Dynamic topology optimization of structure weakly coupled with two-phase flow

This study presents a new topology optimization method for transient two-phase fluid-structure interaction (FSI) problem. From a topology optimization point of view, it is formidable challenging to consider the mutual coupling with structure and two-phase flow and the evolution of sharp interface between two-phase flow (tracking interface). To tackle these formidable issues, the monolithic design approach incorporating with the deformation tensor is applied and the simulation of the two-phase flow is carried out with the volume of fluid (VOF). The spatially varying design variables in topology optimization determines whether the corresponding domains or elements are solid or fluid (two-phase flow) to maximize or minimize objective function. To simplify the coupling procedure and maintain the numerical convergence, the one-way coupling between two-phase fluid and structure is assumed rather than the two-way coupling. To carry out the topology optimization, the Darcy's force determined by the design variable is added to the Navier-Stokes equation and the Young's modulus and the structural density are also interpolated with respect to the design variables. In addition, the phase-field equation in the VOF method is also modified to take into account the evolution of the design variable and the front of the phase field value. To investigate the effect of the two-phase fluid-structure interaction, several transient two-dimensional problems are considered.