Development of a Moving-Least-Square-based Immersed Boundary Method for the simulation of viscous Compressible Flows

In this paper, a Moving-Least-Squares (MLS)-based immersed boundary method (IBM) for simulating viscous compressible flows is proposed. For this method, the compressible lattice Boltzmann flux solver (LBFS) is used to solve the flow field on the Eulerian mesh and the MLS-based IBM introduced in present paper is used to implement boundary condition. The discrete Lagrangian points are used to represent the Solid boundaries. A second-order MLS interpolation is used for numerical exchange between two grids of IBM. The forced implicit boundary condition is adopted to ensure that the physical boundary condition can be accurately satisfied. The present method is able to achieve a higher numerical accuracy than traditional IBM, which use the Delta function for interpolation. Some numerical validation tests are used for the validation of proposed method. The order and accuracy of the MLS approximation are tested by using a classical example of flow past a cylinder. Test of flow past the NACA0012 airfoil at different Mach numbers, angles of attack and Reynolds numbers is applied to verified the accuracy.