The q-homotopy analysis method for a solution of the Cahn–Hilliard equation in the presence of advection and reaction terms

Abstract

In this paper, we provide a solution to the Cahn–Hilliard equation using the q-homotopy analysis method (q-HAM). The q-HAM is a more general, simple and widely used method for solving stiff nonlinear partial differential equations. The Cahn–Hilliard equation is a classical model in material sciences that describe spinodal decomposition and phase separation in two-phase flows. Using the q-HAM, the effect of various parameters of physical interest such as diffusive parameter, thickness parameter, advection and reaction terms on concentration is studied. The comparison of the computed solution with the exact solution is presented for some fixed parameter values to validate the solution obtained using the q-HAM.

Keywords

• The Cahn–Hilliard equation
• the q-homotopy analysis method
• advection and reaction terms
• thickness of transition layer
• diffusion parameter