A combined ghost-point-forcing / direct-forcing immersed boundary method (IBM) for compressible flow simulations

Abstract

The present manuscript describes the implementation of an immersed boundary method (IBM) into a compressible reactive multicomponent Navier-Stokes solver. The latter makes use of high-order accuracy discretization schemes applied on structured Cartesian grids. For the immersed boundary method, both direct-forcing and ghost-point-forcing schemes are considered. The direct-forcing source term, which is added to the three components of the Navier–Stokes (NS) equations, i.e. the momentum equations, is used to impose the no-slip boundary conditions at the fluid-body interface. It is combined with a ghost-point-forcing scheme to enforce both mass conservation and boundary conditions in the scalar equations (density, energy and species mass fractions). The discretization of the three-dimensional surface associated to the solid geometry is obtained from a triangulation, which is handled within the stereo-lithography (STL) data format. The immersed boundary is thus represented with a finite number of Lagrangian points, which are associated to the centers of gravity of the elementary triangles. The major components of the IBM procedure include the data structure itself, the determination of the status of the computational nodes, i.e. fluid, ghost or solid, the interpolation rules and the forcing model. The performance of the resulting immersed boundary scheme is investigated by considering a large set of two-dimensional benchmarks including a cylinder placed in either subsonic or supersonic flows, a subsonic airflow on a flat plate, moving-shock interactions with various obstacles. Numerical results are satisfactorily compared with available theoretical, experimental, and numerical data. The capabilities of the method are then illustrated on more representative flowfields such as two-dimensional non-reactive and reactive high-speed flows developing over rectangular cavities and three-dimensional supersonic flows over a rigid body.