Fluid Structure Interaction Using Modal Superposition and Lagrangian CFD

Abstract

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa.