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.

Grid refinement in the three-dimensional hybrid recursive regularized lattice Boltzmann method for compressible aerodynamics.

Grid refinement techniques are of paramount importance for computational fluid dynamics approaches relying on the use of Cartesian grids. This is especially true of solvers dedicated to aerodynamics, in which the capture of thin shear layers require the use of small cells. In this paper, a three-dimensional grid refinement technique is developed within the framework of hybrid recursive regularized lattice Boltzmann method (HRR-LBM) for compressible high-speed flows, which is an efficient collide-stream-type method on a compact D3Q19 stencil. The proposed method is successfully assessed considering several test cases, namely, an isentropic vortex propagating through transition interface, shock-vortex interaction with intersection between grid refinement interface and shock corrugation, and transonic flows over three-dimensional DLR-M6 wing with seven levels of grid refinement.

Minimum enstrophy principle for two-dimensional inviscid flows around obstacles.

Large-scale coherent structures emerging in two-dimensional flows can be predicted from statistical physics inspired methods consisting in minimizing the global enstrophy while conserving the total energy and circulation in the Euler equations. In many situations, solid obstacles inside the domain may also constrain the flow and have to be accounted for via a minimum enstrophy principle. In this work, we detail this extended variational formulation and its numerical resolution. It is shown from applications to complex geometries containing multiple circular obstacles that the number of solutions is enhanced, allowing many possibilities of bifurcations for the large-scale structures. These phase change phenomena can explain the downstream recombinations of the flow in rod-bundle experiments and simulations.

Low Mass-Damping Vortex-Induced Vibrations of a Single Cylinder at Moderate Reynolds Number.

The feasibility and accuracy of large eddy simulation is investigated for the case of three-dimensional unsteady flows past an elastically mounted cylinder at moderate Reynolds number. Although these flow problems are unconfined, complex wake flow patterns may be observed depending on the elastic properties of the structure. An iterative procedure is used to solve the structural dynamic equation to be coupled with the Navier-Stokes system formulated in a pseudo-Eulerian way. A moving mesh method is involved to deform the computational domain according to the motion of the fluid structure interface. Numerical simulations of vortex-induced vibrations are performed for a freely vibrating cylinder at Reynolds number 3900 in the subcritical regime under two low mass-damping conditions. A detailed physical analysis is provided for a wide range of reduced velocities, and the typical three-branch response of the amplitude behavior usually reported in the experiments is exhibited and reproduced by numerical simulation.

Trajectory of an optical vortex in atmospheric turbulence.

Trajectory of an optical vortex has been identified for its propagation in atmospheric turbulence using numerical simulations. An analytical expression has been found, relating the radial departure of the vortex in plane perpendicular to the direction of propagation, to the refractive index structure function parameter and the inner scale of turbulence. The angular orientation of the vortex in the same transverse plane is found to be related to the anisotropy of the medium. The obtained results provide an alternative way to find turbulent parameters with the help of optical vortices.

Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows.

An exact relationship for the local skin friction is derived for the compressible turbulent wall-bounded flow (channel, pipe, flat plate). This expression is an extension of the compressible case of that derived by Fukagata [Phys. Fluids 14, L73 (2002)] in the case of incompressible wall-bounded flows. This decomposition shows that the skin friction can be interpreted as the contribution of four physical processes, i.e., laminar, turbulent, compressible, and a fourth coming from the interaction between turbulence and compressibility. Compressible numerical simulations show that, even at Mach number M=2 , the main contribution comes from the turbulence, i.e., the Reynolds stress term.