A $\mathbb{P}_N × \mathbb{P}_N$ Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equations
Year: 2008
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 3 : pp. 275–296
Abstract
In this paper, we present a $\mathbb{P}_N × \mathbb{P}_N$ spectral element method and a detailed comparison with existing methods for the unsteady incompressible Navier-Stokes equations. The main purpose of this work consists of: (i) detailed comparison and discussion of some recent developments of the temporal discretizations in the frame of spectral element approaches in space; (ii) construction of a stable $\mathbb{P}_N × \mathbb{P}_N$ method together with a $\mathbb{P}_N → \mathbb{P}_{N-2}$ post-filtering. The link of different methods will be clarified. The key feature of our method lies in that only one grid is needed for both velocity and pressure variables, which differs from most well-known solvers for the Navier-Stokes equations. Although not yet proven by rigorous theoretical analysis, the stability and accuracy of this one-grid spectral method are demonstrated by a series of numerical experiments.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-NMTMA-6052
Numerical Mathematics: Theory, Methods and Applications, Vol. 1 (2008), Iss. 3 : pp. 275–296
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: $\mathbb{P}_N × \mathbb{P}_N$ Navier-Stokes equations spectral element methods.