Special Session 139: Recent advances in modeling and simulation of interfacial dynamics

How does Tspan4 shape migrasomes?

Zhenlin Guo Beijing Computational Science Research Center Peoples Rep of China Co-Author(s):    Zhenlin Guo

Abstract: Migrasomes are membrane-bound organelles whose mechanics remain poorly understood. Here, we develop a phase-field model to reveal how Tspan4 regulates migrasome behavior via membrane tension redistribution. We show that growth-induced membrane stretching generates tension gradients and stiffness heterogeneity, driving vertical elongation and a strong correlation between geometry and stiffness. By varying Tspan4 expression, we demonstrate that increased Tspan4 enhances bending rigidity and accelerates tension redistribution, stabilizing migrasomes, whereas Tspan4 depletion leads to central tension accumulation and higher rupture susceptibility. These findings identify membrane tension redistribution as a key mechanism linking Tspan4 expression to migrasome mechanics and stability

Geometric local parameterization for solving Hele-Shaw problems with surface tension

Wenrui Hao Penn State University USA Co-Author(s):

Abstract: We present a computational framework for solving the two-dimensional Hele Shaw free boundary problem with surface tension using a mesh free point cloud representation of the moving interface. By avoiding global parameterization, the method naturally accommodates complex and evolving geometries. Our approach leverages Generalized Moving Least Squares to construct local geometric charts on the boundary, enabling accurate approximation of geometric quantities such as curvature directly from scattered points. This local structure is used to discretize the boundary integral formulation of the problem, with singular integrals evaluated through analytical expressions to maintain high accuracy. We provide a convergence analysis establishing consistency and stability of the spatial discretization, with error bounds depending on point cloud density, boundary smoothness, and quadrature order. Numerical experiments confirm spatial convergence and demonstrate robust evolution of complex initial interfaces toward circular equilibrium under surface tension.

Heterogeneous simulations for interfacial magnetization dynamics

Guanghui Hu University of Macau Macau Co-Author(s):    Zheng Zekai

Abstract: The precise capture of interfacial magnetization dynamics, such as domain wall motion and skyrmion evolution at heterostructure interfaces, remains a formidable challenge in computational spintronics due to the high non-linearity and multiscale nature of the governing equations. This talk presents recent progress in developing a high-performance simulation framework for the Landau-Lifshitz-Gilbert equation. We focus on a synergistic approach that integrates high-order structure-preserving numerical schemes with GPU-accelerated heterogeneous computing. The numerical framework consists of a structure preserving temporal discretization and finite element spatial discretization. A treecode algorithm is designed and implemented in GPU to significantly accelerate the simulations. Numerical experiments demonstrate that our framework provides competitive performance and flexibility on handling complex geometry of the domain, for resolving the dynamics of the domain wall, as well as skyrmion structures.

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

Ming-Chih Lai National Yang Ming Chiao Tung University Taiwan Co-Author(s):    Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Chieh-Hsin Lai

Abstract: Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space-time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades accuracy and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose Time-Induced Neural Networks (TINNs), a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg-Marquardt method. Experiments on various time-dependent PDEs show up to $4\times$ improved accuracy and $10\times$ faster convergence compared to PINNs and strong baselines.

A structure-preserving finite element scheme and its error analysis for a diffuse-interface tumor growth model

Ping Lin University of Dundee Scotland Co-Author(s):

Abstract: We will discuss a diffuse-interface (phase-field) model for tumor growth that takes into account nutrient consumption and chemotaxis. For this tumor growth model described by a nonlinear system consisting of a Cahn--Hilliard-type equation coupled with a reaction-diffusion equation, we constructed an efficient scheme based on the idea of the scalar auxiliary variable (SAV), which we show are not only decoupled and easy to implement, but also have the properties of mass conservation and unconditional energy stability. Furthermore, we derive rigorous error estimates for the fully discrete finite element scheme. Several numerical examples are presented to validate the accuracy, mass conservation and energy dissipation of the proposed scheme, and to illustrate complex biological phenomena, including the aggregation of multiple tumors of varying shapes and chemotaxis-driven growth patterns. The talk is based on two joint papers with Z Wang and J Yang, and with A Soenjaya and T Tran.

Variational Modelling and Numerical Simulations for Evaporating Thin Droplets and Coffee-Ring Effect

Tiezheng Qian Hong Kong University of Science and Technology Peoples Rep of China Co-Author(s):

Abstract: Sessile liquid droplets on solid surfaces are ubiquitously found in nature and engineered applications. Out of the many physical processes involved in droplet dynamics, two have been of continuous interest. The first is the moving contact line at which the evolving liquid-gas interface intersects the solid surface. The second is the evaporation at the liquid-gas interface for evaporating droplets. Coupled to both the moving contact line on the substrate and the liquid flow in the droplet, interfacial evaporation plays a critical role in controlling droplet dynamics. Based on our earlier works on moving contact line and thin-film dynamics, we derive a continuum model for evaporating thin droplets by applying Onsager`s variational principle. This approach ensures thermodynamical consistency in describing the coupling of many dissipative processes, including viscous momentum transport, contact line motion, evaporation, and vapor diffusion. Numerical results are presented to exhibit the diffusion-limited regime and the transition-limited regime, which are distinct from each other. The coffee-ring phenomena are also numerically investigated for particle-laden droplets. This work is supported by the Hong Kong RGC General Research Fund (No. 16302525) and the Key Project of the National Natural Science Foundation of China (No. 12131010).

Mathematical modeling, analysis and numerical investigation of ion active transport with free boundaries

Yuzhe Qin Shanxi University Peoples Rep of China Co-Author(s):    Huaxiong Huang, Zilong Song, Shixin Xu

Abstract: We study a diffusive interface model for ion active transport through free boundaries. By an energy-variation approach, we derive a phase-field system that couples the order parameter, species concentrations, electrostatic potential, and incompressible flow, and establish an energy dissipation law. A sharp interface limit analysis is carried out to connect the diffuse-interface model with the corresponding free-boundary formulation. Based on the thermodynamically consistent structure, we design an unconditionally energy stable scheme. Numerical tests in one and two dimensions validate the model and demonstrate key features of active transport, with additional comparisons to results reported in the literature. The proposed framework provides a consistent modeling and simulation tool for ion transport with restricted diffusion across membranes.

Moving contact lines on elastic sheets

Weiqing Ren National University of Singapore Singapore Co-Author(s):

Abstract: We investigate the motion of a thin liquid drop on highly bendable elastic sheets. Under the lubrication approximation, we derive a coupled system of fourth-order partial differential equations, together with appropriate boundary and contact line conditions, to describe the evolution of both the fluid interface and the elastic sheet. Using matched asymptotic analysis in the limit of small slip length, we extend the classical Cox-Voinov relation to incorporate the effects of substrate elasticity. The extended relation is validated through numerical simulations. One key implication is that, compared with a rigid substrate, a soft substrate retards drop spreading but enhances receding dynamics.

Macroscopic modeling and simulations for thin film with moving contact lines

Xianmin XU Chinese Academy of Sciences Peoples Rep of China Co-Author(s):    Si Xiao

Abstract: Thin liquid films with contact lines are common in nature and in engineering applications. The existence of free boundaries and singularities poses significant challenges for both modeling and computation. In this talk, we present a unified framework for the derivation and numerical approximation of a fourth-order thin film equation with mesoscopic dynamic boundary conditions. The reduced model is systematically derived using the Onsager variational principle in conjunction with lubrication theory, yielding a thermodynamically consistent formulation that accounts for capillarity, gravity, and external force. To solve the resulting free boundary problem, we develop adaptive moving mesh methods based on a discrete Onsager variational principle, including a stabilized semi-implicit scheme to improve computational efficiency. Numerical results confirm the optimal convergence of the proposed methods and accurately capture key wetting behaviors, including contact angle hysteresis on rough substrates. This work offers a robust framework for simulating thin film flows with complex geometries.

Multilevel Schwarz Methods for the Coupled Stokes-Darcy Problem

Haicheng Zhang Heidelberg University Germany Co-Author(s):

Abstract: We present a monolithic multigrid solver for a strongly mass-conservative mixed finite element discretization of the coupled Stokes-Darcy problem. An overlapping Schwarz smoother is employed, and different treatments of boundary degrees of freedom are compared. In particular, we investigate the effect of velocity and pressure boundary conditions in the Darcy subdomain, as well as the inclusion of boundary unknowns in the vertex patches. Numerical results show that the convergence behavior, especially for the pressure, strongly depends on the smoother design. With a consistent treatment of boundary degrees of freedom, the proposed method is robust and requires less than 10 iterations for high-order discretizations.