An improved volumetric LBM boundary approach and its extension for sliding mesh simulation
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The lattice Boltzmann method (LBM) has been emerging as a promising alternative CFD approach for complex fluid flows. With LBM, no-slip/free-slip wall boundary conditions are implemented via straightforward particle bounce-back/specular reflections on a solid surface, thus enable the use of Cartesian grid for accurate boundary representation. For curved boundary that is commonly encountered with complex geometry, available point-wise based LBM extrapolation/interpolation boundary schemes can not guarantee the exact hydrodynamic flux conditions. To address this fundamental issue, a volumetric LBM boundary scheme was proposed in 1998, which ensures an exact treatment of hydrodynamic fluxes on solid surface and establishes a generic framework for realizing hydrodynamic boundary conditions on curved surface.
This dissertation presents the development of an improved volumetric LBM boundary scheme. The basic idea is when reflecting (scattering) back the fluid particles from solid boundary, particles should be distributed in the affected volume according to local flow information rather than uniformly as in the original volumetric LBM boundary formulation. To realize this, a scattering correction procedure is formulated and added to the originally proposed volumetric LBM boundary scheme framework. In particular, the procedure redistributes the surface scattered particles based on local velocity variation. As a result, it reduces the solution dependence on actual boundary location/orientation with respect to the computational grid, demonstrates an improved order of accuracy for flow solutions with arbitrarily located boundary. Accuracy of this approach has been demonstrated on typical flow benchmark problems that involve curved boundaries. In the second part of this dissertation, the proposed volumetric LBM boundary scheme is extended to sliding-mesh interface condition for flow simulation involving rotating geometries. A volumetric LBM sliding-mesh interface scheme couples the flow solutions on both sides of sliding interface, and conserves the mass and momentum flux across it. Accuracy of this scheme is demonstrated by performing a LBM-sliding mesh simulation of flow past a rotating propeller.