A mesh-based SDF reconstruction method and its application in multiphase fluid–structure interaction

Fictitious domain methods are widely used in fluid–structure interaction (FSI) simulations, where solid regions are commonly represented on a fixed Eulerian grid by indicator or level set functions. For practical engineering bodies with complex geometries, however, deriving an analytical signed distance function (SDF) is often difficult or impractical. To address this issue, we propose a mesh-based local projection (MLP) method for reconstructing the structural SDF directly from finite element surface meshes. The method combines nearest-node local projection with pseudo-normal sign determination, and a cell-linked list strategy is introduced to reduce the cost of repeated nearest-node searches. Accuracy tests show that the proposed method achieves approximately second-order convergence in the L 1 norm and an order of about 1.7 in the L 2 norm, while the L ∞ norm remains close to first order. The proposed MLP method is further compared with the second-order accurate mesh-based nearest-element (MNE) method, which provides higher pointwise accuracy through element-wise closest-distance evaluation. Although the MLP method is less accurate than the MNE method, the numerical results show that its accuracy is sufficient for practical FSI simulations. In the 2D wedge and 3D sphere cases, the rigid-body responses obtained with the MLP-reconstructed SDF are nearly identical to those obtained with analytical and MNE-reconstructed SDFs. The 2D bow-flare ship section and 3D inclined-cylinder cases further demonstrate the applicability of the method to complex geometries and 6-DOF water-entry dynamics. In practical water-entry simulations, replacing an analytical SDF with the cell-linked-list MLP reconstruction increases the wall-clock time by only 5.9% in two dimensions and 10.7% in three dimensions. The proposed method provides an efficient and practical approach for SDF construction in multiphase FSI simulations involving complex moving geometries.