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Splitting methods for high order solution of the incompressible Navier–Stokes equations in 3D
Author(s) -
Brüger Arnim,
Gustafsson Bertil,
Lötstedt Per,
Nilsson Jonas
Publication year - 2005
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.863
Subject(s) - curvilinear coordinates , discretization , mathematics , pressure correction method , navier–stokes equations , mathematical analysis , hagen–poiseuille equation , compressibility , grid , dimension (graph theory) , finite difference method , space (punctuation) , flow (mathematics) , incompressible flow , geometry , physics , mechanics , computer science , pure mathematics , operating system
The incompressible Navier–Stokes equations are discretized in space by a hybrid method and integrated in time by the method of lines. The solution is determined on a staggered curvilinear grid in two space dimensions and by a Fourier expansion in the third dimension. The space derivatives are approximated by a compact finite difference scheme of fourth‐order on the grid. The solution is advanced in time by a semi‐implicit method. In each time step, systems of linear equations have to be solved for the velocity and the pressure. The iterations are split into one outer iteration and three inner iterations. The accuracy and efficiency of the method are demonstrated in a numerical experiment with rotated Poiseuille flow perturbed by Orr–Sommerfeld modes in a channel. Copyright © 2005 John Wiley & Sons, Ltd.