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A projection‐based time‐splitting algorithm for approximating nematic liquid crystal flows with stretching
Author(s) -
Cabrales Roberto C.,
GuillénGonzález Francisco,
GutiérrezSantacreu Juan Vicente
Publication year - 2017
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600247
Subject(s) - piecewise , scalar (mathematics) , liquid crystal , projection (relational algebra) , mathematics , projection method , computation , mathematical analysis , interpolation (computer graphics) , dykstra's projection algorithm , algorithm , physics , geometry , classical mechanics , optics , motion (physics)
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system couples the velocity vector, the scalar pressure and the director vector representing the direction along which the molecules are oriented. The scheme is designed by using finite elements in space and a time‐splitting algorithm to uncouple the calculation of the variables: the velocity and pressure are computed by using a projection‐based algorithm and the director is computed jointly to an auxiliary variable. Moreover, the computation of this auxiliary variable can be avoided at the discrete level by using piecewise constant finite elements in its approximation. Finally, we use a pressure stabilization technique allowing a stable equal‐order interpolation for the velocity and the pressure. Numerical experiments concerning annihilation of singularities are presented to show the stability and efficiency of the scheme.