Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 24: Poster I

DY 24.58: Poster

Mittwoch, 28. März 2007, 16:00–18:00, Poster D

Combined path-following and time integration methods applied to lubrication equations — •Philippe Beltrame and Uwe Thiele — Current address: Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany

Pattern formation in thin liquid films represents a highly nonlinear phenomena far from equilibrium. To understand the evolution beyond the weakly nonlinear stage requires a numerical treatment of the of the full nonlinear system either by time integration of the dynamics or by path-following to track the (relative) equilibria directly. We develop a code unifying the time integration and path following tasks for generic lubrication equations [1] following similar projects for the Navier-Stokes equations [2]. However, the presence of the bilaplacian operator in the curvature term deteriorates drastically the Jacobian matrix conditioning which is the crucial point in such methods. Furthermore the presence of an ultrathin precursor film (typically below 100 nm thickness) leads to a strong scale separation for macroscopic drops. In order to tackle these specific problems we developed an original algorithm using exponential propagation. The code proves its reliability and efficiency compared to more classical methods. Our common numerical framework is applied to 2D sliding drops and 2D/3D depinning problem.

References [1] Oron, A et al. Reviews of Modern Physics, 1997, 69, 931-980 [2] Tuckerman, L. et al., Doedel (Eds) Bifurcation analysis for timesteppers Springer, New York, 2000