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In this paper, we recall the linear version of the lattice Boltzmann schemes in the framework proposed by d’Humières. According to the equivalent equations we introduce a definition for a scheme to be isotropic at some order. This definition is chosen such that the equivalent equations are preserved by orthogonal transformations of the frame. The property… (More)

- Adeline Augier, François Dubois, Loïc Gouarin, Benjamin Graille
- Computers & Mathematics with Applications
- 2013

Abstract. In this paper, we investigate the numerous parameters choices for linear lattice Boltzmann schemes according to the definition of the isotropic order given in [3]. This property—written in a general framework including all of the DdQq schemes—can be read through a group operation. It implies some relations on the parameters of the scheme… (More)

In this paper we study the acoustic properties of a microstructured material such as glass wool or foam. In our model, the solid matrix is governed by linear elasticity and the surrounding fluid obeys Stokes equations. The microstructure is assumed to be periodic at some small scale ε and the viscosity coefficient of the fluid is assumed to be of order ε.… (More)

- Adeline Augier, François Dubois, Benjamin Graille, Pierre Lallemand
- Computers & Mathematics with Applications
- 2014

We propose the derivation of acoustic-type isotropic partial differential equations that are equivalent to linear lattice Boltzmann schemes with a density scalar field and a momentum vector field as conserved moments. The corresponding linear equivalent partial differential equations are generated with a new “Berliner version” of the Taylor expansion… (More)

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