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Von Neumann stability analysis for MRT LBM
Research Areas
  • Aeronautical engineering
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 .
26th International Conference on Discrete Simulation of Fluid Dynamics
Erlange, Alemania
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26th International Conference on Discrete Simulation of Fluid Dynamics
  • Autor: Miguel Chavez Modena (UPM)
  • Autor: Esteban Ferrer Vaccarezza (UPM)
  • Autor: Gonzalo Rubio Calzado (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Métodos y Aplicaciones Numéricas a la Tecnología Aeroespacial
  • Departamento: Matemática Aplicada a la Ingeniería Aeroespacial
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