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Descripción
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| In Lattice Boltzmann methods (LBM), the responsibility of modelling the physic correctly lies with the collision operator, which it has an strong e?ect in the numerical stability. The single-relaxation time (SRT) based on the BGK [1] approximation is the most popular collision operator. The multiple-relaxation time, with raw moments (MRT-RM), was introduced [2] to overcome SRT stability limitations. In the latter, the collision process is carried out in momentum space instead of the usual velocity space. It has been demonstrated that the MRT-RM model is more stable than the SRT model [3], because the di?erent relaxation times can be individually adjusted to improve numerical stability. Despite its enhances properties, the MRT-RM has shown instabilities when selecting small viscosities [4]. This is to the lack of enough Galilean invariance. Consequently, the MRT with cascade central moments (MRT-CCM) was introduced [4, 5]. Unlike the MRT-RM where the di?erent relaxation times are adjusted individually for each moment; in the MRT-CCM, the higher moments are relaxed using the relaxation time of the lower moments. To understand the numerical behaviour of each model, von Neumann analysis has been introduced [3, 8, 7]. It is a procedure based on the Fourier decomposition that provides stability information and dispersion and dissipation errors. The aim of this work is to demonstrate the advantages of MRT-CCM against SRT and MRT-RM approaches through a von Neumann analysis. Figure shows the eigenvalues (?) against the wavenumber (k); where the scheme is unstable when Max(j?j) > 1. It can be seen that the MRT-RM becomes unstable at low viscosity while MRT-CCM remains stable . | |
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Internacional
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Si |
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Entidad
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26th International Conference on Discrete Simulation of Fluid Dynamics |
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Lugar
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Erlange, Alemania |
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Referencia/URL
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Tipo de publicación
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Ponencia |