Linear lattice Boltzmann schemes for acoustic: Parameter choices and isotropy properties

Isotropy Conditions for Lattice Boltzmann Schemes . Application to D 2 Q 9 ∗

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 of isotropy can be read through a group...

Implicit Schemes for the Lattice Boltzmann Equation

Adjoint Lattice Boltzmann Equation for Parameter Identification

The Lattice Boltzmann Equation is briefly introduced using moments to clearly separate the propagation and collision steps in the dynamics. In order to identify unknown parameters we introduce a cost function and adapt control theory to the Lattice Boltzmann Equation to get expressions for the derivatives of the cost function vs. parameters. This leads to an equivalent of the adjoint method wit...

On rotational invariance of lattice Boltzmann schemes

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 method. The details of the implementation ar...

Towards higher order lattice Boltzmann schemes

In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of the lattice Boltzmann scheme proposed by d’Humières [11] at an arbitrary order of accuracy. We derive formally the associated dynamical equations for classical thermal and linear fluid models in one to three space dimensions. We use this approach...