Analysis, numerics, and implementation of Kinetic-Continuum coupling using Lattice-Boltzmann methods

The direct simulation of the acoustic far-field generated by turbulent flows comprises very different scales, from the Kolmogorov scale for the turbulent flow to the far-field of acoustics. The disparity of these scales is further increased if porous materials are introduced as silencers. In order to allow for simulations of real world problems, a coupled approach applying appropriate solvers to the turbulent near-field and the acoustic far-field is required. This thesis is part of an effort applying a Lattice-Boltzmann solver solving the weakly compressible Navier-Stokes equations to the turbulent flow and a very-high-order Discontinuous Galerkin solver solving the linearized Euler equations to the acoustic far-field. A two-step coupling methodology, reducing the viscosity on the Lattice-Boltzmann level with subsequent coupling to macroscopic quantities on the Discontinuous Galerkin level, and corresponding building blocks are proposed. For this, consistent Lattice-Boltzmann methods for the linearized Navier-Stokes and lineraized Euler equations are developed for compressible flows with vanishing background velocity and isothermal flows with and without background velocity. A priori stability results are found for compressible and isothermal flows with vanishing background velocity and for inviscid, isothermal flows with background velocity and backed by numerical results. Additional novel Lattice-Boltzmann methods for isothermal flows with background velocity are presented. A consistent approach for gradual reduction of the viscosity on the Lattice-Boltzmann level is derived and numerically confirmed. A strategy for approximation of spatial derivatives of macroscopic from mesoscopic quantities is presented but found to suffer from problematic error constants