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Stability of a Crank–Nicolson pressure correction scheme based on staggered discretizations
Author(s) -
Boyer F.,
Dardalhon F.,
Lapuerta C.,
Latché J.C.
Publication year - 2013
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.3837
Subject(s) - discretization , mathematics , dissipative system , flux limiter , finite volume method , conservation law , context (archaeology) , euler's formula , finite element method , mathematical analysis , mechanics , physics , quantum mechanics , paleontology , biology , thermodynamics
SUMMARY In the context of LES of turbulent flows, the control of kinetic energy seems to be an essential requirement for a numerical scheme. Designing such an algorithm, that is, as less dissipative as possible while being simple, for the resolution of variable density Navier–Stokes equations is the aim of the present work. The developed numerical scheme, based on a pressure correction technique, uses a Crank–Nicolson time discretization and a staggered space discretization relying on the Rannacher–Turek finite element. For the inertia term in the momentum balance equation, we propose a finite volume discretization, for which we derive a discrete analogue of the continuous kinetic energy local conservation identity. Contrary to what was obtained for the backward Euler discretization, the dissipation defect term associated to the Crank–Nicolson scheme is second order in time. This behavior is evidenced by numerical simulations. Copyright © 2013 John Wiley & Sons, Ltd.