An adaptive harmonic polynomial cell method with immersed boundaries: Accuracy, stability, and applications

We present a 2D high-order and easily accessible immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method to solve fully nonlinear wave-structure interaction problems in marine hydrodynamics using potential-flow theory. To reduce the total number of cells without losing accuracy, quad-tree refinements are employed close free-surface structure boundaries. The is simpler implement than existing IB-HPC alternatives, that it uses standard square both fluid domain at boundaries, thus having use more complex expensive overlapping grids or irregular cells. spurious force oscillations on moving structures, which known issue for immersed boundary methods (IBMs), eliminated this study by solving separate value problem (BVP) Lagrangian acceleration potential. also demonstrate similar BVP corresponding Eulerian potential far less satisfactory due involved second derivatives velocity body-boundary condition, very difficult calculate accurately an IBM-based approach. In addition, we present, perhaps first time since HPC was developed, linear matrix-based stability analysis time-domain IB-AHPC method. used as general guide design robust stable numerical algorithms, particular related treatment conditions intersection between Dirichlet Neumann boundary, essential analyses IBMs. confirm theoretically through have best properties. has been verified validated satisfactorily various cases hydrodynamics, including infinite fluid, wave generation propagation, diffraction radiation ship cross section.