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Gradient based enhanced finite element formulation for diffuse phase interfaces
Author(s) -
Krauss Matthias,
Münch Ingo
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610218
Subject(s) - finite element method , interpolation (computer graphics) , polygon mesh , a priori and a posteriori , degrees of freedom (physics and chemistry) , phase (matter) , field (mathematics) , dimension (graph theory) , mathematical analysis , domain (mathematical analysis) , geometry , mathematics , computer science , topology (electrical circuits) , physics , classical mechanics , motion (physics) , philosophy , epistemology , quantum mechanics , pure mathematics , thermodynamics , combinatorics
Interfaces between adjacent phases, so‐called domain walls, appear as non‐linear gradients of order parameters in diffuse phase field models. Usually, the interface width is much smaller than the dimension of the simulated region. Since the position of domain walls is not known a priori the maximum size of finite elements needs to be adapted to the length scale of interfaces within the entire region. We suggested a selective finite element method to improve the numerical solution of diffuse phase field models [1, 2]. It enhances the finite element interpolation space using supplementary local degrees of freedom. However, corresponding additional nodes are strictly located in the interior of elements, thus, C 0 ‐continuity at element border is guaranteed. Since C 0 ‐continuity limits the performance of this method we propose in this paper a relaxation of C 0 ‐requirements perpendicular to the gradient of the order parameter. Therefore, the direction of interfaces is analyzed as additional information for further adaptive improvement of the interpolation space. A dual phase field model is used to validate the proposed method. The analytical solution of a stationary domain wall allows error analysis of regular and distorted finite element meshes. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)