Stable and unstable formulations of the convection operator in spectral element simulations

Wilhelm, Dirk; Kleiser, Leonhard

doi:10.1016/S0168-9274(99)00093-8

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Stable and unstable formulations of the convection operator in spectral element simulations
Authors:	Wilhelm, Dirk Kleiser, Leonhard
DOI:	10.1016/S0168-9274(99)00093-8
Published in:	Applied Numerical Mathematics
Volume(Issue):	33
Issue:	1-4
Page(s):	275
Pages to:	280
Issue Date:	May-2000
Publisher / Ed. Institution:	Elsevier
ISSN:	0168-9274 1873-5460
Language:	English
Subjects:	Spectral element method; Navier–Stokes simulation; Numerical instability; Incompressible flow; Formulation of convection operator
Subject (DDC):	510: Mathematics
Abstract:	We show that for the PN–PN−2 spectral element method (SEM), in which the velocity and pressure are approximated by polynomials of order N and N−2, respectively, numerical instabilities may occur in Navier–Stokes simulations. These instabilities depend on the formulation of the convection operator. The numerical scheme is stable for the convective form and one version of the rotational form but unstable for the divergence form and the skew-symmetric form. Further numerical analysis indicates that this instability is not caused by nonlinear effects but occurs also for the linearized momentum equations. We demonstrate that the instability is a consequence of the staggered grid between velocity and pressure, as often used in SEM.
URI:	https://digitalcollection.zhaw.ch/handle/11475/13746
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Departement:	School of Engineering
Appears in collections:	Publikationen School of Engineering

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Wilhelm, D., & Kleiser, L. (2000). Stable and unstable formulations of the convection operator in spectral element simulations. Applied Numerical Mathematics, 33(1-4), 275–280. https://doi.org/10.1016/S0168-9274(99)00093-8

Wilhelm, D. and Kleiser, L. (2000) ‘Stable and unstable formulations of the convection operator in spectral element simulations’, Applied Numerical Mathematics, 33(1-4), pp. 275–280. Available at: https://doi.org/10.1016/S0168-9274(99)00093-8.

D. Wilhelm and L. Kleiser, “Stable and unstable formulations of the convection operator in spectral element simulations,” Applied Numerical Mathematics, vol. 33, no. 1-4, pp. 275–280, May 2000, doi: 10.1016/S0168-9274(99)00093-8.

WILHELM, Dirk und Leonhard KLEISER, 2000. Stable and unstable formulations of the convection operator in spectral element simulations. Applied Numerical Mathematics. Mai 2000. Bd. 33, Nr. 1-4, S. 275–280. DOI 10.1016/S0168-9274(99)00093-8

Wilhelm, Dirk, and Leonhard Kleiser. 2000. “Stable and Unstable Formulations of the Convection Operator in Spectral Element Simulations.” Applied Numerical Mathematics 33 (1-4): 275–80. https://doi.org/10.1016/S0168-9274(99)00093-8.

Wilhelm, Dirk, and Leonhard Kleiser. “Stable and Unstable Formulations of the Convection Operator in Spectral Element Simulations.” Applied Numerical Mathematics, vol. 33, no. 1-4, May 2000, pp. 275–80, https://doi.org/10.1016/S0168-9274(99)00093-8.