arXiv subjects

Xin Bian

Publications and source records attributed to Xin Bian.

At least 19 recordsLinked to original sources

arXiv2026

An SPH--mesh Coupling for Vesicle Dynamics in Shear Flow

We present a novel computational framework that couples smoothed particle hydrodynamics~(SPH) with a triangulated membrane mesh to simulate the dynamics of vesicles suspended in fluids. A novel interface-tracking approach enforces membrane impermeability naturally, without resorting to non-physical constraints such as particle reflection or bounce-back boundary conditions. The membrane model incorporates four distinct bending energy formulations, namely the minimal model, the spontaneous curvature (SC) model, the bilayer couple (BC) model, and the area difference elasticity (ADE) model, providing a versatile tool for diverse biophysical scenarios. The framework is rigorously validated against equilibrium shapes and tank-treading motion of a vesicle, demonstrating excellent agreement with previous theoretical and numerical studies. A systematic investigation into the effects of each bending model on the vesicle's inclination angle, revolution frequency, and morphology in shear flow reveals key physical insights. Notably, spontaneous curvature has a negligible effect on steady-state orientation but profoundly alters rotational dynamics at low reduced volumes through the emergence of dumbbell-like shapes with deep constrictions. In contrast, the BC and ADE models induce characteristic asymmetric and stomatocyte morphologies. Our results establish the proposed SPH--mesh coupling as an accurate and robust tool for exploring the complex, shape-dependent dynamics of vesicles in fluid flows.

physics.flu-dyn↗

arXiv2026

Emergence of a Flow-Assisted Casting Strategy for Olfactory Navigation via Memory-Augmented Reinforcement Learning

In dynamic flow fields, various animals exhibit remarkable odor search capabilities despite relying on stochastic detections. Interestingly, there exists an optimal time window for integrating these detections that maximizes search efficiency. To understand the underlying mechanism, we investigate the navigation performance of Reinforcement Learning (RL) agents in unsteady flows under varying memory lengths and flow conditions. Without any predefined models, the agents develop a flow-assisted casting strategy and adaptively adjust both the geometry of their search trajectories and the concentration threshold for initiating casting to maximize the success rate. The agent's average speed toward the odor source exhibits a non-monotonic dependence on memory length, which can be explained by the "sector-search" model.

cs.LG↗

arXiv2026

Deep learning accelerated solutions of incompressible Navier-Stokes equations on non-uniform Cartesian grids

In incompressible flow simulations, non-uniform grids efficiently capture localized flow features; however, their spatially varying resolutions severely exacerbate computational complexity. The pressure Poisson equation (PPE) formulated on these grids yields highly complex linear systems, forming the primary computational bottleneck in fractional step method. To address this, we develop an extended hybrid framework tailored for non-uniform Cartesian grids, integrating deep learning with classical iterative solvers to accelerate PPE solutions. Specifically, the framework employs a deep operator network with a U-Net-based branch network. To effectively capture spatially varying resolutions, we propose a multi-level distance vector map construction strategy that computes discrete grid-spacing information corresponding to each hierarchical level of the U-Net. This grid-spacing information is explicitly fused into feature maps prior to convolution operations. Empowered by this grid-spacing-aware architecture, the framework seamlessly extends to simulate flows interacting with solid structures using a decoupled immersed boundary projection method. By training exclusively on fabricated linear systems rather than conventional flow-dependent datasets, the model generalizes effortlessly across diverse immersed obstacle geometries with fixed network weights. Benchmark results demonstrate that the framework significantly outperforms standalone preconditioned conjugate gradient methods and its standard convolution counterpart, underscoring its exceptional potential for real-world computational fluid dynamics applications.

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arXiv2025

Effects of External Magnetic Fields on the Multi-mode Rayleigh-Taylor Instability

The magneto-Rayleigh-Taylor instability (mRTI) is a key process in inertial confinement fusion and is thought to be widespread in the interstellar medium, where it can concentrate plasma into discrete structures. We present resistive MHD simulations of the nonlinear evolution of multi-mode mRTI in both two and three dimensions, examining the effects of uniform external magnetic fields oriented either parallel or perpendicular to the initial interface. In both 2-D and 3-D, weak parallel fields enhance mixing-zone growth, whereas stronger fields suppress it. For perpendicular fields, growth is initially inhibited but becomes enhanced at later times. These behaviors arise from magnetic tension, which modifies flow anisotropy, buoyancy, drag, and vortex dynamics. The interplay of these mechanisms governs the distinct ways in which magnetic fields influence mRTI evolution.

physics.flu-dyn↗

arXiv2025

Hybrid deep learning and iterative methods for accelerated solutions of viscous incompressible flow

The pressure Poisson equation, central to the fractional step method in incompressible flow simulations, incurs high computational costs due to the iterative solution of large-scale linear systems. To address this challenge, we introduce HyDEA, a novel framework that synergizes deep learning with classical iterative solvers. It leverages the complementary strengths of a DeepONet - capable of capturing large-scale features of the solution - and the CG or a PCG method, which efficiently resolves fine-scale errors. Specifically, within the framework of line-search methods, the DeepONet predicts search directions to accelerate convergence in solving sparse, symmetric-positive-definite linear systems, while the CG/ PCG method ensures robustness through iterative refinement. The framework seamlessly extends to flows over solid structures via the decoupled immersed boundary projection method. Crucially, the DeepONet is trained on fabricated linear systems rather than flow specific data, endowing it with inherent generalization across geometric complexities and Reynolds numbers without retraining. Benchmarks demonstrate superior efficiency and accuracy of HyDEA over the CG/PCG methods for flows with no obstacles, single or multiple stationary obstacles, and one moving obstacle - using fixed network weights. Remarkably, HyDEA also exhibits super-resolution capability: although the DeepONet is trained on a 128*128 grid for Re=1000, the hybrid solver delivers accurate solutions on a 512*512 grid for Re=10000 via interpolation, despite discretizations mismatch. In contrast, a purely data-driven DeepONet fails for complex flows, underscoring the necessity of hybridizing deep learning with iterative methods. Robustness, efficiency, and generalization across geometries, resolutions, and Reynolds numbers of HyDEA highlight its potential as a transformative solver for real world fluid dynamics problems.

physics.flu-dyn↗

arXiv2025

Physics-informed neural networks for hidden boundary detection and flow field reconstruction

Simultaneously detecting hidden solid boundaries and reconstructing flow fields from sparse observations poses a significant inverse challenge in fluid mechanics. This study presents a physics-informed neural network (PINN) framework designed to infer the presence, shape, and motion of static or moving solid boundaries within a flow field. By integrating a body fraction parameter into the governing equations, the model enforces no-slip/no-penetration boundary conditions in solid regions while preserving conservation laws of fluid dynamics. Using partial flow field data, the method simultaneously reconstructs the unknown flow field and infers the body fraction distribution, thereby revealing solid boundaries. The framework is validated across diverse scenarios, including incompressible Navier-Stokes and compressible Euler flows, such as steady flow past a fixed cylinder, an inline oscillating cylinder, and subsonic flow over an airfoil. The results demonstrate accurate detection of hidden boundaries, reconstruction of missing flow data, and estimation of trajectories and velocities of a moving body. Further analysis examines the effects of data sparsity, velocity-only measurements, and noise on inference accuracy. The proposed method exhibits robustness and versatility, highlighting its potential for applications when only limited experimental or numerical data are available.

physics.flu-dyn↗

arXiv2025

Dynamics of an elliptical cylinder in confined Poiseuille flow under Navier slip boundary conditions

A comprehensive understanding of surface wetting phenomena in microchannels is essential for optimizing particle transport and filtration processes. This study numerically investigates the dynamics of a freely suspended elliptical cylinder in confined Poiseuille flow, with a focus on Navier slip boundary conditions. The smoothed particle hydrodynamics method is employed, which is advantageous for its Lagrangian framework in handling dynamic fluid-solid interfaces with slip. Our results demonstrate that the slip conditions enable precise control over inertial focusing positions and particle motion modes. Compared to no-slip scenarios, unilateral wall slip induces two novel motion types: "leaning" and "rolling". When equal slip lengths are applied to both walls, even small slip values facilitate off-center inertial focusing and elevate equilibrium positions. Slip on the cylinder surface further enhances inertial lift while suppressing rotational dynamics. In particular, under strong confinement or with large particle-surface slip lengths, we identify an additional distinct motion regime termed "inclined." These findings provide new insights for active particle manipulation in microfluidic applications.

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arXiv2024

An unstructured adaptive mesh refinement for steady flows based on physics-informed neural networks

Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain, where gradients or error estimates of the solution are often considered as the refining criteria. In many scenarios, however, these indicators can lead to unnecessary refinement over a large region, making the process a matter of trial and error and resulting in slow convergence of the computation. To this end, we propose a heuristic strategy that employs the residuals of the governing partial differential equations (PDEs) as a novel criterion to adaptively guide the mesh refining process. In particular, we leverage on the physics-informed neural networks (PINNs) to integrate imprecise data obtained on a coarse mesh and the governing PDEs. Once trained, PINNs are capable of identifying regions of highest residuals of the Navier-Stokes/Euler equations and suggesting new potential vertices for the coarse mesh cells. Moreover, we put forth two schemes to maintain the quality of the refined mesh through the strategic insertion of vertices and the implementation of Delaunay triangulation. By applying the residuals-guided AMR to address a multitude of typical incompressible/compressible flow problems and comparing the outcomes with those of gradient-based methods, we illustrate that the former effectively attains a favorable balance between the computational accuracy and cost.

physics.flu-dyn↗

arXiv2024

Simulating squirmers with smoothed particle dynamics

Microswimmers play an important role in shaping the world around us. The squirmer is a simple model for microswimmer whose cilia oscillations on its spherical surface induce an effective slip velocity to propel itself. The rapid development of computational fluid dynamics methods has markedly enhanced our capacity to study the behavior of squirmers in aqueous environments. Nevertheless, a unified methodology that can fully address the complexity of fluid-solid coupling at multiple scales and interface tracking for multiphase flows remains elusive, posing an outstanding challenge to the field. To this end, we investigate the potential of the smoothed particle dynamics (SPD) method as an alternative approach for simulating squirmers. The Lagrangian nature of the method allows it to effectively address the aforementioned difficulty. By introducing a novel treatment of the boundary condition and assigning appropriate slip velocities to the boundary particles, the SPD-squirmer model is able to accurately represent a range of microswimmer types including pushers, neutral swimmers, and pullers. We systematically validate the steady-state velocity of the squirmer, the resulting flow field, its hydrodynamic interactions with the surrounding environment, and the mutual collision of two squirmers. In the presence of Brownian motion, the model is also able to correctly calculate the velocity and angular velocity autocorrelation functions at the mesoscale. Finally, we simulate a squirmer within a multiphase flow by considering a droplet that encloses a squirmer and imposing a surface tension between the two flow phases. We find that the squirmer within the droplet exhibits different motion types.

physics.flu-dyn↗

arXiv2024

Data-driven modeling of unsteady flow based on deep operator network

Time-dependent flow fields are typically generated by a computational fluid dynamics (CFD) method, which is an extremely time-consuming process. However, the latent relationship between the flow fields is governed by the Navier-Stokes equations and can be described by an operator. We therefore train a deep operator network, or simply DeepONet, to learn the temporal evolution between flow snapshots. Once properly trained, given a few consecutive snapshots as input, the network has a great potential to generate the next snapshot accurately and quickly. Using the output as a new input, the network iterates the process, generating a series of successive snapshots with little wall time. Specifically, we consider 2D flow around a circular cylinder at Reynolds number 1000, and prepare a set of high-fidelity data using a high-order spectral/hp element method as ground truth. Although the flow fields are periodic, there are many small-scale features in the wake flow that are difficult to generate accurately. Furthermore, any discrepancy between the prediction and the ground truth for the first snapshots can easily accumulate during the iterative process, which eventually amplifies the overall deviations. Therefore, we propose two alternative techniques to improve the training of DeepONet. The first one enhances the feature extraction of the network by harnessing the "multi-head non-local block". The second one refines the network parameters by leveraging the local smooth optimization technique. Both techniques prove to be highly effective in reducing the cumulative errors and our results outperform those of the dynamic mode decomposition method.

physics.flu-dyn↗

arXiv2023

Self-supervised learning based on Transformer for flow reconstruction and prediction

Machine learning has great potential for efficient reconstruction and prediction of flow fields. However, existing datasets may have highly diversified labels for different flow scenarios, which are not applicable for training a model. To this end, we make a first attempt to apply the self-supervised learning (SSL) technique to fluid dynamics, which disregards data labels for pre-training the model. The SSL technique embraces a large amount of data ($8000$ snapshots) at Reynolds numbers of $Re=200$, $300$, $400$, $500$ without discriminating between them, which improves the generalization of the model. The Transformer model is pre-trained via a specially designed pretext task, where it reconstructs the complete flow fields after randomly masking $20\%$ data points in each snapshot. For the downstream task of flow reconstruction, the pre-trained model is fine-tuned separately with $256$ snapshots for each Reynolds number. The fine-tuned models accurately reconstruct the complete flow fields based on less than $5\%$ random data points within a limited window even for $Re=250$ and $600$, whose data were not seen in the pre-trained phase. For the other downstream task of flow prediction, the pre-training model is fine-tuned separately with $128$ consecutive snapshot pairs for each corresponding Reynolds number. The fine-tuned models then correctly predict the evolution of the flow fields over many periods of cycles. We compare all results generated by models trained via SSL and models trained via supervised learning, where the former has unequivocally superior performance. We expect that the methodology presented here will have wider applications in fluid mechanics

physics.flu-dyn↗

arXiv2023

Physics-informed neural networks for unsteady incompressible flows with time-dependent moving boundaries

Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel extension, which enables PINNs to solve incompressible flows with time-dependent moving boundaries. More specifically, we impose Dirichlet constraints of velocity at the moving interfaces and define new loss functions for the corresponding training points. Moreover, we refine training points for flows around the moving boundaries for accuracy. This effectively enforces the no-slip condition of the moving boundaries. With an initial condition, the extended PINNs solve unsteady flow problems with time-dependent moving boundaries and still have the flexibility to leverage partial data to reconstruct the entire flow field. Therefore, the extended version inherits the amalgamation of both physics and data from the original PINNs. With a series of typical flow problems, we demonstrate the effectiveness and accuracy of the extended PINNs. The proposed concept allows for solving inverse problems as well, which calls for further investigations.

physics.flu-dyn↗

arXiv2023

Dynamics of a droplet in shear flow by smoothed particle hydrodynamics

We employ a multi-phase smoothed particle hydrodynamics (SPH) method to study droplet dynamics in shear flow. With an extensive range of Reynolds number, capillary number, wall confinement, and density/viscosity ratio between the droplet and the matrix fluid, we are able to investigate systematically the droplet dynamics such as deformation and breakup. We conduct the majority of the simulations in two dimensions due to economical computations, while perform a few representative simulations in three dimensions to corroborate the former. Comparison between current results and those in literature indicates that the SPH method adopted has an excellent accuracy and is capable of simulating scenarios with large density or/and viscosity ratios. We generate slices of phase diagram in five dimensions, scopes of which are unprecedented. Based on the phase diagram, critical capillary numbers can be identified on the boundary of different states. As a realistic application, we perform simulations with actual parameters of water droplet in air flow to predict the critical conditions of breakup, which is crucial in the context of atomization.

physics.flu-dyn↗

arXiv2023

Arbitrary slip length for fluid-solid interface of arbitrary geometry in smoothed particle dynamics

We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity at quasi-steady state near the interface, an arbitrary slip length $b$ can be specified and correspondingly, an artificial velocity for every boundary particle can be calculated. Therefore, $b$ as an input parameter affects the calculation of dissipative and random forces near the interface. For $b \to 0$, the no-slip is recovered while for $b \to \infty$, the free-slip is achieved. Technically, we devise two different approaches to calculate the artificial velocity of any boundary particle. The first has a succinct principle and is competent for simple geometries, while the second is subtle and affordable for complex geometries. Slip lengths in simulations for both steady and transient flows coincide with the expected ones. As demonstration, we apply the two approaches extensively to simulate curvy channel flows, dynamics of an ellipsoid in pipe flow and flows within complex microvessels, where desired slip lengths at fluid-solid interfaces are prescribed. The proposed methodology may apply equally well to other particle methods such as dissipative particle dynamics and moving particle semi-implicit methods.

physics.flu-dyn↗

arXiv2022

Chemotaxis of sea urchin sperm cells through deep reinforcement learning

By imitating biological microswimmers, microrobots can be designed to accomplish targeted delivery of cargos and biomedical manipulations at microscale. However, it is still a great challenge to enable microrobots to maneuver in a complex environment. Machine learning algorithms offer a tool to boost mobility and flexibility of a synthetic microswimmer, hence could help us design truly smart microrobots. In this work, we investigate how a model of sea urchin sperm cell can self-learn chemotactic motion in a chemoattractant concentration field. We employ an artificial neural network to act as a decision-making agent and facilitate the sperm cell to discover efficient maneuver strategies through a deep reinforcement learning (DRL) algorithm. Our results show that chemotactic behaviours, very similar to the realistic ones, can be achieved by the DRL utilizing only limited environmental information. In most cases, the DRL algorithm discovers more efficient strategies than the human-devised one. Furthermore, the DRL can even utilize an external disturbance to facilitate the chemotactic motion if the extra flow information is also taken into account by the artificial neural network. Our results provide insights to the chemotactic process of sea urchin sperm cells and also prepare guidance for the intelligent maneuver of microrobots.

cs.NE↗

arXiv2021

Scaling of Turbulent Viscosity and Resistivity: Extracting a Scale-dependent Turbulent Magnetic Prandtl Number

Turbulent viscosity $ν_t$ and resistivity $η_t$ are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number $Pr_t\equiv ν_t/η_t$ has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these ''effective transport'' coefficients acting at different length-scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades [Bian & Aluie 2019]. By analyzing the kinetic and magnetic energy cascades from a suite of high-resolution simulations, we show that our definitions of $ν_t$, $η_t$, and $Pr_t$ have power-law scalings in the ''decoupled range.'' We observe that $Pr_t\approx1 \text{~to~}2$ at the smallest inertial-inductive scales, increasing to $\approx 5$ at the largest scales. However, based on physical considerations, our analysis suggests that $Pr_t$ has to become scale-independent and of order unity in the decoupled range at sufficiently high Reynolds numbers (or grid-resolution), and that the power-law scaling exponents of velocity and magnetic spectra become equal. In addition to implications to astrophysical systems, the scale-dependent turbulent transport coefficients offer a guide for large eddy simulation modeling.

physics.flu-dyn↗

arXiv2019

Revisiting the Late-Time Growth of Single-mode Rayleigh-Taylor Instability and the Role of Vorticity

Growth of the single-fluid single-mode Rayleigh-Taylor instability (RTI) is revisited in 2D and 3D using fully compressible high-resolution simulations. We conduct a systematic analysis of the effects of perturbation Reynolds number ($Re_p$) and Atwood number ($A$) on RTI's late-time growth. Contrary to the common belief that single-mode RTI reaches a terminal bubble velocity, we show that the bubble re-accelerates when $Re_p$ is sufficiently large, consistent with [Ramaparabhu et al. 2006, Wei and Livescu 2012]. However, unlike in [Ramaparabhu et al. 2006], we find that for a sufficiently high $Re_p$, the bubble's late-time acceleration is persistent and does not vanish. Analysis of vorticity dynamics shows a clear correlation between vortices inside the bubble and re-acceleration. Due to symmetry around the bubble and spike (vertical) axes, the self-propagation velocity of vortices points in the vertical direction. If viscosity is sufficiently small, the vortices persist long enough to enter the bubble tip and accelerate the bubble [Wei and Livescu 2012]. A similar effect has also been observed in ablative RTI [Betti and Sanz 2006]. As the spike growth increases relative to that of the bubble at higher $A$, vorticity production shifts downward, away from the centerline and toward the spike tip. We modify the Betti-Sanz model for bubble velocity by introducing a vorticity efficiency factor $η=0.45$ to accurately account for re-acceleration caused by vorticity in the bubble tip. It had been previously suggested that vorticity generation and the associated bubble re-acceleration are suppressed at high $A$. However, we present evidence that if the large $Re_p$ limit is taken first, bubble re-acceleration is still possible. Our results also show that re-acceleration is much easier to occur in 3D than 2D, requiring smaller $Re_p$ thresholds.

physics.flu-dyn↗

arXiv2019

Bending models of lipid bilayer membranes: spontaneous curvature and area-difference elasticity

We preset a computational study of bending models for the curvature elasticity of lipid bilayer membranes that are relevant for simulations of vesicles and red blood cells. We compute bending energy and forces on triangulated meshes and evaluate and extend four well established schemes for their approximation: Kantor and Nelson 1987, Phys. Rev. A 36, 4020, Jülicher 1996, J. Phys. II France 6, 1797, Gompper and Kroll 1996, J. Phys. I France 6, 1305, and Meyer et. al. 2003 in Visualization and Mathematics III, Springer, p35, termed A, B, C, D. We present a comparative study of these four schemes on the minimal bending model and propose extensions for schemes B, C and D. These extensions incorporate the reference state and non-local energy to account for the spontaneous curvature, bilayer coupling, and area-difference elasticity models. Our results indicate that the proposed extensions enhance the models to account for shape transformation including budding/vesiculation as well as for non-axisymmetric shapes. We find that the extended scheme B is superior to the rest in terms of accuracy, and robustness as well as simplicity of implementation. We demonstrate the capabilities of this scheme on several benchmark problems including the budding-vesiculating process and the reproduction of the phase diagram of vesicles.

cs.CE↗