A unified interpolation stencil for ghost-cell immersed boundary method for flow around complex geometries

We propose a unified interpolation stencil that is used for a ghost-cell immersed boundary method to satisfy wall boundary conditions in Cartesian-based numerical simulation of fluid flow with complex boundaries. As other ghost-cell methods do, the numerical boundary point is considered in the solid region and the required velocity is interpolated directly from the proximate points in the fluid region. In this paper, we propose a unified interpolation scheme based on a sequence of one-dimensional interpolations. Different interpolation stencils are examined and their convergence rates are compared by solving a benchmark problem on the flow between the concentric cylinders. In contrast to typical standard stencils, the proposed ones are versatile and do not require to be altered according to the irregularities in boundary shape. Namely, the boundary condition can be accurately imposed with a unique stencil for all numerical boundary points while preserving the convergence rate of the flow solver. Performance of the proposed method is studied by solving two-dimensional incompressible flows around a circular cylinder, a square cylinder, and a square cylinder inclined with respect to the main flow. Comparison with the existing numerical and experimental data shows good agreement, which confirms the capability of the proposed method.