A multiphase IFED method for fluid-structure interactions

Wei Chang

doi:10.1016/j.jcp.2026.114699

A multiphase IFED method for fluid-structure interactions

2026-01-22

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AI

魏昶 (Wei Chang)

H

Haotian Liu

DOI：10.1016/j.jcp.2026.114699

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The immersed finite element/difference (IFED) method is a numerical framework for modeling fluid-structure interaction in single-phase flows. In this work, the IFED method is extended to multiphase FSI with emphasis on deformable structures. The proposed approach preserves the geometric flexibility for deformable structures and integrates the level set method to capture phase interfaces. The gas-liquid interface is tracked by advecting a level set, whereas the structural level set is explicitly reconstructed to produce a discrete signed distance field on the Cartesian grid. Once the level set fields are available, fluid density and viscosity are assigned via regularized Heaviside functions to smooth interfacial transitions. Fluid-structure coupling follows the IFED method, in which a force-spreading operator spreads Lagrangian forces onto the Cartesian grid, and a velocity-restriction operator transfers Eulerian velocities back to the structural mesh. These operators are implemented within the multiphase framework. A limitation of the original IFED formulation is the homogeneous time-step coupling that imposes the same time step on fluid and solid subdomains. To address this, a time-splitting scheme is proposed using two Lagrangian representations: the original mesh interacts with the fluid without structural constitutive response, and the auxiliary mesh is coupled to the former via a penalty force formulation. This allows the structural elastodynamic equations to be solved multiple times within each fluid time step using a standard Galerkin finite element method on the auxiliary mesh. The resulting material response is transmitted back to the original mesh as another penalty body force, which is subsequently used to compute the Eulerian force density. The proposed scheme is applicable to both the original IFED method and its multiphase extension. Two 2D dam-break tests indicate that the multiphase IFED method provides accurate predictions for deformable structures with low to moderate stiffness. For high-stiffness structures, the time-splitting scheme achieves achieves a speedup of about 3.8 times in the Turek-Hron test at Gs=2×107 Pa relative to the original version, solely by increasing structural substeps. A dam-break impact test involving a deformable body with Es=5.0×1010 Pa further demonstrates the effectiveness of the time-splitting scheme. The study provides new insights into the modeling of multiphase FSI problems involving deformable structures.

A multiphase IFED method for fluid-structure interactions

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