## Abstract

A three-level consistent time-split group finite element formulation is described for a stream function vorticity representation of incompressible laminar separated flow. A consistent time-splitting is achieved by explicitly extracting directional mass and difference operators. It is shown that application of linear rectangular elements to the convective terms with a non-uniform grid introduces an artificial viscosity, but that a simple modification removes this effect. The three-level fully implicit marching algorithm is shown to converge to the steady solution faster than a Crank-Nicolson scheme when combined with a banded Gauss elimination procedure along each grid-line in turn. The present method is applied to the flow past rearward- and forward-facing steps for which the vorticity solution is known to be singular at the sharp corners. To isolate the sharp corners from the computational domain a surface layer is introduced across which the computational solution is matched to an analytic solution for the corner flow. A one-dimensional integration of the energy function and transverse extrapolation is used to obtain the pressure distribution on the body. Results, for a range of step-height Reynolds numbers of up to 250, demonstrate good agreement with corresponding experimental results.

Original language | English |
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Pages (from-to) | 297-322 |

Number of pages | 26 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 41 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1983 |