A combined volume penalization / selective frequency damping approach for immersed boundary methods applied to high-order schemes

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with high-order methods (e.g., discontinuous Galerkin). For this combination effective, an analysis errors essential. In work, we apply, for first time, modified equation (based volume penalization) and nodal Galerkin methods) analyze priori practical guidelines selection parameters. performed linear advection-diffusion Dirichlet conditions. Three ways penalize immerse are considered, penalizes solution inside region (classic approach), whilst second third derivatives solution. We find optimal combinations penalization parameters, including penalizing derivatives, resulting in minimum errors. validate theoretical experiments one- two-dimensional equations.