arXiv subjects

Shahab Mirjalili

Publications and source records attributed to Shahab Mirjalili.

15 recordsLinked to original sources

arXiv2026

Turbulence anisotropy in a bubbly vertical channel flow with topological change

High-fidelity numerical simulations of bubble-laden, vertical channel flow in the upward configuration, where the bubbles undergo topological changes (breakup and coalescence), were performed with the purpose of exploring the effect of the surface tension on the turbulence anisotropy in the carrier phase. A qualitative analysis shows that velocity fluctuations are enhanced in the wake of large bubbles. Moreover, as shown by the velocity spectra, these structures seem to scale with bubble size and interact with those closer to the wall. Finally, a barycentric map and other indicators of turbulence anisotropy clarify that, except at the core of the channel where the largest bubbles reside, the multiphase flow cases are actually more isotropic than the single-phase flow at a matching friction Reynolds number. This unexpected behavior is attributed to a better redistribution of energy due to an enhancement of sweep events (high-speed fluid towards the wall) in the presence of large bubbles.

physics.flu-dyn↗

arXiv2026

A universal diffuse interface modeling framework for surfactants

We propose a universal diffuse-interface modeling framework for surfactant transport in two-phase flows, applicable to all solubility scenarios and to any conservative phase field method. The foundation of our framework is a general three-scalar non-equilibrium model governing the surfactant concentrations in each bulk phase and at the interface, which builds on our prior consistent scalar transport framework and is locally and globally conservative, leakage-free, Galilean-invariant, and reduction-consistent. Assuming thermochemical equilibrium, we derive two one-scalar models: one for a surfactant in full equilibrium between both bulk phases and the interface, and one for a surfactant confined to a single bulk phase and the interface. All models are coupled to the Navier-Stokes equations through a surface tension force that incorporates the Marangoni stress arising from non-uniform interfacial surfactant distributions. While diffuse-interface surfactant models have been developed for the Cahn-Hilliard equation and, more recently, for the conservative Allen-Cahn (CAC) equation, existing models for CAC address only the insoluble and single-phase-soluble cases, leaving the general scenario of partial solubility in both bulk phases unaddressed; furthermore, these models lack Galilean invariance and reduction consistency, and are not applicable beyond the CAC setting. The framework is validated against analytical solutions in one-dimensional transport tests, assessed for convergence in two-dimensional advection-diffusion simulations, and demonstrated in fully-coupled drop-in-shear flow simulations covering insoluble, soluble, and partially-soluble surfactant scenarios.

physics.flu-dyn↗

arXiv2026

Solid adsorption: the missing mechanism for surfactant contact lines -- a phase-field approach

We develop a thermodynamically consistent phase-field model for soluble surfactants in two-phase flows, incorporating both interfacial and solid surface adsorption. The model is derived via variational principles consistent with the second law of thermodynamics, resulting in modified free energies and boundary conditions that capture surfactant transport, adsorption, and wetting dynamics. A key contribution of this work is the inclusion of surfactant adsorption on solid walls, which leads to qualitative agreement with experimental observations: unlike prior numerical studies that predicted hydrophilic surfaces becoming more hydrophilic and hydrophobic surfaces more hydrophobic, our model shows a shift toward increased hydrophilicity across all contact angles-consistent with experimental trends. Our results establish that solid adsorption provides the missing mechanism required for predictive modelling of surfactant-laden contact line dynamics.

cond-mat.soft↗

arXiv2026

An LES model with finite-rate phase change and subgrid spray based on a thermodynamically consistent four-equation multiphase model

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $Σ$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $Σ$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

physics.flu-dyn↗

arXiv2025

Convolutional autoencoders for the reconstruction of three-dimensional interfacial multiphase flows

We present a systematic investigation of convolutional autoencoders for the reduced-order representation of three-dimensional interfacial multiphase flows. Focusing on the reconstruction of phase indicators, we examine how the choice of interface representation, including sharp, diffuse, and level-set formulations, impacts reconstruction accuracy across a range of interface complexities. Training and validation are performed using both synthetic datasets with controlled geometric complexity and high-fidelity simulations of multiphase homogeneous isotropic turbulence. We show that the interface representation plays a critical role in autoencoder performance. Excessively sharp interfaces lead to the loss of small-scale features, while overly diffuse interfaces degrade overall accuracy. Across all datasets and metrics considered, a moderately diffuse interface provides the best balance between preserving fine-scale structures and achieving accurate reconstructions. These findings elucidate key limitations and best practices for dimensionality reduction of multiphase flows using autoencoders. By clarifying how interface representations interact with the inductive biases of convolutional neural networks, this work lays the foundation for decoupling the training of autoencoders for accurate state compression from the training of surrogate models for temporal forecasting or input-output prediction in latent space.

cs.CE↗

arXiv2025

A thermodynamically consistent and robust four-equation model for multi-phase multi-component compressible flows using ENO-type schemes including interface regularization

In this work, a concise and robust computational framework is proposed to simulate compressible multi-phase multi-component flows. To handle both shocks and material interfaces, a positivity-preserving ENO-type scheme is coupled with multi-phase interface regularization terms. The positivity-preserving limiter is conservative and is applied locally for minimal degradation of the baseline ENO-type scheme. The interface regularization terms are extended from the conservative diffuse interface (CDI) model to accommodate multi-phase, multi-component flows. The ENO-type scheme is designed to be consistent with the thermodynamic equilibrium assumptions of the four-equation multi-phase model, naturally enforcing the interface equilibrium condition - preventing oscillations in pressure, velocity, and temperature around isothermal material interfaces - without requiring additional equations for volume fraction or mixture equation of state parameters, as is commonly done for the five-equation model. Additionally, non-dilute species diffusion models are extended to the multi-phase, multi-component setting. We show that this consistent framework is equally applicable for regimes ranging from single-phase to multi-phase multi-component flows. The proposed models and numerical schemes are implemented in the highly parallel Hypersonic Task based Research (HTR) Solver, and high-resolution simulations are performed using both CPUs and GPUs.

physics.flu-dyn↗

arXiv2024

A mass-conserving contact line treatment for second-order conservative phase field methods based on the generalized Navier boundary condition

A mass-conserving contact line treatment for second-order conservative phase field methods is presented and applied to the conservative diffuse interface (CDI) model. The treatment centers on a no-flux boundary condition for the phase field along with a slip boundary condition for the velocity that is based on the generalized Navier boundary condition (GNBC). Since the CDI model is a second-order partial differential equation, it does not permit a second (contact angle) boundary condition, in contrast to the popular fourth-order Cahn-Hilliard model. As such, we use one-sided stencils and extrapolations from the interior of the domain to compute phase-field-related quantities on and near the wall. Additionally, we propose novel modifications to the GNBC on the continuous and discrete levels that reduce spurious slip velocity when the contact angle achieves its equilibrium value. The proposed treatment is validated with the equilibrium drop and two-phase Couette flow test cases.

physics.flu-dyn↗

arXiv2024

Diffuse interface treatment in generalized curvilinear coordinates with grid-adapting interface thickness

A general approach for transforming phase field equations into generalized curvilinear coordinates is proposed in this work. The proposed transformation can be applied to isotropic, non-isotropic, and curvilinear grids without adding any ambiguity in determining the phase field parameters. Moreover, it accurately adapts the interface thickness to the local grid-size for a general curvilinear grid without creating oscillations. Three canonical verification tests are presented on four grids with varying skewness levels. The classic advection and drop in shear tests are extended to curvilinear grids and show that the original phase field on Cartesian grids and the proposed curvilinear form have an identical order of convergence. Additionally, the proposed method is shown to provide grid-independent convergence on a two-way coupled compressible Rayleigh-Taylor instability. These simulations illustrate the robustness and accuracy of the proposed method for handling complex interfacial structures on generalized curvilinear grids.

physics.comp-ph↗

arXiv2023

Inverse asymptotic treatment: capturing discontinuities in fluid flows via equation modification

A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities, which manifest themselves as interfaces between different phases in multi-phase flows, or as shock and contact discontinuities in compressible flows. When a quick response is required to rapidly emerging challenges, the complexity of bespoke discretization schemes impedes a swift transition from problem formulation to computation, which is exacerbated by the need to compose multiple interacting physics. We introduce "inverse asymptotic treatment" (IAT) as a unified framework for capturing discontinuities in fluid flows that enables building directly computable models based on off-the-shelf numerics. By capturing discontinuities through modifications at the level of the governing equations, IAT can seamlessly handle additional physics and thus enable novice end users to quickly obtain numerical results for various multi-physics scenarios. We outline IAT in the context of phase-field modeling of two-phase incompressible flows, and then demonstrate its generality by showing how localized artificial diffusivity (LAD) methods for single-phase compressible flows can be viewed as instances of IAT. Through the real-world example of a laminar hypersonic compression corner, we illustrate IAT's ability to, within just a few months, generate a directly computable model whose wall metrics predictions for sufficiently small corner angles come close to that of NASA's VULKAN-CFD solver. Finally, we propose a novel LAD approach via "reverse-engineered" PDE modifications, inspired by total variation diminishing (TVD) flux limiters, to eliminate the problem-dependent parameter tuning that plagues traditional LAD. We demonstrate that, when combined with second-order central differencing, it can robustly and accurately model compressible flows.

physics.comp-ph↗

arXiv2022

Spectral analysis of multidimensional current-driven plasma instabilities and turbulence in hollow cathode plumes

Large-amplitude current-driven instabilities in hollow cathode plumes can generate energetic ions responsible for cathode sputtering and spacecraft degradation. A 2D2V (two dimensions each in configuration [D] and velocity [V] spaces) grid-based Vlasov--Poisson (direct kinetic) solver is used to study their growth and saturation, which comprises four stages: linear growth, quasilinear resonance, nonlinear fill-in, and saturated turbulence. The linear modal growth rate, nonlinear saturation process, and ion velocity and energy distribution features in the turbulent regime are analyzed. Backstreaming ions are generated for large electron drifts, several ion acoustic periods after the potential field becomes turbulent. Interscale phase-space transfer and locality are analyzed for the Vlasov equation. The multidimensional study sheds light on the interactions between longitudinal and transverse plasma instabilities, as well as the inception of plasma turbulence.

physics.plasm-ph↗

arXiv2022

Assessment of an energy-based surface tension model for simulation of two-phase flows using second-order phase field methods

Second-order phase field models have emerged as an attractive option for capturing the advection of interfaces in two-phase flows. Prior to these, state-of-the-art models based on the Cahn-Hilliard equation, which is a fourth-order equation, allowed for the derivation of surface tension models through thermodynamic arguments. In contrast, the second-order phase field models do not follow a known energy law, and deriving a surface tension term for these models using thermodynamic arguments is not straightforward. In this work, we justify that the energy-based surface tension model from the Cahn-Hilliard context can be adopted for second-order phase field models as well and assess its performance. We test the surface tension model on three different second-order phase field equations; the conservative diffuse interface model of Chiu and Lin [1], and two models based on the modified Allen-Cahn equation introduced by Sun and Beckermann [2]. Additionally, we draw the connection between the energy-based model with a localized variation of the continuum surface force (CSF) model. Using canonical tests, we illustrate the lower magnitude of spurious currents, better accuracy, and superior convergence properties of the energy-based surface tension model compared to the CSF model, which is a popular choice used in conjunction with second-order phase field methods, and the localized CSF model. Importantly, in terms of computational expense and parallel efficiency, the energy-based model incurs no penalty compared to the CSF models.

physics.flu-dyn↗

arXiv2019

Consistent, energy-conserving momentum transport for simulations of two-phase flows using the phase field equations

Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving momentum transport scheme in the context of a second order mass-conserving phase field method. This is achieved by (1) accounting for the mass flux associated with the right-hand-side of the phase field equation in the convective flux of the conservative form of the momentum transport equation---a correction absent in previous phase field simulations (2) utilization of non-dissipative spatial discretization. We demonstrate accuracy and robustness improvements from our proposed scheme via numerical tests, including a turbulent case of a water jet subject to air cross-flow. Our proposed modifications to the momentum transport equation can be quite readily extended to general conservative phase field methods. Additionally, in the framework of this phase field method, we present a free energy-based surface tension force calculation scheme. This scheme, which significantly reduces spurious currents, is based on a general paradigm that can also be extended to other two-phase flow methods.

physics.flu-dyn↗

arXiv2018

High Fidelity Simulations of Micro-Bubble Shedding from Retracting Thin Gas Films in the Context of Liquid-Liquid Impact

Micro-bubbles are of significant interest due to the long-living signature they leave behind naval ships. In order to numerically model and predict these bubbles in naval applications, subgrid-scale models are required because of the extreme separation of length- and time-scales between the macroscopic geometries and the physical processes leading to the formation of these bubbles. Yet, there is much that is unknown about the mechanism behind the entrainment of such bubbles. Furthermore, quantitative information regarding their size distribution and dependence on flow parameters is very limited. Impact events are hypothesized to be the main contributor to the generation of micro-bubbles. This is due to a phenomenon known as Mesler entrainment, which has been observed in the context of the drop-pool impact problem. Namely, when a water droplet with diameter of $\mathcal{O}(1mm)$ impacts a deep water pool with an impact velocity of $\mathcal{O}(1m/s)$, hundreds of air micro-bubbles are entrained into the pool. These bubbles have been found to be remnants of a very thin air film entrapped between the two liquid bodies. These films have extremely high aspect ratios and after being punctured, shed micro-bubbles while retracting on time scales much shorter than the outer flow time scales. This separation of time-scales, along with a lacking of studies on retracting thin gas films has motivated us to study this fundamental problem with numerical simulations in two and three dimensions. Using a diffuse interface method, we perform two-phase simulations of retracting thin gas films in initially static liquid backgrounds to gain understanding regarding this problem and gather statistics that can be potentially used in a subgrid-scale model to predict micro-bubble shedding from a thin gas film. Coupling a model like this to a model that predicts the thin film characteristics ...

physics.flu-dyn↗

arXiv2018

A conservative diffuse interface method for two-phase flows with provable boundedness properties

Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show however, for an incompressible flow, in the context of a specific diffuse interface model, one can maintain the boundedness of the phase field while also taking advantage of the low cost and ease of implementation of central differences to construct a non-dissipative discretization scheme for the advective terms. This is made possible by combining the advection and reinitialization steps of a conservative level set scheme introduced by Olsson and Kreiss [J. Comput. Phys., 210, 225 (2005)] to form a phase field equation similar to that of Chiu and Lin [J. Comput. Phys., 230, 185 (2011)]. Instead of resorting to specialized upwind methods as in these articles, we prove that the boundedness of the phase field is guaranteed for certain choices of the free parameters ($ε$ and $γ$) for a specific central difference scheme that we propose. The proposed discretely conservative and bounded phase field equation, which is free of any reinitialization or mass redistribution, possesses desirable properties that can be leveraged in the coupled finite difference discretization of the two-phase momentum equation. Additionally, as compared to the state-of-the-art conservative and bounded two-phase flow methods, the proposed method boasts competitive accuracy-vs-cost trade-off, small memory requirements, ease of implementation and excellent parallelizability, providing a viable alternative for realistic two-phase flow calculations.

physics.flu-dyn↗

arXiv2018

Comparison between the diffuse interface and volume of fluid methods for simulating two-phase flows

A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially when they are coupled to the momentum equation and applied in physically relevant regimes. In this article, we compare two techniques for simulating two-phase flows that possess attractive qualities, but belong to the two distinct classes of diffuse interface (DI) and volume of fluid (VOF) methods. Both of these methods allow for mass-conserving schemes that can naturally capture large interfacial topology changes omnipresent in realistic two phase flows. The DI solver used in this work is based on a conservative and bounded phase field method, developed recently. Similar to level set methods, this diffuse interface method takes advantage of the smoothness of the phase field in computing curvature and surface tension forces. Geometric VOF methods track the fractional tagged volume in a cell. The specific geometric VOF scheme used here is a discretely conservative and bounded implementation that uses geometric algorithms for unsplit advection and interface reconstruction, while employing height functions for normal and curvature calculation. We present a quantitative comparison of these methods on Cartesian meshes in terms of their accuracy, convergence rate, and computational cost using canonical two-dimensional (2D) two-phase test cases: a very dense drop moving through a quiescent gas, the Rayleigh-Taylor instability, an equilibrium static drop, an oscillating drop and the damped surface wave. We further compare these methods in their ability to resolve thin films by simulating the impact of a water drop on a deep water pool. Using results of these studies, we suggest qualitative guidelines for selection of schemes for two-phase flow calculations.

physics.flu-dyn↗