Abstract:
PURPOSE – For a partial differential equation with a fourth-order derivative such as the Cahn-Hilliard
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.
