Adaptive mesh refinement for a sharp immersed boundary method

Advancements to an adaptive mesh refinement (AMR) method for sharp immersed boundary (IB) methods within a block-structured Cartesian mesh are presented. The block-structured Cartesian mesh is organized by a refinement level-based quad/octree data structure. The guard cell filling and prolongation-restriction operators that are used to transfer data between the different refinement levels rely on the use of guard cells which extend beyond the block boundary. In the presence of refinement jumps at the immersed boundary, the regular guard cell filling and prolongation-restriction operators fail. In this work, irregular operators are obtained which purely rely on the availability of valid solution data in the fluid domain. The method was implemented and tested within a higher-order immersed boundary method (IBM) Cartesian framework for solving the compressible Navier-Stokes equations (CNS). Error convergence studies were performed employing the method of manufactured solutions (MMS). Various test cases which utilize this method to solve different flow problems are also presented.