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Pré-Publication, Document De Travail Année : 2015

Stability of a bidimensional relative velocity lattice Boltzmann scheme

Résumé

In this contribution, we study the theoretical and numerical stabilityof a bidimensional relative velocity lattice Boltzmann scheme. These relativevelocity schemes introduce a velocity field parameter called “relative velocity” functionof space and time. They generalize the d’Humières multiple relaxation timesscheme and the cascaded automaton. This contribution studies the stability of afour velocities scheme applied to a single linear advection equation according tothe value of this relative velocity. We especially compare when it is equal to 0(multiple relaxation times scheme) or to the advection velocity (“cascaded like”scheme). The comparison is made in terms of L1 and L2 stability. The L1stability area is fully described in terms of relaxation parameters and advectionvelocity for the two choices of relative velocity. These results establish that nohierarchy of these two choices exists for the L1 notion. Instead, choosing theparameter equal to the advection velocity improves the numerical L2 stability ofthe scheme. This choice cancels some dispersive terms and improve the numericalstability on a representative test case. We theoretically strengthen these resultswith a weighted L2 notion of stability.
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Dates et versions

hal-01150210 , version 1 (05-06-2015)

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François Dubois, Tony Février, Benjamin Graille. Stability of a bidimensional relative velocity lattice Boltzmann scheme. 2015. ⟨hal-01150210⟩
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