83 research outputs found
An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces
Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressurecorrection approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces
A Deep Learning Approach for the Computation of Curvature in the Level-Set Method
We propose a deep learning strategy to estimate the mean curvature of
two-dimensional implicit interfaces in the level-set method. Our approach is
based on fitting feed-forward neural networks to synthetic data sets
constructed from circular interfaces immersed in uniform grids of various
resolutions. These multilayer perceptrons process the level-set values from
mesh points next to the free boundary and output the dimensionless curvature at
their closest locations on the interface. Accuracy analyses involving irregular
interfaces, both in uniform and adaptive grids, show that our models are
competitive with traditional numerical schemes in the and norms. In
particular, our neural networks approximate curvature with comparable precision
in coarse resolutions, when the interface features steep curvature regions, and
when the number of iterations to reinitialize the level-set function is small.
Although the conventional numerical approach is more robust than our framework,
our results have unveiled the potential of machine learning for dealing with
computational tasks where the level-set method is known to experience
difficulties. We also establish that an application-dependent map of local
resolutions to neural models can be devised to estimate mean curvature more
effectively than a universal neural network.Comment: Submitted to SIAM Journal on Scientific Computin
A Hybrid Inference System for Improved Curvature Estimation in the Level-Set Method Using Machine Learning
We present a novel hybrid strategy based on machine learning to improve
curvature estimation in the level-set method. The proposed inference system
couples enhanced neural networks with standard numerical schemes to compute
curvature more accurately. The core of our hybrid framework is a switching
mechanism that relies on well established numerical techniques to gauge
curvature. If the curvature magnitude is larger than a resolution-dependent
threshold, it uses a neural network to yield a better approximation. Our
networks are multilayer perceptrons fitted to synthetic data sets composed of
sinusoidal- and circular-interface samples at various configurations. To reduce
data set size and training complexity, we leverage the problem's characteristic
symmetry and build our models on just half of the curvature spectrum. These
savings lead to a powerful inference system able to outperform any of its
numerical or neural component alone. Experiments with static, smooth interfaces
show that our hybrid solver is notably superior to conventional numerical
methods in coarse grids and along steep interface regions. Compared to prior
research, we have observed outstanding gains in precision after training the
regression model with data pairs from more than a single interface type and
transforming data with specialized input preprocessing. In particular, our
findings confirm that machine learning is a promising venue for reducing or
removing mass loss in the level-set method.Comment: Submitte
Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method
We propose a data-driven mean-curvature solver for the level-set method. This
work is the natural extension to of our two-dimensional strategy
in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of
[DOI: 10.1016/j.jcp.2022.111291][2]. However, in contrast to [1,2], which built
resolution-dependent neural-network dictionaries, here we develop a pair of
models in , regardless of the mesh size. Our feedforward networks
ingest transformed level-set, gradient, and curvature data to fix numerical
mean-curvature approximations selectively for interface nodes. To reduce the
problem's complexity, we have used the Gaussian curvature to classify stencils
and fit our models separately to non-saddle and saddle patterns. Non-saddle
stencils are easier to handle because they exhibit a curvature error
distribution characterized by monotonicity and symmetry. While the latter has
allowed us to train only on half the mean-curvature spectrum, the former has
helped us blend the data-driven and the baseline estimations seamlessly near
flat regions. On the other hand, the saddle-pattern error structure is less
clear; thus, we have exploited no latent information beyond what is known. In
this regard, we have trained our models on not only spherical but also
sinusoidal and hyperbolic paraboloidal patches. Our approach to building their
data sets is systematic but gleans samples randomly while ensuring
well-balancedness. We have also resorted to standardization and dimensionality
reduction and integrated regularization to minimize outliers. In addition, we
leverage curvature rotation/reflection invariance to improve precision at
inference time. Several experiments confirm that our proposed system can yield
more accurate mean-curvature estimations than modern particle-based interface
reconstruction and level-set schemes around under-resolved regions
A sharp cartesian method for the simulation of air-water interface
Abstract: We firstly present a sharp cartesian method for the simulation of incompressible flows with high density and viscosity ratios, like air-water interfaces. This method is inspired from the second-order cartesian method for elliptic problems with immersed interfaces developed i
Direct simulation of drying colloidal suspension on substrate using immersed free surface model
This paper presents a new direct simulation method for a drying colloidal suspension on a substrate. A key issue of the present method is the immersed free surface model proposed by the authors, which enables us to estimate accurately and efficiently capillary forces exerted on particles on a free surface. Using the immersed free surface model along with immersed boundary method and level set method, the present method leads to a three-way coupling of the fluid flow, the free surface motion and the particle motion. In addition, the present method includes a way of curvature estimation using virtual grid differencing to calculate accurately a surface tension. The way of curvature estimation is quantitatively validated through the simulation of a still droplet. The immersed free surface model is quantitatively validated through the simulation of a sphere moving across a free surface and the simulation of two spheres moving along a free surface. Finally, simulations of drying colloidal suspension containing 130 particles are performed to demonstrate the applicability of the present method to actual systems.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/)
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