arXiv subjects

Kiwon Um

Publications and source records attributed to Kiwon Um.

12 recordsLinked to original sources

arXiv2026

On the hydrodynamic behaviour of the immersed boundary -- lattice Boltzmann method for wetting problems

We study the hydrodynamic behaviour of a mesoscale numerical model for wetting dynamics based on the immersed boundary - lattice Boltzmann (IBLB) method. This IBLB model features a wetting potential to capture the interaction between a non-ideal droplet interface and a solid boundary; it is designed to prevent abrupt curvature changes near the contact line. As this approach prevents direct contact between the droplet and the solid, it forms a thin film beneath the droplet, which could compromise the hydrodynamic consistency in this region. This paper presents detailed comparisons against two other hydrodynamic solvers, respectively based on a boundary element method (BEM) and a volume of fluid (VoF) method, in order to examine the hydrodynamic behaviour of this IBLB scheme, elucidate its limits of validity in wetting applications, and explore the properties of its contact-line model.

physics.flu-dyn↗

arXiv2026

On the importance of stochasticity in closures of turbulence

Deterministic closures for coarse-grained turbulence models help reproduce mean statistics, but often fail to capture the finite-time growth of uncertainty. Using the framework of shell models as a quantitative multi-scale testbed, we compare fully resolved simulations with large-eddy simulations using either stochastic or deterministic subgrid closures. While in the fully resolved system a single microscopic perturbation is rapidly amplified by strongly chaotic dynamics, truncation produces a strong delay and suppression of variance growth when uncertainty is introduced through initial condition perturbations only. We show that a data-driven Langevin-type stochastic closure restores the correct timing and magnitude of variance growth across scales, demonstrating that sustained stochasticity is essential for predictability in reduced turbulent dynamics.

physics.flu-dyn↗

arXiv2025

A posteriori closure of turbulence models: are symmetries preserved?

Turbulence modeling remains a longstanding challenge in fluid dynamics. Recent advances in data-driven methods have led to a surge of novel approaches aimed at addressing this problem. This work builds upon our recent work [Phys. Rev. Fluids 10, 044602 (2025)], where we introduced a new closure for a shell model of turbulence using an a posteriori (or solver-in-the-loop) approach. Unlike most deep learning-based models, our method explicitly incorporates physical equations into the neural network framework, ensuring that the closure remains constrained by the underlying physics benefiting from enhanced stability and generalizability. In this paper, we further analyze the learned closure, probing its capabilities and limitations. In particular, we look at joint probability density functions between resolved and unresolved variables, as well as the scale invariance of multipliers (ratios between adjacent shells) within the inertial range. Although our model excels in reproducing high-order statistical moments, it breaks this known symmetry near the cutoff, indicating a fundamental limitation. We discuss the implications of these findings for subgrid-scale modeling in 3D turbulence and outline directions for future research.

physics.flu-dyn↗

arXiv2025

Immersed boundary - lattice Boltzmann method for wetting problems

We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to model the non-ideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid: this interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary - lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any pre-calibration study on model parameters to be used. Model validations against theoretical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed.

physics.flu-dyn↗

arXiv2024

Solver-in-the-loop approach to closure of shell models of turbulence

This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations.

physics.flu-dyn↗

arXiv2023

Exploring Physical Latent Spaces for High-Resolution Flow Restoration

We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work, this paper treats the degrees of freedom of the simulated space purely as tools to be used by the neural network. We demonstrate this concept for learning reduced representations, as it is extremely challenging to faithfully preserve correct solutions over long time-spans with traditional reduced representations, particularly for solutions with large amounts of small scale features. This work focuses on the use of such physical, reduced latent space for the restoration of fine simulations, by training models that can modify the content of the reduced physical states as much as needed to best satisfy the learning objective. This autonomy allows the neural networks to discover alternate dynamics that significantly improve the performance in the given tasks. We demonstrate this concept for various fluid flows ranging from different turbulence scenarios to rising smoke plumes.

cs.LG↗

arXiv2021

Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting for effects not captured by the discretized PDE. We target the problem of reducing numerical errors of iterative PDE solvers and compare different learning approaches for finding complex correction functions. We find that previously used learning approaches are significantly outperformed by methods that integrate the solver into the training loop and thereby allow the model to interact with the PDE during training. This provides the model with realistic input distributions that take previous corrections into account, yielding improvements in accuracy with stable rollouts of several hundred recurrent evaluation steps and surpassing even tailored supervised variants. We highlight the performance of the differentiable physics networks for a wide variety of PDEs, from non-linear advection-diffusion systems to three-dimensional Navier-Stokes flows.

physics.comp-ph↗

arXiv2020

Perceptual Evaluation of Liquid Simulation Methods

This paper proposes a novel framework to evaluate fluid simulation methods based on crowd-sourced user studies in order to robustly gather large numbers of opinions. The key idea for a robust and reliable evaluation is to use a reference video from a carefully selected real-world setup in the user study. By conducting a series of controlled user studies and comparing their evaluation results, we observe various factors that affect the perceptual evaluation. Our data show that the availability of a reference video makes the evaluation consistent. We introduce this approach for computing scores of simulation methods as visual accuracy metric. As an application of the proposed framework, a variety of popular simulation methods are evaluated.

cs.GR↗

arXiv2020

ScalarFlow: A Large-Scale Volumetric Data Set of Real-world Scalar Transport Flows for Computer Animation and Machine Learning

In this paper, we present ScalarFlow, a first large-scale data set of reconstructions of real-world smoke plumes. We additionally propose a framework for accurate physics-based reconstructions from a small number of video streams. Central components of our algorithm are a novel estimation of unseen inflow regions and an efficient regularization scheme. Our data set includes a large number of complex and natural buoyancy-driven flows. The flows transition to turbulent flows and contain observable scalar transport processes. As such, the ScalarFlow data set is tailored towards computer graphics, vision, and learning applications. The published data set will contain volumetric reconstructions of velocity and density, input image sequences, together with calibration data, code, and instructions how to recreate the commodity hardware capture setup. We further demonstrate one of the many potential application areas: a first perceptual evaluation study, which reveals that the complexity of the captured flows requires a huge simulation resolution for regular solvers in order to recreate at least parts of the natural complexity contained in the captured data.

cs.GR↗

arXiv2020

Learning Similarity Metrics for Numerical Simulations

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.

cs.LG↗

arXiv2019

Spot the Difference: Accuracy of Numerical Simulations via the Human Visual System

Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have inherent shortcomings when faced with the under-resolved solutions of real-world simulation problems. We show how to leverage crowd-sourced user studies in order to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies, which inherently rely on the human visual system, yield a very robust metric and consistent answers for complex phenomena without any requirements for proficiency regarding the physics at hand. This holds even for cases away from convergence where traditional metrics often end up inconclusive results. More specifically, we evaluate results of different essentially non-oscillatory (ENO) schemes in different fluid flow settings. Our methodology represents a novel and practical approach for scientific evaluations that can give answers for previously unsolved problems.

physics.data-an↗

arXiv2018

Liquid Splash Modeling with Neural Networks

This paper proposes a new data-driven approach to model detailed splashes for liquid simulations with neural networks. Our model learns to generate small-scale splash detail for the fluid-implicit-particle method using training data acquired from physically parametrized, high resolution simulations. We use neural networks to model the regression of splash formation using a classifier together with a velocity modifier. For the velocity modification, we employ a heteroscedastic model. We evaluate our method for different spatial scales, simulation setups, and solvers. Our simulation results demonstrate that our model significantly improves visual fidelity with a large amount of realistic droplet formation and yields splash detail much more efficiently than finer discretizations.

cs.GR↗