LAUSR

Abstract In this paper, a fully Lagrangian formulation for solving rigid–liquid coupling system with free surface is proposed, in which the spatial absolute nodal coordinates and the pressure of liquid are taken as the independent variables, combining the stabilized particle finite element method and multibody algorithms for unified modeling. The virtual contact elements generated in the remeshing process are used to identify the contact nodes on the liquid–solid interface, and the free-slip boundary constraints are imposed by the Lagrange multipliers. For the position deviation of the interface nodes on the concave-curved boundary at a large time step, a position correction strategy is given. In addition, in order to control the numerical dissipation in the simulation, the implicit generalized- α time integration strategy with second-order accuracy is used to solve the differential algebraic equations of the system. Finally, several numerical examples are studied to verify the mass conservation characteristics of the algorithm under coarse mesh and relatively large time steps, and the pressure calculation results are compared with the experimental results reported in the literature, which shows the stability and accuracy of the algorithms proposed.