Regensburg 2002 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 40: Wachstumsprozesse und Grenzfl

DY 40.5: Vortrag

Donnerstag, 14. März 2002, 10:45–11:00, H2

Phase Separation Dynamics: Stable Time Steps for the Cahn-Hilliard Equation — •Benjamin Vollmayr-Lee1 and Andrew Rutenberg21Department of Physics, Bucknell University, Lewisburg PA 17387, USA — 2Department of Physics, Dalhousie University, Halifax NS, B3H 3J5 Canada

Eyre has recently derived unconditionally stable time steps for the Cahn-Hilliard equation, a model for conserved scalar coarsening. As a result, the stability criterion no longer determines the size of the time step, allowing accuracy criteria to be considered instead. We show that accuracy provides the theoretical upper limit Δ tt2/3 for a time step at asymptotically late time t. In this case, after taking n steps, one reaches a time tn3! Next, we classify all possible stable first order steps, expanding on the parameter range given by Eyre. Finally, we study the time scaling of the truncation error to all orders in Δ t. From this analysis we conclude that the theoretical maximum time step is unattainable as a stable algorithm and that Eyre’s proposed algorithms give Δ tt1/3. We find an efficient algorithm capable of Δ tt4/9.

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