We present a simple and efficient fluid-solid coupling method in two and three spatial dimensions. In particular, we consider the numerical approximation of the Navier-Stokes equations on irregular domains and propose a novel approach for solving the Hodge projection step on arbitrary shaped domains. This method is straightforward to implement and leads to a symmetric positive definite linear system for both the projection step and for the implicit treatment of the viscosity. We demonstrate the accuracy of our method in the L1 and L∞ norms and present its removing the errors associated with the conventional rasterization-type discretizations. We apply this method to the simulation of a flow past a cylinder in two spatial dimensions and show that our method can reproduce the known stable and unstable regimes as well as correct lift and drag forces. We also apply this method to the simulation of a flow past a sphere in three spatial dimensions at low and moderate Reynolds number to reproduce the known steady axisymmetric and non-axisymmetric flow regimes. We further apply this algorithm to the coupling of flows with moving rigid bodies.
Bibliographical noteFunding Information:
The research of Y.T. Ng and F. Gibou were supported in part by a Sloan Research Fellowship in Mathematics, by the National Science Foundation under grant agreement DMS 0713858 , by the Institute for Collaborative Biotechnologies through contract No. W911NF-09-D-0001 from the U.S. Army Research Office and by the Department of Energy under grant agreement DE-FG02-08ER15991 . The research of C. Min was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) ( KRF-2008-331-C00045 ).
- Hodge decomposition
- Irregular domain
- Navier-Stokes equations
- Solid-fluid interaction