TY - JOUR
T1 - Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation
JO - Communications in Computational Physics
VL - 2
SP - 448
EP - 460
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0260
UR - https://global-sci.org/intro/article_detail/cicp/12758.html
KW - Cahn–Hilliard equation, convex splitting, effective time step, Fourier analysis.
AB - <p style="text-align: justify;">We analyze the effective time step size of a nonlinear convex splitting scheme
for the Cahn–Hilliard (CH) equation. The convex splitting scheme is unconditionally
stable, which implies we can use arbitrary large time-steps and get stable numerical
solutions. However, if we use a too large time-step, then we have not only discretization
error but also time-step rescaling problem. In this paper, we show the time-step
rescaling problem from the convex splitting scheme by comparing with a fully implicit
scheme for the CH equation. We perform various test problems. The computation results
confirm the time-step rescaling problem and suggest that we need to use small
enough time-step sizes for the accurate computational results.</p>