Comparison Between Different Immersed Boundary Conditions for Simulation of Complex Fluid Flows

In the literature immersed boundary methods are employed tosimulate complex flows around moving arbitrary bodies without thenecessity of remeshing. These methods employ a regular Eulerian meshto simulate the fluid flow and a Lagrangian representation of theboundary of the bodies. The two representations can be coupled throughan immersed boundary condition constraining the fluid to exactlyfollow the boundary of the bodies (immersed boundaries). Typicallysuch methods suffer from accuracy problems, that arise from spuriousmass fluxes over the immersed boundary (IB), pressure boundaryconditions or high density ratios. The mirroring IB method Mark(2008); Mark and van Wachem (2008) resolves these problems by ensuringzero mass flux over the IB instead of employing a pressure boundarycondition. In this work the mirroring IB method together with a hybridIB condition are implemented and validated in IBOFLOW. IBOFLOW is anincompressible finite-volume based fluid flow solver. TheNavier-Stokes' equations are coupled with the SIMPLEC Doormaal andRaithby (1984) method and discretized on a Cartesian octree grid thatcan be dynamically refined and coarsened, enabling grid refinement tofollow moving bodies. The variables are stored in a co-locatedconfiguration and pressure weighted flux interpolation Rhie and Chow(1983) is employed to prevent pressure oscillations. In theimplemented IB method the immersed bodies are represented by ananalytical description or by a triangulation. The method models thepresence of the bodies inside the fluid by an implicitly formulated IBcondition, which constrains the fluid velocity to the boundaryvelocity with second-order accuracy. The original mirroring IBcondition mirrors the velocity field over the local IB and the hybridIB condition mirrors and extrapolates the fluid velocity onto the IB.These IB conditions generate a fictitious velocity field inside thebodies, which is excluded in the continuity equation to ensure zeromass flux over the boundary. The fluid flow over an immersed sphere issimulated to validate and compare the different IB conditions. Thesimulated drag force is compared to experimental findings withexcellent agreement and a detailed convergence study of the error ofthe fluid velocity integrated over the immersed boundary is performedto show the strictly second-order accuracy of the implemented IBconditions. It is shown that the error is reduced with the hybrid IBcondition compared to the original mirroring IB condition. Inaddition, a sedimenting sphere with a moving grid refinement issimulated to validate the hybrid method and show the potential of thedynamic octree grid.