Tatsuro Yashiki

Three-dimensional finite element adaptive analysis of incompressible flow based on control of node density distribution and a posteriori error estimation

Abstract In finite element analysis, it is not economical to use a uniformly fine mesh in the whole domain in order to obtain the required accuracy. However, in the analysis of fluid flows it is hard to predict the locations of the region with large gradients, and, especially in time-dependent problems, the large gradient regions might change their shapes and locations, or even disappear. Thus, it is difficult for the engineers to control empirically the mesh size and construct a proper mesh. For constructing a proper mesh, it is important to estimate the error appropriately as well as to make automatically a faithful mesh reflecting the error distributions. In this paper, the mesh generator is incorporated into the adaptive analysis strategy based on an a posteriori error estimation, and this adaptive procedure is applied to the analyses of three-dimensional incompressible viscous flows. The global percentage error, the degree of freedom and the accuracy of the solution are compared with those of the conventional method using the regular mesh. Numerical examples of the 3-D driven cavity flows of Re = 1000 and Re = 3200 have shown the very high performance of the proposed adaptive procedure.