Open Access

ARTICLE

A new incompressible Navier-Stokes solver combining Fourier pseudo-spectral and immersed boundary methods

F.P. Mariano¹, L.Q. Moreira¹, A. Silveira-Neto¹, C.B. da Silva², J.C.F. Pereira²

1 Laboratory Mechanical of Fluids - MFlab, Faculty of Mechanical Engineering - FEMEC, Federal University of Uberlândia - UFU, Uberlândia-MG, Brasil.
2 Instituto Superior Técnico, LASEF, Lisboa, Portugal.

Computer Modeling in Engineering & Sciences 2010, 59(2), 181-216. https://doi.org/10.3970/cmes.2010.059.181

Abstract

A new numerical methodology combining Fourier pseudo-spectral and immersed boundary methods - IMERSPEC - is developed for fluid flow problems governed by the incompressible Navier-Stokes equations. The numerical algorithm consists in a classical Fourier pseudo-spectral methodology using the collocation method where wall boundary conditions are modelled by using an immersed boundary method (IBM). The performance of that new methodology is exemplified in two-dimensional numerical simulations of Green-Taylor decaying vortex, lid-driven cavity and flow over a square cylinder. The convergence rate, the accuracy, the influence of the Reynolds number and the external domain size are analyzed. This new method combines some advantages of high accuracy and low computational cost provided by Fourier pseudo-spectral methods (FPSM) with the possibility of tackling complex geometries given by immersed boundary method.

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