arXiv subjects

Shintaro Matsushita

Publications and source records attributed to Shintaro Matsushita.

4 recordsLinked to original sources

arXiv2026

Weakly Compressible Subcycling for Accelerating Simulations of Surface-Tension-Dominated Incompressible Two-Phase Flows

Simulations of surface-tension-dominated incompressible two-phase flows are computationally expensive due to the severe capillary time-step constraint. Although many studies have proposed time-implicit discretizations of surface tension to allow larger time-step sizes and accelerate simulations, these methods suffer from either artificial dissipation or complex implementation. Here, we propose a simple and novel approach: an incompressible solver with weakly compressible subcycling. The proposed approach relaxes the capillary time-step constraint, thereby accelerating simulations by more than $8.6\times$ without relying on artificially dissipative stabilization or requiring complex implementation. The key idea is to introduce lightweight substeps using a weakly compressible solver to assist the main incompressible solver. These substeps enable the main incompressible solver to use accurately computed fluxes and surface tension force, even with large time-step sizes. Numerical tests demonstrate the effectiveness of the proposed approach for practical problems, including the Rayleigh--Plateau instability and two-phase flows in porous media. This study paves the way for a new paradigm in which a weakly compressible solver serves as an assistant to an incompressible solver.

physics.flu-dyn↗

arXiv2026

Efficient Pattern Matching for Unordered Term Tree Patterns under Generalized Height-Constrained Bindings

Unordered trees are useful for modeling hierarchical structures in which the order among siblings is irrelevant. To represent flexible structural patterns in such data, unordered term tree patterns with height-constrained variables provide a natural framework. In our previous work, we studied the pattern matching problem for rooted unordered term tree patterns with height-constrained variables under the restriction that the child port of each variable must correspond to a leaf of a binding tree. In this paper, we remove this restriction and generalize the binding model so that the child port may correspond to any non-root vertex of a binding tree. Under generalized bindings, we formulate the corresponding membership problem and present a polynomial-time pattern matching algorithm. We also implement the proposed algorithm and conduct computational experiments to evaluate its running time. The experimental results show that the proposed method achieves practical running times.

cs.DS↗

arXiv2026

Efficient Pattern Matching in Unordered Term Tree Patterns with Height Constraints

Unordered trees appear in applications where the order among child vertices is insignificant, such as abstract syntax trees and chemical structures. To describe patterns in such trees, we propose unordered term tree patterns, which employ height-constrained variables that restrict trunk length and subtree height. We formalize the pattern matching problem between an unordered term tree pattern and an unordered tree, and present an $O(N \cdot \max\{nD^{3/2}, \mathcal{S}\})$-time algorithm, where $n$ and $N$ are the numbers of vertices in the pattern and tree, $D$ is the maximum vertex degree, and $\mathcal{S}$ is the sum of trunk constraints. Computational results show that the algorithm runs efficiently in practice.

cs.DS↗

arXiv2026

Enhanced numerical approaches for modeling insoluble surfactants in two-phase flows with the diffuse-interface method

Surfactants reside at the interface of two-phase flows and significantly influence the flow dynamics. Numerical simulations are essential for a comprehensive understanding of such surfactant-laden flows and require a method that can accurately simulate surfactant transport along the interface. In this study, we focus on interfacial transport models for insoluble surfactants based on the diffuse-interface method and propose two approaches to improve their accuracy: (a) adopting a formulation that avoids the spatial derivatives of variables with sharp gradients and (b) allowing the width of the delta function to be specified independently of the interface width. These approaches are simple and practical in that they do not lead to significant increases in computational cost, implementation complexity, or degradation of interface-capturing accuracy. Moreover, they preserve the discrete conservation of both fluid and surfactant mass. We conduct a series of numerical tests to demonstrate the effectiveness of the proposed approaches. Finally, we present a challenging test case that is difficult to solve accurately and has not been previously discussed. We expect this case to serve as a valuable benchmark for evaluating and comparing the performances of various methods proposed in the literature.

physics.flu-dyn↗