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Projection‐based variational multiscale method for incompressible Navier–Stokes equations in time‐dependent domains
Author(s) -
Pal Birupaksha,
Ganesan Sashikumaar
Publication year - 2016
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.4338
Subject(s) - mathematics , turbulence modeling , finite element method , projection method , navier–stokes equations , projection (relational algebra) , basis function , mathematical analysis , eulerian path , tensor (intrinsic definition) , airfoil , incompressible flow , compressibility , flow (mathematics) , geometry , physics , turbulence , mechanics , algorithm , lagrangian , thermodynamics , grating
Summary A variational multiscale method for computations of incompressible Navier–Stokes equations in time‐dependent domains is presented. The proposed scheme is a three‐scale variational multiscale method with a projection‐based scale separation that uses an additional tensor valued space for the large scales. The resolved large and small scales are computed in a coupled way with the effects of unresolved scales confined to the resolved small scales. In particular, the Smagorinsky eddy viscosity model is used to model the effects of unresolved scales. The deforming domain is handled by the arbitrary Lagrangian–Eulerian approach and by using an elastic mesh update technique with a mesh‐dependent stiffness. Further, the choice of orthogonal finite element basis function for the resolved large scale leads to a computationally efficient scheme. Simulations of flow around a static beam attached to a square base, around an oscillating beam and around a plunging aerofoil are presented. Copyright © 2016 John Wiley & Sons, Ltd.