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Derivation and analysis of lattice Boltzmann schemes for the linearized Euler equations. (English) Zbl 1357.76070
Summary: We derive Lattice Boltzmann (LBM) schemes to solve the linearized Euler equations in 1D, 2D, and 3D with the future goal of coupling them to an LBM scheme for Navier Stokes equations and a finite volume scheme for linearized Euler equations. The derivation uses the analytical Maxwellian in a BGK model. In this way, we are able to obtain second-order schemes. In addition, we perform an \(L^2\)-stability analysis. Numerical results validate the approach.

MSC:
76M28 Particle methods and lattice-gas methods
76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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