In the literature immersed boundary methods are employed to simulate complex flows around moving arbitrary bodies without the necessity of remeshing. These methods employ a regular Eulerian mesh to simulate the fluid flow and a Lagrangian representation of the boundary of the bodies. The two representations can be coupled through an immersed boundary condition constraining the fluid to exactly follow the boundary of the bodies (immersed boundaries). Typically such methods suffer from accuracy problems, that arise from spurious mass fluxes over the immersed boundary (IB), pressure boundary conditions or high density ratios.
The mirroring IB method Mark (2008); Mark and van Wachem (2008) resolves these problems by ensuring zero mass flux over the IB instead of employing a pressure boundary condition. In this work the mirroring IB method together with a hybrid IB condition are implemented and validated in IBOFLOW. IBOFLOW is an incompressible finite-volume based fluid flow solver. The Navier-Stokes’ equations are coupled with the SIMPLEC method by Doormaal and Raithby (1984) and discretized on a Cartesian octree grid that can be dynamically refined and coarsened, enabling grid refinement to follow moving bodies. The variables are stored in a co-located configuration and pressure weighted flux interpolation by Rhie and Chow (1983) is employed to prevent pressure oscillations. In the implemented IB method the immersed bodies are represented by an analytical description or by a triangulation. The method models the presence of the bodies inside the fluid by an implicitly formulated IB condition, which constrains the fluid velocity to the boundary velocity with second-order accuracy. The original mirroring IB condition mirrors the velocity field over the local IB and the hybrid IB condition mirrors and extrapolates the fluid velocity onto the IB. These IB conditions generate a fictitious velocity field inside the bodies, which is excluded in the continuity equation to ensure zero mass flux over the boundary.
The fluid flow over an immersed sphere is simulated to validate and compare the different IB conditions. The simulated drag force is compared to experimental findings with excellent agreement and a detailed convergence study of the error of the fluid velocity integrated over the immersed boundary is performed to show the strictly second-order accuracy of the implemented IB conditions. It is shown that the error is reduced with the hybrid IB condition compared to the original mirroring IB condition. In addition, a sedimenting sphere with a moving grid refinement is simulated to validate the hybrid method and show the potential of the dynamic octree grid.
This work was supported in part by the Swedish Governmental Agency for Innovation Systems, VINNOVA, through the FFI Sustainable Production Technology program, and in part by the Sustainable Production Initiative and the Production Area of Advance at Chalmers. The support is gratefully acknowledged.
AUTHORS AND AFFILIATIONS
- R. Rundqvist, Fraunhofer-Chalmers Centre
- A. Mark, Fraunhofer-Chalmers Centre
- F. Edelvik, Fraunhofer-Chalmers Centre