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Regularized characteristic boundary conditions for the lattice-Boltzmann methods at high Reynolds number flows. (English) Zbl 1378.76097

Summary: This paper reports the investigations done to adapt the characteristic boundary conditions (CBC) to the lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then, all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (\(Re = 10^5\)), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (finite difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.

MSC:

76M28 Particle methods and lattice-gas methods
76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics

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