An Interpolation-Based Lattice Boltzmann Method For Non-Conforming Orthogonal Meshes

We propose an interpolation-based lattice Boltzmann formulation that is applicable to non-conforming orthogonal meshes. This interpolation configuration allows the use of localized and directional refinement that reduces mesh sizes and makes them well adapted for solving flows in various configurations, including aerodynamic shapes in free streams. The novel aspect of the proposed method lies in the interpolation scheme selection algorithm, which uses local mesh topology for choosing a suitable combination of nodes and polynomial terms. The objective of this study consists of validating the scheme accuracy with well documented laminar incompressible flow test cases. The results demonstrate the capability of the proposed interpolation method to successfully solve closed and open flows with either straight or curved walls. Simulations for the flow over a NACA 0012 airfoil show that the aerodynamic coefficients are captured correctly using a mesh with large aspect