Pinelli, Alfredo

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Universidad Complutense de Madrid
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Ciencias Matemáticas
Matemática Aplicada
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Now showing 1 - 5 of 5
  • Publication
    Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations
    (Wiley, 1994) Pinelli, Alfredo; Vacca, A.
    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 C1 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.
  • Publication
    A spectral multidomain method for the numerical simulation of turbulent flows
    (Elsevier, 1997) Pinelli, Alfredo; Vacca, A.; Quarteroni, A.
    The primitive variable formulation of the unsteady incompressible Navier-Stokes equations in three space dimensions is discretized with a combined Fourier-Legendre spectral method. A semi-implicit pressure correction scheme is applied to decouple the velocity from the pressure. The arising elliptic scaler problems are first diagonalized in the periodic Fourier direction and then solved by a multidomain Legendre collocation method in the two remaining space coordinates. In particular, both an iterative and a direct version of the so-called projection decomposition method (PDM) are introduced to separate the equations for the internal nodes from the ones governing the interface unknowns. The PDM method, first introduced by V. Agoshkov and E. Ovtchinnikov and later applied to spectral methods by P. Gervasio, E. Ovtchinnikov, and A. Quarteroni is a domain decomposition technique for elliptic boundary value problems, which is based on a Galerkin approximation of the Steklov-Poincare equation for the unknown variables associated to the grid points lying on the interface between subdomains. After having shown the exponential convergence of the proposed discretization technique, some issues on the efficient implementation of the method are given. Finally, as an illustration of the potentialities of the algorithm for the numerical simulation of turbulent flows, the results of a direct numerical simulation (DNS) of a fully turbulent plane channel flow are presented.