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Implicit time discretization schemes for least‐squares finite element formulations to model incompressible flows
Author(s) -
Averweg Solveigh,
Schwarz Alexander,
Nisters Carina,
Schröder Jörg
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800166
Subject(s) - discretization , mathematics , finite element method , interpolation (computer graphics) , compressibility , reynolds number , flow (mathematics) , incompressible flow , cylinder , pressure correction method , drag coefficient , moving least squares , mathematical analysis , drag , mechanics , geometry , turbulence , classical mechanics , physics , motion (physics) , engineering , structural engineering
In the present contribution different implicit time integration schemes to model incompressible flow problems are investigated. Amongst the tested methods are the fully implicit Newmark, Houbolt and Crank‐Nicolson schemes. The first‐order system for the proposed formulation is given in terms of stresses and velocities as introduced in [1]. Raviart‐Thomas and standard Lagrange interpolation functions are used to approximate the stresses and velocities, respectively. For the comparison of all time discretization schemes, the unsteady two‐dimensional laminar flow around a cylinder at Reynolds number Re = 100 is chosen. For a rating on the accuracy, the obtained results for the drag coefficient are benchmarked against reference solutions by [2].