Eigensolution analysis of immersed boundary method based on volume penalization: Applications to high-order schemes

This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization the linear advection equation. approach is used to analyze behavior of flux reconstruction (FR) discretization, including influence polynomial order parameter numerical errors stability. Through a semi-discrete analysis, we find that inclusion IBM adds additional dissipation without changing significantly dispersion original discretization. agrees with physical intuition in this type approach, solid wall modelled as porous medium vanishing viscosity. From stability point view, selection penalty can be analyzed fully-discrete which leads practical guidelines parameter. Numerical experiments indicate term needs increased damp oscillations inside (i.e. region), undesirable time step restrictions. As an alternative, propose include second-order no-slip condition. Results show by adding improve overall accuracy relaxed restriction. indicates optimal value damping carefully chosen obtain more accurate scheme. Finally, approximated relationship between these two parameters obtained guideline select optimum terms Navier-Stokes solver, simulate flow past cylinder.