A monolithic Lagrangian meshfree scheme for Fluid–Structure Interaction problems within the OTM framework

We present a monolithic Lagrangian meshfree solution for Fluid–Structure Interaction (FSI) problems within the Optimal Transportation Meshfree (OTM) framework. The governing equations of the fluid and structure are formulated in the Lagrangian configuration and solved simultaneously in a monolithic way. Mainly, the fully discretized equations are constructed by leveraging on the OTM method to address the challenges in the Lagrangian description of the fluid domain. In this approach, the fluid–structure interface becomes an internal surface of the entire field, and the continuity and force equilibrium on the interface are automatically satisfied without any extra computations. The monolithic Lagrangian solution provides enhanced stability comparing to partitioning approaches and eliminates the problem of free surface and material interface tracking. The presented method enables a Direct Numerical Simulation (DNS) of the fluid flow with the absence of the convective terms. The accuracy and robustness of the OTM FSI approach are systematically investigated by the classical Blasius solution of the boundary layer problem. Furthermore, we illustrate the range and scope of the method through two examples: the impact of a rigid body on the fluid domain in a container and the interaction between the fluid and highly flexible structures in an open channel.