Y Uchibori &I J Sobey
Numerical Analysis Group Research Report NA-92/14
The effect of numerical algorithm on the calculated structure of a bifurcation phenomena in a sharp edged symmetric expansion is studied. A time marching method is used to calculate the flow, and the stream function vorticity form of the equations are discretised by three finite difference methods, a central difference,a conservative and a nonconservative upwind difference in the advective term of the vorticity transport equation. A backward facing step is firstly investigated to assess the prediction of each algorithm. Next a symmetric expansion with a 3:1 expansion ratio is examined. In evaluating the influence of numerical techniques on a bifurcation structure, we measure the transverse velocity at the middle point in the channel. Additionally we use an asymmetry measure to see other aspects of the flow. The calculation results are compared with existing results including the calculated data of Fearn, Mullin and Cliffe. It is shown that a central difference algorithm is able to correctly calculate this sensitive bifurcation, but both first order upwind schemes fail.
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