Titlebook: Spectral Methods for Incompressible Viscous Flow; Roger Peyret Textbook 2002 Springer Science+Business Media New York 2002 Navier-Stokes e

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Stiff and singular problemsut exhibits large variations in a region of small extent. For convergence reasons, the collocation points cannot be clustered arbitrarily in the rapid variation region, so that an appropriate distribution of the collocation points must be obtained through a coordinate transformation, preferably self

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Domain Decomposition Methodich the solution is calculated by taking into account some transmission conditions at the interfaces between the subdomains. This chapter addresses some usual Chebyshev domain decomposition methods for elliptic problems: influence matrix, iterative Dirichlet/Neumann, and spectral-element methods. Th

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Domain Decomposition Methodtidomain solution of the Stokes problem will be considered for both formulations: vorticity-streamfunction and velocity-pressure. Lastly, examples of application to the Navier-Stokes equations will be presented.

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Chebyshev methodo that it possesses the valuable properties of the latter concerning, in particular, the convergence and the possible use of the FFT. On the other hand, the Chebyshev series expansion is exempt from the Gibbs phenomenon at the boundaries.

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Navier-Stokes equations for incompressible fluidset received large attention in the field of spectral methods. However, recent works (Clercx, 1997; Trujillo and Karniadakis, 1999) have shown that Chebyshev solutions of the vorticity-velocity equations could be envisaged with success.

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