Thermal hydraulic analysis by skew upwind finite element method.

Abstract

In multi-dimensional thermal hydraulic analysis, when flow is oblique to computational grid lines, false or numerical diffusion is generated by the upwind difference scheme which is almost essential at high-Peclet-number flow. This diffusion causes a large computational error, especially in the pure upwind difference scheme; therefore, some measures have been devised to improve the finite difference method. Also in the finite element method, the Streamline Upwind/Petrov-Galerkin method, and equivalent to this, the Balancing Dissipation method have been used to remedy the above problem. In this paper, however, it is shown that these finite element methods often provide numerical solutions with over-and undershoot or with spatial oscillation, which are caused by indirect 'upwinding'. As a replacement of these methods, a straightforward 'upwinding' in the finite element method is introduced in this study. The present method provides numerical solutions without causing the above problem, and is applicable to a wide range of the Peclet number.