Premium
Performance aspects of a mixed s‐v LSFEM for the incompressible Navier‐Stokes equations with improved mass conservation
Author(s) -
Schwarz Alexander,
Schröder Jörg,
Serdas Serdar,
Turek Stefan,
Ouazzi Abderrahim,
Nickaeen Masoud
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310249
Subject(s) - compressibility , mathematics , finite element method , incompressible flow , vector field , conservation of mass , newtonian fluid , navier–stokes equations , flow (mathematics) , minification , basis (linear algebra) , mathematical analysis , mathematical optimization , physics , geometry , classical mechanics , mechanics , thermodynamics
In the present contribution we propose an improved mixed least‐squares finite element method (LSFEM) and compare it with standard LSFEMs with respect to performance aspects. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier‐Stokes equations. The basis for the associated symmetric minimization problem is a reduced stress‐velocity (s‐v) two‐field approach, see e.g. CAI ET AL. [1] and SCHWARZ & SCHRÖDER [2]. The main idea for the proposed formulation is to add an additional equation, which yields an overconstrained first‐order system. This approach does not introduce additional unknowns, so the advantage of two variables (stresses and velocities) remains. Finally, we present a numerical example in order to show the capability of the proposed formulation. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)