An immersed boundary method for time-dependent, three-dimensional, incompressible flows is presented in this paper. The incompressible Navier-Stokes equations are discretized using a low-diffusion flux splitting method for the inviscid fluxes and second-order central-differences for the viscous components. Higher-order accuracy achieved by using weighted essentially non-oscillatory (WENO) or total variation diminishing (TVD) schemes. An implicit method based on artificial compressibility and dual-time stepping is used for time advancement. The immersed boundary surfaces are defined as clouds of points, which may be structured or unstructured. Immersed-boundary objects are rendered as level sets in the computational domain, and concepts from computational geometry are used to classify points as being outside, near, or inside the immersed boundary. The velocity field near an immersed surface is determined from separate interpolations of the components tangent and normal to the surface. The tangential velocity near the surface is constructed as a power-law function of the local wall normal distance. Appropriate choices of the power law enable the method to approximate the energizing effects of a turbulent boundary layer for higher Reynolds number flows. Five different flow problems (flow over a circular cylinder, an in-line oscillating cylinder, a NACA0012 airfoil, a sphere, and a stationary mannequin) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational and experimental results. Finally, the flow induced by realistic human walking motion is simulated as an example of a problem involving multiple moving immersed objects.
Bibliographical noteFunding Information:
This work has been supported by the US Environmental Protection Agency under contract 4C-R138-NAEX and by the Defense Advanced Research Projects Agency (DARPA) under Grant HR0011-04-1-0057. Computer resources were provided by the High Performance Computing component of North Carolina State University’s Information Technology Division ( www.ncsu.edu/itd/hpc ). The first author is grateful to Prof. HyungSeok Kim of Konkuk University and Dr. Xudong Xiao of North Carolina State University for their helpful suggestions regarding the surface definition of CAD-based immersed objects.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics