
Incompressible FlowAn incompressible fluid passes through a channel with three obstacles (flow speed v=3). The velocity distribution can be computed by solving the boundary value problem for the potential u(x,y). At the left end of the channel g=3, and g=3 at the right end. These natural boundary conditions do not enter explicitly in the variational formulation. Hence, websplines without weighting can be used for the finite element approximation. The velocity is visualized in the following Figure. The next Figure shows the streamlines, along which the potential is constant. Below, the classification of the tensor product Bsplines is illustrated. The majority of Bsplines (marked blue) does not have to be modified. The percentage of Bsplines, coupled with outer Bsplines (marked red) tends to zero as the grid is refined. As a consequence of the regular grid structure, the finite element solution can be computed very efficiently. LiteratureK. Höllig, U. Reif, J. Wipper: BSpline approximation of Neumann problems. Mathematisches Institut A, University of Stuttgart, Preprint 20012.See Publications for a complete list of WEBpublications.
Author: Joachim Wipper ; Last modification: 2006/08/31 09:36:55 UTC.
