A three-dimensional curve interface reconstruction algorithm for two-phase fluid flow

The curve interface reconstruction algorithm has received significant attention in the context of two-dimensional two-phase flow. However, it remains absent in the three-dimensional scenario. This paper proposes a novel three-dimensional curve interface reconstruction (CIR) algorithm to address this challenge within structured meshes for the first time. Specifically, a portion of the spherical surface is employed to reconstruct the three-dimensional curve interface segment, with the radius and center coordinates determined by curvature and mass conservation constraints, respectively. To enhance curvature accuracy, a sphere-based iterative reconstruction (SIR) algorithm is proposed to calculate the reconstructed distance function (RDF) for the three-dimensional curve interface. Various tests involving the interface reconstruction of spherical, ellipsoidal, and cubic objects demonstrate that the coupled SIR and CIR (SIR-CIR, simplified by SCIR) method achieves higher accuracy than many popular methods, particularly with coarse mesh resolutions. Additionally, the SCIR method offers the advantages of straightforward implementation and coding for interface reconstruction in two-phase flow research. This advantage results in reduced computational costs compared to the coupled volume-of-fluid and level set (VOSET) method, which also utilizes an iterative method to solve RDF.