High-order stable interpolations for immersed boundary methods

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange, and least squares high-order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier-Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two-dimensional Taylor-Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three-dimensional flow in an air-conditioning exhaust pipe.