Regensburg 2002 – scientific programme

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DY: Dynamik und Statistische Physik

DY 40: Wachstumsprozesse und Grenzfl
ächeneigenschaften

DY 40.5: Talk

Thursday, March 14, 2002, 10:45–11:00, H2

Phase Separation Dynamics: Stable Time Steps for the Cahn-Hilliard Equation — •Benjamin Vollmayr-Lee¹ and Andrew Rutenberg² — ¹Department 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 t ∼ t^2/3 for a time step at asymptotically late time t. In this case, after taking n steps, one reaches a time t ∼ n³! 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 t ∼ t^1/3. We find an efficient algorithm capable of Δ t ∼ t^4/9.