerical methods: finite differences, finite volume, finite elements and mesh-free diffuse approximation method. A primary aim of the exercise is to define a new numerical benchmark solution for natural convection problems, which includes challenging configuration of strongly non-linear buoyancy term. This configuration is used to test the performance of two popular commercial codes (Fluent and Fidap) and to compare them with two ||classical|| finite difference codes and the new promising mesh-free implementation.

Keywords: numerical simulation; numerical benchmarks; mesh-free methods; natural convection; density variation; water; finite difference method; finite volume method; finite element method; FEM; mesh-free diffuse approximation method; heat transfer; freezing point.

DOI: 10.1504/PCFD.2005.006751

Progress in Computational Fluid Dynamics, An International Journal, 2005 Vol.5 No.3/4/5, pp.158 - 170

Published online: 05 Apr 2005 *

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