A hybrid lattice Boltzmann - Navier-Stokes method for unsteady aerodynamic and aeroacoustic computations
Résumé
A hybrid numerical method coupling the standard lattice Boltzmann method and a compressible finite-volume Navier-Stokes solver is proposed in the context of unsteady aerodynamic and aeroacoustic simulations. The trend being towards more realistic and detailed simulations in a reasonable amount of CPU time, lattice Boltzmann and Navier-Sokes methods can be combined to solve the same problem. The present hybrid method relies on a zonal decomposition of the computational domain thus allowing to exploit the numerical features of both methods to their optimal extent in specific flow regions.
The key issue when combining the lattice Boltzmann method with a Navier-Stokes solver is to ensure a smooth transition of the flow variables at the two-way coupling interface. While existing approaches consider overlapping meshes, a direct grid coupling is here derived. The mapping from the macroscopic flow variables to the set of lattice Boltzmann distribution functions is performed analytically thanks to a Chapman-Enskog expansion and draws a direct link to advanced regularised collision operators. Unsteady computations are enabled by coupling the lattice Boltzmann stream and collide algorithm with explicit and implicit Navier-Stokes time-stepping schemes. The hybrid method is then assessed on four time-dependent test cases representative of aerodynamic and aeroacoustic problems. The proposed approach is proven to yield very accurate results while keeping the numerical advantages of both methods and reducing the overall computational cost of direct noise computations.
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