Computations of Natural Convection Flow Using Hermite Stream Function Method

J. Ocean Eng. Technol. 2009;23(5):1-8.

Kim Jin-Whan

Department of Mechanical Engineering Dong-Eui University

Hermite 유동함수법에 의한 자연대류 유동 계산

김진환

동의대학교 기계공학과

Keywords: Natural convection, Divergence-free element, Vector potential, Solenoidal basis function, Irrotational basis function

핵심용어: 자연대류, 무발산 요소, 벡터 포텐셜, 회전 기저 함수, 비회전 기저 함수

Abstract

This paper is a continuation of the recent development on Hermite-based divergence free element method and deals with a non-isothermal fluid flow thru the buoyancy driven flow in a square enclosure with temperature difference across the two sides. The basis functions for the velocity field consist of the Hermite function and its curl while the basis functions for the temperature field consists of the Hermite function and its gradients. Hence, the number of degrees of freedom at a node becomes 6, which are the stream function, two velocities, the temperature and its x and y derivatives. This paper presents numerical results for Ra = 105, and compares with those from a stabilized finite element method developed by Illinca et al. (2000). The comparison has been done on 32 by 32 uniform elements and the degree of approximation of elements used for the stabilized finite element are linear (Deg. 1) and quadratic (Deg. 2). The numerical results from both methods show well agreements with those of De vahl Davi (1983).