Creeping Flow

Abstract

As the last topic of the basic concepts of the finite element method in fluid flows, creeping flow problem of the incompressible fluid is discussed in this chapter. The flow is highly viscous and moves with slow velocity, whose acceleration effect is negligible. Thus, the problem turns out to be linear. This type of flow is not practical, i.e., we can only count melting candle flow and few other examples. However, the analysis of the flow includes important technique, namely, the mixed interpolation. The interpolation for velocity is one order or more higher than that for pressure. The incompressibility is assumption of some sort of limit state. Therefore, special treatment should be required. To simplify the problem, we confine our attention to the two-dimensional analysis. However, extension to the three-dimensional analysis is straightforward.