A high order 3D multiresolution immersed interface flow solver for flow-body interactions

We present a high order 3D multiresolution immersed interface solver for the incompressible Navier-Stokes equations with static and moving boundaries. The solver employs a finite difference discretization with immersed interface corrections near the boundaries to ensure a formally high order accurate treatment of complex, moving geometries. A modified pressure projection method is used within a Runge-Kutta time integration scheme to achieve high order spatial and temporal accuracy for both velocity and pressure. This algorithm is implemented within the wavelet-based multi-resolution adaptive grid framework 'MURPHY', where multilevel block-structured grids are represented using octree data structures. Dynamic grid adaptation and ghost reconstruction are performed using sixth order wavelets. In this algorithm, the pressure is computed using a fourth-order multigrid-preconditioned matrix-free iterative solver. We show convergence results for static and moving boundaries, along with results of verification cases and applications. In addition, we demonstrate the implementation's parallel scalability and performance on adaptive grids and complex boundaries, validating its effectiveness for large-scale simulations on massively parallel computing platforms.