In this paper, numerical results of different flow problems for the three-dimensional incompressible Navier–Stokes equations are presented. The problems describe a flow around an obstacle as well as a flow through a system of pipes. Furthermore, chemical species are added in case of the pipe flow. This additionally comprises a transport problem for the introduced species. The numerical approximation is accomplished with a finite element characteristic projection method based on the schemes of Chorin and Vankan. The numerical method for solving the three-dimensional Navier–Stokes equations and the species equations using the parallel adaptive finite element framework padfem are illustrated. Mean values like lift and drag coefficient, pressure decay and species distribution are presented and compared with existing reference values. Finally, some efficiency results of the used solvers are given.
[Show abstract][Hide abstract] ABSTRACT: This paper presents a numerical study of the 3D flow around a cylinder which was defined as a benchmark problem for the steady state Navier-Stokes equations within the DFG high priority research program Flow Simulation with High-Performance Computers by SchSfer and Turek (1996). The first part of the study is a comparison of several finite element discretizations with respect to the accuracy of the computed benchmark parameters. It turns out that boundary fitted higher order finite element methods are in general most accurate. Our numerical study improves the hitherto existing reference values for the benchmark parameters considerably. The second part of the study deals with efficient and robust solvers for the discrete saddle point problems. All considered solvers are based on coupled multigrid methods. The flexible GMRES method with a multiple discretization multigrid methods proves to be the best solver.
International Journal for Numerical Methods in Fluids 10/2002; 40(6). DOI:10.1002/fld.377 · 1.24 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The problem of partitioning a graph into a number of pieces is one of the fundamental tasks in computer science and has a number of applications e.g. in computational mechanics or VLSI design. Finding optimal partitions according to different measures is in most cases NP-complete. Nevertheless, a large number of efficient partitioning heuristics have been developed during recent years. The performance of these methods in terms of computation time as well as quality of approximation is heavily influenced by choices of parameters and certain implementation details. Fortunately, the partitioning problem itself is clearly defined and its description leads to a small interface. Thus, efficient implementations of approximation heuristics can be re-used for different applications. The PARTY partitioning library serves a variety of different partitioning methods in a very simple and easy way. Instead of implementing the methods directly, the user may take advantage of the ready implemented me...
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