A stabilised immersed boundary method on hierarchical b-spline grids for fluid–rigid body interaction with solid–solid contact

Abstract

An accurate, efficient and robust numerical scheme is presented for the simulation of the interaction between flexibly-supported rigid bodies and incompressible fluid flow with topology changes and solid–solid contact. The solution of the incompressible Navier–Stokes equations is approximated by employing a stabilised formulation on Cartesian grids discretised with hierarchical b-splines. The solid is modelled as a rigid body and represented by linear segments along its boundary. Kinematic conditions along the fluid–rigid body interface are enforced weakly using Nitsche’s method, while ghost penalty operators are employed to avoid excessive ill-conditioning of the system matrix arising from small cut cells. A staggered scheme is used for resolving the coupled fluid–rigid body interaction. The contact between moving or moving and fixed solid bodies is modelled with Lagrange multipliers. The excellent performance and wide range of applicability of the proposed scheme are demonstrated in a number of benchmark tests as well as industrially relevant model problems. The examples cover the galloping phenomena, particulate flow, hydraulic check valves and a model turbine.