A study of time integration schemes for the numerical modelling of ...

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A. MALIDI, S. DUFOUR AND D. N’DRIFigure 6. Plots at t = t ref for the Von Karman vortex street problem: (a) horizontal velocity component;(b) vertical velocity component; and (c) pressure.variations of t n . This can be explained by the fact that when the drop reaches its steadystateshape, we still observe very small deformations of the free surface that are captured bythe transient error estimator. Figure 8 illustrates the time evolution of the jump in pressure.The fact that (p 1 − p 2 ) → 1 is an indication that the steady-state is reached. Streamlines arealso useful to determine if the steady-state of a free surface ow is reached. It can be seenin Figure 9(a) that the streamlines do not cross the free surface, which is another goodindication that the numerical strategy allows us to reach the steady-state of this problem, withno parasitic currents. Another indication that the surface tension-driven ow simulation isperformed accurately is the smooth transition of pressure, with no irregularities, as illustratedin Figure 9(b).Copyright ? 2005 John Wiley & Sons, Ltd.Int. J. Numer. Meth. Fluids (in press)
A STUDY OF TIME INTEGRATION SCHEMES FOR MODELLING FREE SURFACE FLOWS0.16 Laplace’s Problem0.140.12Time-Step Sizes0.10.080.060.040.0200 50 100 150 200 250 300Time StepsFigure 7. Time-step sizes computed by the ABDF scheme for Laplace’s problem.Laplace’s Problemreference∆ p1Pressure Jump00 100 200 300 400Time StepsFigure 8. Time evolution of the jump in pressure for Laplace’s problem.Copyright ? 2005 John Wiley & Sons, Ltd.Int. J. Numer. Meth. Fluids (in press)
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