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On steady state computation of turbulent flows using \(k-\varepsilon\) models approximated by the time splitting method. (English) Zbl 1094.76047
Summary: The time splitting method is frequently used in numerical integration of flow equations with source terms since it allows almost independent programming for the source part. In this paper we consider the question of convergence to steady state of the time splitting method applied to \(k-\varepsilon\) turbulence models. This analysis is derived from a properly defined scalar study and is carried out for the coupled \(k-\varepsilon\) equations. It is found that the time splitting method does not allow convergence to steady state for any choice of finite values of the time step. Numerical experiments for some typical turbulent compressible flows support the fact that the time splitting method is always nonconvergent, while its nonsplitting counterpart is convergent.
MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76F60 \(k\)-\(\varepsilon\) modeling in turbulence
76F50 Compressibility effects in turbulence
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