Derivation and Analysis of Lattice Boltzmann Schemes for the Linearized Euler Equations
This work provides a foundational step for coupling LBM with other solvers, but the results are incremental as they extend existing methods to a new set of equations.
The authors derive Lattice Boltzmann schemes for the Linearized Euler Equations in 1D, 2D, and 3D, achieving second-order accuracy and demonstrating stability via L^2 analysis, with numerical validation.
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 an 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.