Characteristic boundary conditions in the lattice Boltzmann method for fluid and gas dynamics

For numerically solving fluid dynamics problems efficiently one is often facing the problem that one has to confine the computational domain to a small domain of interest introducing so-called non-reflecting boundary conditions (NRBCs). In this work we address the problem of supplying NRBCs in fluid simulations in two space dimensions using the lattice Boltzmann method (LBM): socalled characteristic boundary conditions are revisited and transferred to the framework of lattice Boltzmann simulations. Numerical tests show clearly that the unwanted unphysical reflections can be reduced significantly by applying our newly developed methods. Hereby the key idea is to transfer and generalize Thompson’s boundary conditions originally developed for the nonlinear Euler equations of gas dynamics to the setting of lattice Boltzmann methods. Finally, we give strong numerical evidence that the proposed methods possess a long-time stability property.