Regensburg 2002 – wissenschaftliches Programm
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 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 ∼ t2/3 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 ∼ t1/3. We find an efficient algorithm capable of Δ t ∼ t4/9.