# On a fractional step-splitting scheme for the Cahn-Hilliard equation

 dc.contributor.author Aderogba, Adebayo Abiodun dc.contributor.author Chapwanya, Michael dc.contributor.author Djoko, J.K. (Jules Kamdem) dc.date.accessioned 2015-03-24T09:48:38Z dc.date.available 2015-03-24T09:48:38Z dc.date.issued 2014 dc.description.abstract PURPOSE – For a partial differential equation with a fourth-order derivative such as the Cahn-Hilliard en_ZA equation, it is always a challenge to design numerical schemes that can handle the restrictive time step introduced by this higher order term. The purpose of this paper is to employ a fractional splitting method to isolate the convective, the nonlinear second-order and the fourth-order differential terms. DESIGN / METHODOLOGY / APPROACH – The full equation is then solved by consistent schemes for each differential term independently. In addition to validating the second-order accuracy, the authors will demonstrate the efficiency of the proposed method by validating the dissipation of the Ginzberg-Lindau energy and the coarsening properties of the solution. FINDINGS – The scheme is second-order accuracy, the authors will demonstrate the efficiency of the proposed method by validating the dissipation of the Ginzberg-Lindau energy and the coarsening properties of the solution. ORIGINALITY / VALUE – The authors believe that this is the first time the equation is handled numerically using the fractional step method. Apart from the fact that the fractional step method substantially reduces computational time, it has the advantage of simplifying a complex process efficiently. This method permits the treatment of each segment of the original equation separately and piece them together, in a way that will be explained shortly, without destroying the properties of the equation. dc.description.librarian hb2015 en_ZA dc.description.uri http://www.emeraldinsight.com/loi/ec en_ZA dc.identifier.citation A.A. Aderogba M. Chapwanya J.K. Djoko, (2014),"On a fractional step-splitting scheme for the Cahn-Hilliard equation", Engineering Computations, Vol. 31 Iss 7 pp. 1151 - 1168. http://dx.doi.org/10.1108/EC-09-2012-0223 en_ZA dc.identifier.issn 0264-4401 (print) dc.identifier.issn 1758-7077 (online) dc.identifier.other 10.1108/EC-09-2012-0223 dc.identifier.uri http://hdl.handle.net/2263/44135 dc.language.iso en en_ZA dc.publisher Emerald en_ZA dc.rights © Emerald Group Publishing Limited en_ZA dc.subject Cahn-Hilliard equation en_ZA dc.subject Finite volume methods en_ZA dc.subject Fractional step-splitting en_ZA dc.subject Numerical solution en_ZA dc.title On a fractional step-splitting scheme for the Cahn-Hilliard equation en_ZA dc.type Postprint Article en_ZA
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