A highly efficient and accurate Lagrangian–Eulerian stabilized collocation method (LESCM) for the fluid–rigid body interaction problems with free surface flow

Abstract

A Lagrangian–Eulerian stabilized collocation method (LESCM) for the fluid–structure interaction problems involving free surface flow is presented in this work, in which the structure is modeled by a rigid body. This method is an evolution of the material point method and particle-in-cell methods which are based on the hybrid Lagrangian–Eulerian description. The problem domain of the fluid and structures is discretized into the Lagrangian particles which carry the information, and the problem domain covering the entire movement space is discretized into the uniformly distributed Eulerian background nodes. The coupling governing equations of the fluid, structures and interfaces are solved by the meshfree stabilized collocation method (SCM) employing the reproducing kernel (RK) approximation on the Eulerian nodes. The solution is very efficient since the Eulerian nodes are set to be the initial positions in each time step and it is no need to reconstruct the shape function. The information mappings between the Lagrangian particles and the Eulerian nodes are also conducted by the RK approximation which can keep the mass and momentum conservation of the solution. The cell-cut algorithm is introduced to couple the fluid and the structures which can solve the fluid pressure and the fluid–structure interactional force simultaneously and avoid the complicated iterations of the traditional interaction algorithms. Several numerical examples including the collapse of water column with a rigid barrier, water entry of a half-buoyant circular cylinder and a rigid box rotating and sinking in water are simulated, which demonstrate the high accuracy, high efficiency and good stability of the proposed method. This method can be extensively applied to the engineering applications of fluid–rigid body interactions.