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From level set to volume of fluid and back again at second‐order accuracy
Author(s) -
Detrixhe Miles,
Aslam Tariq D.
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4076
Subject(s) - solver , algorithm , software portability , grid , computation , piecewise linear function , block (permutation group theory) , computer science , stencil , level set (data structures) , tree (set theory) , volume (thermodynamics) , interface (matter) , mathematical optimization , set (abstract data type) , piecewise , function (biology) , computational science , mathematics , parallel computing , geometry , mathematical analysis , physics , bubble , quantum mechanics , artificial intelligence , maximum bubble pressure method , evolutionary biology , biology , programming language
Summary We present methods for computing either the level set function or volume fraction field from the other at second‐order accuracy. Both algorithms are optimal in that O( N ) computations are needed for N total grid points and both algorithms are easily parallelized. This work includes a novel interface reconstruction algorithm in three dimensions that requires a smaller local block of volume fractions than existing algorithms. A compact local solver leads to better algorithm portability and efficiency: for example, fewer restrictions must be imposed on an adaptive mesh, and fewer grid cells must be communicated between processors in a parallel implementation. We also present a fast sweeping method for computing a unique approximation of the signed distance function to a piecewise linear interface. All of the numerical examples confirm second‐order accuracy on both uniform and tree‐based adaptive grids. Copyright © 2015 John Wiley & Sons, Ltd.