Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2305.09020

Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows

Jielin Yang·Ivan C. Christov·Suchuan Dong
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first present a thermodynamically-consistent and reduction-consistent phase field model for two-phase dielectric fluids. The model honors the conservation laws and thermodynamic principles, and has the property that, if only one fluid component is present in the system, the two-phase formulation will exactly reduce to that of the corresponding single-phase system. In particular, this model accommodates an equilibrium solution that is compatible with the zero-velocity requirement based on physics. This property provides a simpler method for simulating the equilibrium state of two-phase dielectric systems. We further present an efficient numerical algorithm, together with a spectral-element (for two dimensions) or a hybrid Fourier-spectral/spectral-element (for three dimensions) discretization in space, for simulating this class of problems. This algorithm computes different dynamic variables successively in an un-coupled fashion, and involves only coefficient matrices that are time-independent in the resultant linear algebraic systems upon discretization, even when the physical properties (e.g. permittivity, density, viscosity) of the two dielectric fluids are different. This property is crucial and enables us to employ fast Fourier transforms for three-dimensional problems. Ample numerical simulations of two-phase dielectric flows under imposed voltage are presented to demonstrate the performance of the method herein and to compare the simulation results with theoretical models and experimental data.

Explore related subjects

math.NAcs.NAphysics.comp-phphysics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jielin Yang, Ivan C. Christov, Suchuan Dong. 2023-05-15. Phase Field Modeling and Numerical Algorithm for Two-Phase Dielectric Fluid Flows. https://doi.org/10.1016/j.jcp.2024.113228

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Stabilized Finite Element Method for a Morpho-Visco-Poroelastic Model

Studying the structure of soft tissues is important and relevant in biology, particularly in some diseases, such as tumor growth and dermal contraction after burn injury. Based on the complicated characteristics of the tissue and for the sake of a better understanding of the underlying biomechanics, we propose a mathematical model that combines elastic, viscous, and porous effects with growth or shrinkage due to microstructural changes. The framework is referred to as morpho-visco-poroelasticity. Although the existence results of the solution to the problem are not given in this study, we assess the stability of the equilibria for both the continuous and semi-discrete versions of the model, and the key features of this modelling framework have been discussed. To obtain reliable numerical solutions, a stabilized finite element (FE) scheme is proposed for the morpho-visco-poroelasticity equations to avoid spurious oscillations in the pressure profile; the success of this FE scheme is verified by numerical simulations and convergence investigation in both spatial and temporal aspects. For a more quantitative assessment, the total variation of the pressure profile is evaluated as a function of the stabilization parameter.

math.NA↗
arXiv2026

Efficient third-order iterative algorithms for computing zeros of special functions

This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation using the trapezoidal rule, this study has derived the proposed third-order method. This work establishes sufficient conditions to ensure the theoretical non-local convergence of the proposed method. This study provides suitable initial guesses for the proposed third-order iterative procedure to compute all zeros in a given interval of the solutions to second-order ordinary differential equations. The orthogonal polynomials like Legendre and Hermite, as well as the special functions like Bessel, Coulomb wave, confluent hypergeometric, and cylinder functions, satisfy the proposed conditions for convergence. Numerical simulations demonstrate the effectiveness of the proposed theory. This work also presents a comparative analysis with recent studies.

math.NA↗
arXiv2026

Machine-Learning-Enhanced Discretize-then-Project Reduced-Order Modeling of Turbulent Flows on Collocated Grids

This study presents a hybrid reduced-order modeling (ROM) framework for incompressible flows on collocated finite-volume grids, combining a discretize-then-project consistent-flux formulation for velocity and pressure with a non-intrusive neural-network closure for turbulent viscosity. The intrusive formulation preserves discrete mass conservation and pressure-velocity coupling, while a reduced pressure reference-cell constraint fixes pressure gauge ambiguity. We evaluate Multilayer Perceptron (MLP), Transformer, and Long Short-Term Memory (LSTM) closures. For a three-dimensional lid-driven cavity at $Re=100$, the LSTM-based ROM achieves relative errors of 0.7% in velocity and 4% in turbulent viscosity. At $Re=3200$, a mode-sensitivity study identifies $N=15$ POD modes as the best overall configuration, balancing accuracy, dimension, robustness, and cost. It yields a final relative velocity error of approximately 12.3% and an online wall-clock speedup of approximately $50\times$ over the full-order model; energy and enstrophy errors remain below 11% for all three architectures. This regime requires case-specific neural-network retraining and pressure reference-cell parameter retuning. In a time-extrapolation test trained on $t\in[0,3]$,s and rolled out to $t=6$,s, the ROM remains bounded, although velocity and pressure errors increase beyond the training window. The LSTM turbulent-viscosity closure remains robust, identifying long-horizon pressure accuracy as the main limitation. These results demonstrate the potential of consistent projection-based modeling combined with data-driven turbulence closure for efficient reduced-order simulation.

math.NA↗