A sharp interface Immersed Boundary approach for Simplified and Highly Stable Lattice Boltzmann Method

The Lattice Boltzmann Method is a mesoscopic approach and has been used for some time as a computational fluid dynamics solver. The recently developed Simplified and Highly Stable Lattice Boltzmann Method(SHSLBM) simplifies the boundary condition implementation to a great extent as it can be implemented using the macroscopic variables instead of distribution functions in traditional Lattice Boltzmann Method. Moreover, it can simulate incompressible flows without evolution of the distribution function, making it less computationally expensive. However, it is still a challenge to implement it for flow around geometry not aligned with the mesh. Immersed Boundary Method is used for the flow around geometries without body fitted mesh; generally a solid body is immersed into the Cartesian mesh. In Lattice Boltzmann Method, usually a Cartesian mesh is used. Therefore, the Immersed Boundary Method is an ideal choice to extend SHSLBM to simulate flow around geometries not aligned with the mesh. In the present work, for the first time a sharp interface Immersed Boundary approach, using ghost nodes, is implemented for the boundary treatment of the non-aligned geometry for SHSLBM. The implementation is verified and validated using multiple test cases. The macroscopic flow variables are extrapolated to the ghost (solid) nodes using a Least-Square technique. The method is implemented for both boundary types namely, Neumann and Dirichlet. The test cases include, Poiseuille flow, inclined Poiseuille flow, Womersley flow, inclined Womersley flow, lid driven cavity flow, inclined lid-driven cavity flow and flow around circular and square cylinders. • Immersed boundary method integrated with the Simplified and Highly Stable LBM. • Accurate simulation of flows around curved and non-mesh-aligned boundaries. • Stable treatment of immersed boundaries with good mass conservation.