Numerical solution of cahn-hilliard system by adaptive least-squares spectral element method

Abstract

There is a growing interest in the phase-field approach to numerically handle the interface dynamics in multiphase flow phenomena because of its accuracy. The numerical solution of phase-field models has difficulties in dealing with non-self-adjoint operators and the resolution of high gradients within thin interface regions. We present an h-adaptive mesh refinement technique for the least-squares spectral element method for the phase-field models. C1 Hermite polynomials are used to give global differentiability in the approximated solution, and a space-time coupled formulation and the element-by-element technique are implemented. Two benchmark problems are presented in order to compare two refinement criteria based on the gradient of the solution and the local residual.