Premium
Development of a hybrid finite volume/element solver for incompressible flows
Author(s) -
Tu Shuangzhang,
Aliabadi Shahrouz
Publication year - 2007
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.1454
Subject(s) - finite volume method , mathematics , solver , pressure correction method , finite element method , incompressible flow , projection method , compressibility , vector field , mathematical analysis , flow (mathematics) , mathematical optimization , geometry , mechanics , physics , dykstra's projection algorithm , thermodynamics
Abstract In this paper, we report our development of an implicit hybrid flow solver for the incompressible Navier–Stokes equations. The methodology is based on the pressure correction or projection method. A fractional step approach is used to obtain an intermediate velocity field by solving the original momentum equations with the matrix‐free implicit cell‐centred finite volume method. The Poisson equation derived from the fractional step approach is solved by the node‐based Galerkin finite element method for an auxiliary variable. The auxiliary variable is closely related to the real pressure and is used to update the velocity field and the pressure field. We store the velocity components at cell centres and the auxiliary variable at cell vertices, making the current solver a staggered‐mesh scheme. Numerical examples demonstrate the performance of the resulting hybrid scheme, such as the correct temporal convergence rates for both velocity and pressure, absence of unphysical pressure boundary layer, good convergence in steady‐state simulations and capability in predicting accurate drag, lift and Strouhal number in the flow around a circular cylinder. Copyright © 2007 John Wiley & Sons, Ltd.