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Published in:
2018 | OriginalPaper | Chapter
Numerical Solution of Cahn-Hilliard System by Adaptive Least-Squares Spectral Element Method
Authors : Keunsoo Park, Marc Gerritsma, Maria Fernandino
Published in: Large-Scale Scientific Computing
Publisher: Springer International Publishing
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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. \(C^1\) 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.