# Regularized characteristic boundary conditions for the Lattice-Boltzmann methods at high Reynolds number flows

## TL;DR

This paper adapts and tests various characteristic boundary conditions within the Lattice-Boltzmann framework for high Reynolds number flows, identifying the most effective methods and necessary regularization for stability.

## Contribution

It introduces and compares three CBC formalisms in LBM for high Reynolds number flows, proposing a regularized finite difference approach for numerical stability.

## Key findings

- LS-LODI best for acoustic waves
- CBC-2D excels with vortices
- Regularized FD approach ensures stability at high Reynolds numbers

## Abstract

This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number ($Re = 10^5$), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (Finite Difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.