On the rate of convergence of the Fourier spectral method for the Navier-Stokes equations

CALCOLO ◽  
1989 ◽  
Vol 26 (2-4) ◽  
pp. 185-195 ◽  
Author(s):  
T. Geveci
Keyword(s):  
Rate Of Convergence ◽  
Spectral Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fourier Spectral Method ◽  
Navier Stokes Equations

Simulation of Flow Around Circular Cylinder Using a Collocation Spectral Method

2005 ◽  
Author(s):  
Johnny J. M. Rizales ◽  
Paulo T. T. Esperanc¸a ◽  
Andre´ Belfort Bueno
Keyword(s):  
Velocity Field ◽  
Circular Cylinder ◽  
Spectral Method ◽  
Stokes Equations ◽  
Curvilinear Coordinates ◽  
Navier Stokes ◽  
Implicit Time ◽  
Integration Scheme ◽  
Navier Stokes Equations ◽  
Collocation Spectral Method

The purpose of this paper is to develop a Fourier-Chebyshev collocation spectral method for computing unsteady two-dimensional viscous incompressible flow past a circular cylinder for low Reynolds numbers. The incompressible Navier-Stokes equations (INSE) are formulated in terms of the primitive variables, velocity and pressure. The incompressible Navier-Stokes equations in curvilinear coordinates are spectrally discretized and time integrated by a second-order mixed explicit/implicit time integration scheme. This scheme is a combination of the Crank-Nicolson scheme operating on the diffusive term and Adams-Bashforth scheme acting on the convective term. The projection method is used to split the solution of the INSE to the solution of two decoupled problems: the diffusion-convection equation (Burgers equation) to predict an intermediate velocity field and the Poisson equation for the pressure, it is used to correct the velocity field and satisfy the continuity equation. Finally, the numerical results obtained for the drag and lift coefficients around the circular cylinder are compared with results previously published.

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