A total energy formulation for lattice Boltzmann method with overset grids
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Modelling rotating geometries immersed in fluid flows remains a challenge for industrial applications today. In particular, in the context of lattice Boltzmann Methods (LBM), a gap remains to be filled regarding rotating geometries in compressible flows. Building on previous developments in the subject, this work proposes a new formulation in the LBM context, based on the hybrid recursive regularized (HRR) collision model and overset grids. A non-inertial rotating grid is used to simulate the movement of a rigid solid, and communicates with a fixed grid through linear interpolations. The total energy equation in the rotating domain is expressed as a function of the relative quantities and solved using a hybrid finite difference-LBM [2] strategy to evaluate the flux part of the equation. The efficiency of the method, as well as its drawbacks, are assessed and discussed through test cases of increasing complexity and at different Mach numbers. The results are compared to previous works to evaluate its capacity to handle flow fields with discontinuities. Finally, the relevance of the method is discussed in the context of rotating geometries at transonic regimes.
