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On the search of more stable second-order lattice-Boltzmann schemes in confined flows. (English) Zbl 1349.76684
J. Comput. Phys. 294, 605-618 (2015); corrigendum ibid. 311, 374 (2016).
Summary: The von Neumann linear analysis, restricted by a heuristic selection of wave-number vectors was applied to the search of explicit lattice Boltzmann schemes which exhibit more stability than existing methods. The relative stability of the family members of quasi-incompressible collision kernels, for the Navier-Stokes equations in confined flows, was analyzed. The linear stability analysis was simplified by assuming a uniform velocity level over the whole domain, where only the wave numbers of the first harmonic normal to the flow direction were permitted. A singular equilibrium function that maximizes the critical velocity level was identified, which was afterwards tested in particular cases of confined flows of interest, validating the resulting procedure.

76M28 Particle methods and lattice-gas methods
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