This article deals with artificial boundaries which you encounter when a large spatial domain is confined to a smaller computational domain. Such an artificial boundary condition should not preferably interact with the fluid at all. Standard boundary conditions, e.g., a pressure or velocity condition, result in unphysical reflections. So far, existing artificial boundary conditions for the lattice Boltzmann method (LBM) are transferred from macroscopic formulations.In this work we propose novel discrete artificial boundary conditions (ABCs) which are tailored on the LBM's mesoscopic level. They are derived directly for the chosen LBM with the aim of higher accuracy. We describe the idea of discrete ABCs in a three velocity (D1Q3) model governing the Navier Stokes equations in one dimension. Numerical results finally demonstrate the superiority of our new boundary condition in terms of accuracy compared to previously used ABCs. (C) 2015 Elsevier Ltd. All rights reserved.

When using a lattice Boltzmann method on an unbounded (or very large) domain one has to confine this spatial domain to a computational domain. This is realized by introducing so-called artificial boundary conditions. Until recently, characteristic boundary conditions for the Euler equations were considered and adapted to the lattice Boltzmann method.In this work we propose novel discrete artificial boundary conditions which are derived directly for the chosen lattice Boltzmann model, i.e., on the discrete level. They represent the first exact artificial boundary conditions for lattice Boltzmann methods. Doing so, we avoid any detour of considering continuous equations and obtain boundary conditions that are perfectly adapted to the chosen numerical scheme. We illustrate the idea for a one dimensional, two velocity (D1Q2) lattice Boltzmann method and show how the computational efficiency can be increased by a finite memory approach. Analytical investigations and numerical results finally demonstrate the advantages of our new boundary condition compared to previously used artificial boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

For numerically solving fluid dynamics problems efficiently one is often facing the problem of having 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): so-called 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.