arXiv subjects

Yunhao Qiu

Publications and source records attributed to Yunhao Qiu.

2 recordsLinked to original sources

arXiv2025

A linear MARS method for three-dimensional interface tracking

For explicit interface tracking in three dimensions, we propose a linear MARS method that (a) represents the interface by a partially ordered set of glued surfaces and approximates each glued surface with a triangular mesh, (b) maintains an $(r,h,\theta)$-regularity on each triangular mesh so that the distance between any pair of adjacent markers is within the range $[rh,h]$ and no angle in any triangle is less than $\theta$, (c) applies to three-dimensional continua with arbitrarily complex topology and geometry, (d) preserves topological structures and geometric features of moving phases under diffeomorphic and isometric flow maps, and (e) achieves second-order and third-order accuracy in terms of the Lagrangian and Eulerian length scales, respectively. Results of classic benchmark tests verify the effectiveness of the novel mesh adjustment algorithms in enforcing the $(r,h,\theta)$-regularity and demonstrate the high accuracy and efficiency of the proposed linear MARS method.

math.NA↗

arXiv2025

On Topology of Three-dimensional Continua with Singular Points

We propose to model the topology of three-dimensional (3D) continua by Yin sets, regular open semianalytic sets with bounded boundary. Our model differs from manifold-based models in that singular points of a 3D continuum, i.e., boundary points where the tangent plane is not uniquely defined, are treated not as anomalies but as a central subject of our theoretical investigation. We characterize the local and global topology of Yin sets. Then we give a unique boundary representation of Yin sets based on the notion of a glued surface, a quotient space of an orientable compact 2-manifold along a one-dimensional CW complex. Our results apply to 3D continua with arbitrarily complex topology and may be useful in a number of scientific and engineering applications such as solid modeling, computer-aided design, and numerical simulations of multiphase flows with topological changes.

math.GT↗