An interface and geometry preserving phase-field method for fully Eulerian fluid-structure interaction

Abstract

We present an interface and geometry preserving (IGP) method for modeling fully Eulerian fluid-structure interaction via phase-field formulation. While the time-dependent mobility model preserves the hyperbolic tangent interface profile, the proposed method maintains the geometry of the solid-fluid interface by minimizing the volume-conserved mean curvature flow. To reduce the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field retains the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the isosurfaces of the order parameter, alleviating the undesired thickening or thinning of the diffuse interface region due to the convection. As a result, the time-dependent mobility coefficient is substantially reduced and there is a lesser volume-conserved mean curvature flow. Furthermore, the GMV ensures that the diffuse interface region moves with the solid bulk despite the fluid flow, such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum and mass conservation equations via the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian fluid-structure interaction solver based on the incompressible viscous fluid and the neo-Hookean solid models. The kinematics of the solid in an Eulerian frame of reference is resolved by evolving the left Cauchy-Green tensor. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces in a prescribed velocity field. The variational fluid-structure interaction framework with the IGP method is then examined on the deformation of a solid block under cavity flow. We next explore the geometry-preserving effect of the proposed framework when the fluid flow passes over a fixed deformable block in a channel. Finally, the vibration of a flexible plate attached behind a stationary cylinder is considered to demonstrate the ability of the framework in solving unsteady fluid-structure interaction problems.