Application of compact and multioperator approximations in the immersed boundary method

Schemes with nonlocal approximations (compact and multioperator) are used in the immersed boundary method. Their accuracy and convergence are analyzed in the case of a model problem. For the flow over a cylinder, the numerical results based on the compressible Navier–Stokes equations are compared with available numerical and experimental data. The cases of low, moderate, and high Reynolds numbers are considered.