Computation of Complex Fluid Flows Using Adaptive Grid Method

This paper continues the efforts of multiple one-dimensional procedures in developing and assessing the ideas of adaptive grid computation. The focus points here are the issue of numerical stability induced by the grid distribution and the accuracy comparison with previously reported work. Two two-dimensional problems with complicated characteristics - namely, flow in a channel with a sudden expansion and natural convection in an enclosed square cavity - are used to demonstrate some salient features of the adaptive grid method. For the channel flow, by appropriate distribution of the grid points the numerical algorithm can more effectively dampen out the instabilities, especially those related to artificial boundary treatments, and hence can converge to a steady-state solution more rapidly. For the problem of natural convection, a combination of a multiple one-dimensional adaptive procedure and a variational formulation is found very useful. Comparisons of the solutions on uniform and adaptive grid computation can play in resolving complicated flow characteristics