Comparison Between Different Immersed Boundary Conditions for Simulation of Complex Fluid Flows
Artikel i vetenskaplig tidskrift, 2011
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 Doormaal and
Raithby (1984) method 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 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.
immersed boundary condition
implicit method
mirroring immersed boundary method