A fast Schur complement method for the spectral element discretization of the incompressible Navier-Stokes equations

Journal Article · Sun Jan 01 04:00:00 EST 1995 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1995.1011· OSTI ID:105463

Couzy, W; Deville, M O ^[1]

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1. Catholic Univ. of Lowain, Lowain-la-Newe (Belgium)

The weak formulation of the incompressible Navier-Stokes equations in three space dimensions is discretized with spectral element approximations and Gauss-Lobatto-Legendre quadratures. The Uzawa algorithm is applied to decouple the velocities from the pressure. The equation that results for the pressure is solved by an iterative method. Within each pressure iteration, a Helmholtz operator has to be inverted. This can efficiently be done by separating the equations for the interior nodes from the equations at the interfaces, according to the Schur method. Fast diagonalization techniques are applied to the interior variables of the spectral elements. Several ways to deal with the resulting interface problem are discussed. Finally, a comparison is made with a more classical method. 18 refs., 2 figs., 5 tabs.

• OSTI ID: 105463
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 116; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
99 GENERAL AND MISCELLANEOUS
INCOMPRESSIBLE FLOW
ITERATIVE METHODS
NAVIER-STOKES EQUATIONS
QUADRATURES
REYNOLDS NUMBER
THREE-DIMENSIONAL CALCULATIONS