Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid
This work provides a numerical analysis for a specific fluid-structure interaction problem, but the results are incremental and lack quantitative benchmarks.
The paper extends a penalization method to model a rigid body moving freely in an incompressible viscous fluid, treating the fluid-solid system as a single variable density flow with a level set interface. Numerical illustrations demonstrate convergence, though no concrete performance numbers are provided.
We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given. [1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)