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Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations
Author(s) -
Pinelli A.,
Vacca A.
Publication year - 1994
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/fld.1650180806
Subject(s) - mathematics , scalar (mathematics) , incompressible flow , collocation method , navier–stokes equations , collocation (remote sensing) , domain decomposition methods , spectral method , chebyshev filter , compressibility , pseudo spectral method , finite element method , mathematical analysis , flow (mathematics) , geometry , computer science , fourier transform , differential equation , physics , fourier analysis , ordinary differential equation , mechanics , machine learning , thermodynamics
Abstract The two‐dimensional incompressible Navier‐Stokes equations in primitive variables have been solved by a pseudospectral Chebyshev method using a semi‐implicit 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 sub‐rectangles. Each scalar problem obtained after spatial collocation is solved by iterating by subdomains. For steady problems a C 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 single‐block 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.