THERMAL SCIENCE

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Jun Zhou

NUMERICAL SIMULATIONS OF THE ENERGY-STABLE SCHEME FOR SWIFT-HOHENBERG EQUATION

ABSTRACT
A collocation Fourier scheme for Swift-Hohenberg equation based on the convex splitting idea is implemented. To ensure an efficient numerical computation, we propose a general framework with linear iteration algorithm to solve the non-linear coupled equations which arise with the semi-implicit scheme. Following the contraction mapping theorem, we present a detailed convergence analysis for the linear iteration algorithm. Various numerical simulations, including verification of accuracy, dissipative property of discrete energy and pattern formation, are presented to demonstrate the efficiency and the robustness of proposed method.
KEYWORDS
Swift-Hohenberg equation, energy stability, collocation Fourier method, linear iteration
PAPER SUBMITTED: 2018-05-15
PAPER REVISED: 2018-09-20
PAPER ACCEPTED: 2018-11-15
PUBLISHED ONLINE: 2019-03-31
DOI REFERENCE: https://doi.org/10.2298/TSCI180515080Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 3, PAGES [S669 - S676]
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Numerical simulations of the energy-stable scheme for Swift-Hohenberg equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence