Compressible lattice Boltzmann method with rotating overset grids.

The numerical instability of the lattice Boltzmann method (LBM) at high Mach or high Reynolds number flow is well identified, and it remains a major barrier to its application in more complex configurations such as moving geometries. This work combines the compressible lattice Boltzmann model with rotating overset grids (the so-called Chimera method, sliding mesh, or moving reference frame) for high Mach flows. This paper proposes to use the compressible hybrid recursive regularized collision model with fictitious forces (or inertial forces) in a noninertial rotating reference frame. Also, polynomial interpolations are investigated, which allow fixed inertial and rotating noninertial grids to communicate with each other. We suggest a way to effectively couple the LBM with the MUSCL-Hancock scheme in the rotating grid, which is needed to account for thermal effect of compressible flow. As a result, this approach is demonstrated to have an extended Mach stability limit for the rotating grid. It also demonstrates that this complex LBM scheme can maintain the second-order accuracy of the classic LBM by appropriately using numerical methods like polynomial interpolations and the MUSCL-Hancock scheme. Furthermore, the method shows a very good agreement on aerodynamic coefficients compared to experiments and the conventional finite-volume scheme. This work presents a thorough academic validation and error analysis of the LBM for simulating moving geometries in high Mach compressible flows.

Impact of collision models on the physical properties and the stability of lattice Boltzmann methods.

The lattice Boltzmann method (LBM) is known to suffer from stability issues when the collision model relies on the BGK approximation, especially in the zero viscosity limit and for non-vanishing Mach numbers. To tackle this problem, two kinds of solutions were proposed in the literature. They consist in changing either the numerical discretization (finite-volume, finite-difference, spectral-element, etc.) of the discrete velocity Boltzmann equation (DVBE), or the collision model. In this work, the latter solution is investigated in detail. More precisely, we propose a comprehensive comparison of (static relaxation time based) collision models, in terms of stability, and with preliminary results on their accuracy, for the simulation of isothermal high-Reynolds number flows in the (weakly) compressible regime. It starts by investigating the possible impact of collision models on the macroscopic behaviour of stream-and-collide based D2Q9-LBMs, which clarifies the exact physical properties of collision models on LBMs. It is followed by extensive linear and numerical stability analyses, supplemented with an accuracy study based on the transport of vortical structures over long distances. In order to draw conclusions as generally as possible, the most common moment spaces (raw, central, Hermite, central Hermite and cumulant), as well as regularized approaches, are considered for the comparative studies. LBMs based on dynamic collision mechanisms (entropic collision, subgrid-scale models, explicit filtering, etc.) are also briefly discussed. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.