Constrained moving least-squares immersed boundary method for fluid-structure interaction analysis

A numerical method is presented for the analysis of interactions of inviscid and compressible flows with arbitrarily shaped stationary or moving rigid solids. The fluid equations are solved on a fixed rectangular Cartesian grid by using a higher-order finite difference method based on the fifth-order WENO scheme. A constrained moving least-squares sharp interface method is proposed to enforce the Neumann-type boundary conditions on the fluid-solid interface by using a penalty term, while the Dirichlet boundary conditions are directly enforced. The solution of the fluid flow and the solid motion equations is advanced in time by staggerly using, respectively, the third-order Runge-Kutta and the implicit Newmark integration schemes. The stability and the robustness of the proposed method have been demonstrated by analyzing 5 challenging problems. For these problems, the numerical results have been found to agree well with their analytical and numerical solutions available in the literature. Effects of the support domain size and values assigned to the penalty parameter on the stability and the accuracy of the present method are also discussed.