Martin Streng

Low-Reynolds-number flow over partially covered cavities

We solve the problem of two-dimensional flow of a viscous fluid over a rectangular approximation of an etched hole. In the absence of inertia, the problem is solved by a technique involving the matching of biorthogonal infinite eigenfunction expansions in different parts of the domain. Truncated versions of these series are used to compute a finite number of unknown coefficients. In this way, the stream function and its derivatives can be determined in any arbitrary point. The accuracy of the results and the influence of the singularities at the mask-edge corners is discussed. The singularities result in a reduced convergence of the eigenfunction expansions on the interfaces of the different regions. However, accurate results can be computed for the interior points without using a lot of computational time and memory. These results can be used as a benchmark for other methods which will have to be used for geometries involving curved boundaries. The effect of hole size on the flow pattern is also discussed. These flow patterns have a strong influence on the etch rate in the different regions.

The effectiveness of domain balancing strategies on workstation clusters demonstrated by viscous flow problems

We consider several aspects of efficient numerical simulation of viscous compressible flow on both homogeneous and heterogeneous workstation-clusters. We consider dedicated systems, as well as clusters operating in a multi-user environment. For dedicated homogeneous clusters, we show that with respect to the turn-around time, there is an optimal number of workstations to solve a given flow-problem. This number depends on the actual implementation of the solver. For non-dedicated heterogeneous clusters we apply dynamic domain-balancing techniques in order to obtain an optimal turn-around time for the flow-simulation job only, taking into account the activities on the cluster arising from the other applications. We show that the decision which technique should be used depends on various aspects, such as the character of the load-fluctuations arising from the other applications, whether the flow-simulation job is computationally intensive, and the underlying hardware. The effects of these aspects on this decision are analyzed. Although it can be concluded that no domain-balancing technique is the best under arbitrary circumstances, such an analysis may guide the decision for a particular load-situation. Moreover, we indicate how such a decision can be supported by a comparison of the various balancing strategies using a simulation study. This is illustrated for a specific load-situation.

Chebyshev approximation in n by curves and linear manifolds

In curve and surface fitting it can be essential to use the principle of uniform (Chebyshev) approximation. We discuss the general problem of approximation by a parameterized curve, the special case of approximation by a straight line and as a generalization the approximation by linear manifolds.