To evaluate the efficiency of the FeatFlow CFD solver one can use the now classic DFG flow over a cylinder CFD benchmark [1][2] for which very accurate reference solutions for drag, lift, and pressure difference have been established [3][4]. The model problem is set up and solved with identical grids and finite element FEM spaces for both the built-in FEATool solver and the dedicated FeatFlow CFD solver. FEATool uses the built-in Matlab and Octave direct solver which currently defaults to Umfpack, while FeatFlow uses a very efficient geometric multigrid approach.

The resulting CPU timings shown in the table and curves below reveal that FeatFlow scales far better than the built-in solver, about 20 times at the finest grid level (with 4 uniform refinements of the initial benchmark grid). In 3D the savings would be even greater and this also does not account for the memory consumption (FeatFlow will use significantly less memory than a direct solver like Umfpack). Thus one should definitely consider using FeatFlow if one has large scale CFD problems to solve.

Grid | FEATool | FeatFlow |
---|---|---|

level | Umfpack | Multigrid |

2 | 2.4 s | 0.1 s |

3 | 4.9 s | 0.3 s |

4 | 17.9 s | 1.2 s |

5 | 100.0 s | 4.8 s |

The entire benchmarking script has been written as a self contained FEATool Matlab m-script file and can be downloaded from the link below.

[1] S. Turek, Efficient Solvers for Incompressible Flow Problems: An Algorithmic and Computational Approach, Series: Lecture Notes in Computational Science and Engineering , Volume 6, Springer-Verlag, 1999.

[2] M. Schafer, S. Turek, F. Durst, E. Krause, R. Rannacher, Benchmark Computations of Laminar Flow Around a Cylinder, in Flow Simulation with High-Performance Computers II,Volume 48 of the series Notes on Numerical Fluid Mechanics (NNFM) pp 547-566, Springer 1996.

[3] G. Nabh, On higher order methods for the stationary incompressible Navier-Stokes equations, PhD Thesis, 1998, Universitat Heidelberg. Preprint 42/98, 1998.

[4] V. John, G. Matthies, Higher-order finite element discretizations in a benchmark problem for incompressible flows, International Journal for Numerical Methods in Fluids, 2001, 37:8:885-903.