Application of a Spectral Finite Difference Scheme to a Complex Configuration

点击翻译按钮获取中文摘要

In the current spectral finite difference scheme, dependent variables are assumed to be expressed in a complete spectral expansion ( in one spatial component ) such as Fourier expansion and Dini expansion, which leads to a system of simultaneous partial differential equations in space normal to the direction(s) of expansion and in time. As a result, no error is introduced in decomposing the original partial differential equations in spatial components, so that the scheme possesses better resolution in space and high computation speed in nature at least for natural convection / forced convection / non-Newtonian fluid flow in a simply-connected region or over a doubly-connected region expressed in terms of a simple analytic function. Under the current project, proposed is introduction of a functional which maps the boundary to a circle in case of a simply-connected region. For several complex configurations, e.g. a semi-infinite rectangular cavity, a Cassini cavity, and a non-circular deformed cavity, a concrete mapping analytic function is determined and found to get to a steady-state solution under laminar natural convection for various combinations of parameters such as a Grashof number, a Prandtl number, and an elatic number (for a viscoelastic fluid).