Comparison of two approaches for implementing stream function boundary conditions in DQ simulation of natural convection in a square cavity

Abstract

In this paper, the global method of generalized differential quadrature (GDQ) is applied to simulate the natural convection in a square cavity. The vorticity-stream function equation is taken as the governing equation. There are two boundary conditions (Drichlet type and Neumann type) for the stream function at each boundary. Two approaches are introduced to implement these two boundary conditions. The first approach converts the two boundary conditions into a two-layer condition. For the second approach, the Neumann condition is built into the GDQ weighting coefficient matrices which are then used to discretize the stream function equation. Thus, the Neumann condition is exactly satisfied in the second approach. The performances of two approaches such as the accuracy and efficiency are comparatively studied in this work.