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A hybrid level set / front tracking approach
Author(s) -
Basting Steffen,
Weismann Martin,
Prignitz Rodolphe
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310156
Subject(s) - polygon mesh , finite element method , classification of discontinuities , level set (data structures) , triangulation , computer science , convergence (economics) , benchmark (surveying) , level set method , set (abstract data type) , representation (politics) , function (biology) , interface (matter) , a priori and a posteriori , mathematical optimization , algorithm , volume mesh , tracking (education) , mesh generation , geometry , mathematics , mathematical analysis , structural engineering , artificial intelligence , engineering , computer graphics (images) , pedagogy , philosophy , law , economic growth , segmentation , maximum bubble pressure method , biology , psychology , geodesy , bubble , epistemology , evolutionary biology , parallel computing , political science , programming language , politics , economics , image segmentation , geography
In finite element simulations of fluid flows with free boundaries, the representation of boundaries and interfaces plays an essential role. Common approaches can be categorized into two groups, interface tracking and interface capturing methods, each with individual pros and cons. The proposed approach provides a hybrid description of the interface. The main ingredient is a mesh optimization technique that aligns a given triangulation to the geometry which is implicitly represented by a level set function. Resulting triangulations are of optimal quality while connectivity of the mesh is retained. Consequently, finite element spaces defined on the aligned triangulations can be efficiently modified to account for solution specific properties such as discontinuities across interfaces. We outline an ALE‐based finite element method which can be used in various application scenarios. We briefly demonstrate the benefits of the method by applying it to two applications: The first application is concerned with a finite element method for particulate flows for which we provide an a priori error estimate. The estimate indicates that by using the proposed approach, h 2 convergence can be obtained on aligned meshes, while a sharp h 1/2 results holds for non‐aligned meshes. The second application is concerned with a fully coupled two‐phase flow benchmark problem. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)