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A spectral–finite difference solution of the Navier–Stokes equations in three dimensions
Author(s) -
Alfonsi Giancarlo,
Passoni Giuseppe,
Pancaldo Lea,
Zampaglione Domenico
Publication year - 1998
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/(sici)1097-0363(19980715)28:1<129::aid-fld707>3.0.co;2-4
Subject(s) - mathematics , boundary value problem , finite difference , navier–stokes equations , compressibility , mathematical analysis , finite difference method , pressure correction method , compact finite difference , spectral method , computational fluid dynamics , domain decomposition methods , partial differential equation , finite element method , mechanics , physics , thermodynamics
A new computational code for the numerical integration of the three‐dimensional Navier–Stokes equations in their non‐dimensional velocity–pressure formulation is presented. The system of non‐linear partial differential equations governing the time‐dependent flow of a viscous incompressible fluid in a channel is managed by means of a mixed spectral–finite difference method, in which different numerical techniques are applied: Fourier decomposition is used along the homogeneous directions, second‐order Crank–Nicolson algorithms are employed for the spatial derivatives in the direction orthogonal to the solid walls and a fourth‐order Runge–Kutta procedure is implemented for both the calculation of the convective term and the time advancement. The pressure problem, cast in the Helmholtz form, is solved with the use of a cyclic reduction procedure. No‐slip boundary conditions are used at the walls of the channel and cyclic conditions are imposed at the other boundaries of the computing domain. Results are provided for different values of the Reynolds number at several time steps of integration and are compared with results obtained by other authors. © 1998 John Wiley & Sons, Ltd.