An Improved Sharp-Interface Immersed Boundary Method for Compressible Flows Using State Observers.

The development of Immersed Boundary Methods (IBM) has increased in popularity during the last decades, especially for the simulation of flows around complex geometries and/or moving objects. Different IBM approaches are available in the literature, whose features are tailored for specific physical conditions. Sharp-interface IBM is generally suited for the simulation of compressible flows as it allows to capture relatively well complex flow features near the immersed boundary. However, the common implementation of this approach needs dedicated flow solvers, where the solid domain is not solved.

In this work, we present a novel sharp-interface IBM which can be easily integrated and used with existing CFD solvers. In the proposed implementation, the solid domain is solved and the immersed boundary conditions (pressure, velocity and temperature) are imposed through optimized source terms in the flow governing equations (mass, momentum and energy equations). These sources are determined via a state observer. This method was implemented in a dedicated C++ library and linked to rhoCentralFoam solver of the open source software OpenFOAM. The simulation of a compressible flow around a sphere at Mach 2 and Reynolds number 300 showed a good agreement with reference results in the literature in terms of the shock standoff distance, the re-circulation bubble size and drag coefficient. In addition, heat exchange features at the surface of the immersed body are also accurately represented.