Cartesian mesh adaptation: Immersed boundary method based on high-order discontinuous Galerkin method

Immersed boundary method (IBM) can easily distinguish fluid and solid regions in the computational region, thereby the workload of complex grid generation can be reduced. To accurately characterize the solid geometry, a large number of cells are required near the solid surface. The h-adaptive algorithm is adopted to reduce the requirement for the number of cells. In addition, considering the inherent adaptability to the h-adaptive Cartesian grids of the discontinuous Galerkin method, a high-order discontinuous Galerkin solver with an IBM is developed. To validate the h-adaptive algorithm and the solver, three cases are tested, including the steady flow past the National Advisory Committee for Aeronautics 0012 airfoil, the steady flow past a cylinder, and the unsteady flow past a cylinder. Compared with the non-adaptive cases, the h-adaptive cases need smaller total number of cells, and the numerical accuracy is significantly improved with an increasing degree of mesh refinement.