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Checkerboard modes and wave equation. (English) Zbl 1173.76027

Handlovičová, Angela (ed.) et al., Algoritmy 2009. 18th conference on scientific computing, Vysoké Tatry – Podbsanské, Slovakia, March 15–20, 2009. Proceedings of contributed papers and posters. Bratislava: Slovak University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry (ISBN 978-80-227-3032-7/pbk). 71-80 (2009).
Summary: Checkerboard modes are unphysical oscillations that sometime appear when the incompressible Navier-Stokes system is solved with a colocated scheme. In this paper, we study the rate of dissipation of these modes when the pressure and the velocity are solution of the linear wave equation solved with a Godunov scheme on a Cartesian mesh. More precisely, we show that the checkerboard modes are the fastest diffused modes when we use the Godunov scheme in monodimensional geometry, and that they are constant modes when the Godunov scheme is modified by centering the discretization of the pressure gradient. This study underlines that, on a Cartesian mesh, the checkerboard modes do not exist at low Mach number when the compressible Navier-Stokes system is solved with a Godunov type scheme, and may appear at large Reynolds numbers when the Godunov type scheme is modified to obtain an accurate scheme at low Mach numbers.
For the entire collection see [Zbl 1158.65005].

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76N15 Gas dynamics (general theory)
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