Chebyshev collocation method and multidomain decomposition for the incompressible NavierStokes equations
Abstract
The twodimensional incompressible NavierStokes equations in primitive variables have been solved by a pseudospectral Chebyshev method using a semiimplicit fractional step scheme. The latter has been adapted to the particular features of spectral collocation methods to develop the monodomain algorithm. In particular, pressure and velocity collocated on the same nodes are sought in a polynomial space of the same order; the cascade of scalar elliptic problems arising after the spatial collocation is solved using finite difference preconditioning. With the present procedure spurious pressure modes do not pollute the pressure field. As a natural development of the present work a multidomain extent was devised and tested. The original domain is divided into a union of patching subrectangles. Each scalar problem obtained after spatial collocation is solved by iterating by subdomains. For steady problems a C(sup 1) solution is recovered at the interfaces upon convergence, ensuring a spectrally accurate solution. A number of test cases have been solved to validate the algorithm in both its singleblock and multidomain configurations. The preliminary results achieved indicate that collocation methods in multidomain configurations might become a viable alternative to the spectral element technique for accurate flow prediction.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 April 1994
 DOI:
 10.1002/fld.1650180806
 Bibcode:
 1994IJNMF..18..781P
 Keywords:

 Chebyshev Approximation;
 Computational Fluid Dynamics;
 Incompressible Flow;
 NavierStokes Equation;
 Spectral Methods;
 Finite Difference Theory;
 Preconditioning;
 Pressure Distribution;
 Primitive Equations;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer