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Volume 25, Issue 2
Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation

Seunggyu Lee & Junseok Kim

DOI: 10.4208/cicp.OA-2017-0260

Commun. Comput. Phys., 25 (2019), pp. 448-460.

Published online: 2018-10

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  • Abstract

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.

  • Keywords

Cahn–Hilliard equation, convex splitting, effective time step, Fourier analysis.

  • AMS Subject Headings

37M05, 65M22, 65T50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-448, author = {Seunggyu Lee and Junseok Kim}, title = {Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {2}, pages = {448--460}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0260}, url = {http://global-sci.org/intro/article_detail/cicp/12758.html} }
TY - JOUR T1 - Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation AU - Seunggyu Lee & Junseok Kim 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 -

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.

Seunggyu Lee and Junseok Kim. (2018). Effective Time Step Analysis of a Nonlinear Convex Splitting Scheme for the Cahn–Hilliard Equation. Communications in Computational Physics. 25 (2). 448-460. doi:10.4208/cicp.OA-2017-0260
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