Projection methods for incompressible flow problems with WENO finite difference schemes

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Date
2015
Volume
2171
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convectiondiffusion equations [?]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several nonincremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.

Description
Keywords
Incompressible Navier–Stokes equations, finite difference, WENO schemes, nonincremental projection methods, incremental projection methods, PSPG-type stabilization
Citation
Frutos, J. d., John, V., & Novo, J. (2015). Projection methods for incompressible flow problems with WENO finite difference schemes (Vol. 2171). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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