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Mathematics
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Modeling of Multiphase Flow Phenomena
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Modeling of Multiphase Flow Phenomena

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 December 2025 | Viewed by 4102

Special Issue Editors

Dr. Siwei Liu

E-Mail Website
Guest Editor
Institute of Fluid Science, Tohoku University, Sendai 980-8577, Japan
Interests: multiphase flows; bubble and droplet; plasma; environmental treatment; fluid engineering
Dr. Hazem El-Rabii

E-Mail Website
Guest Editor
Institut Pprime, CNRS UPR 3346—Université de Poitiers—ISAE-ENSMA, 1 Avenue Clément Ader, 86961 Futuroscope, France
Interests: fluid dynamics‬; combustion‬; acoustics‬; ‪instability‬; plasma

Special Issue Information

Dear Colleagues,

Multiphase flow phenomena encompass a broad spectrum of physics and engineering sciences dealing with complex processes across a wide range of spatial and temporal scales, and whose elucidation relies on a multitude of analytical, numerical, and experimental methodologies. Recent progresses, combined with the continual development of advanced technologies, have given rise to innovative multiphase flow systems of primary interest for many applications, such as in medicine and bioscience, but have also enabled the improvement of our past descriptions by providing access to more detailed and complementary data.

This Special Issue invites original contributions related to the description of multiphase flow phenomena, with a special emphasis on recent theoretical and numerical modeling efforts. Prospective authors are invited to submit papers addressing multiphase flows, including liquid–gas and liquid–liquid flows; bubble and droplet dynamics; plasma in dielectrics; microfluidic devices; and others. Topics covered include, but are not limited to:

  • Multiphase flow simulation;
  • Interface dynamics;
  • Atomization;
  • Bubble and drop dynamics;
  • Bubbly flows;
  • Cavitation;
  • Interaction of gas, liquids and solids;
  • Flow in porous media;
  • Microfluidic devices;
  • Applications in biomedical and industrial fields.

Dr. Siwei Liu
Dr. Hazem El-Rabii
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • theoretical modeling
  • computational fluid dynamics
  • multiphase flow
  • plasma in dielectrics
  • bubble and droplets
  • interfacial instabilities

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Published Papers (4 papers)

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Research

19 pages, 19828 KiB  
Article
Blood Flow Simulation in Bifurcating Arteries: A Multiscale Approach After Fenestrated and Branched Endovascular Aneurysm Repair
by Spyridon Katsoudas, Stavros Malatos, Anastasios Raptis, Miltiadis Matsagkas, Athanasios Giannoukas and Michalis Xenos
Mathematics 2025, 13(9), 1362; https://doi.org/10.3390/math13091362 - 22 Apr 2025
Abstract
Pathophysiological conditions in arteries, such as stenosis or aneurysms, have a great impact on blood flow dynamics enforcing the numerical study of such pathologies. Computational fluid dynamics (CFD) could provide the means for the calculation and interpretation of pressure and velocity fields, wall [...] Read more.
Pathophysiological conditions in arteries, such as stenosis or aneurysms, have a great impact on blood flow dynamics enforcing the numerical study of such pathologies. Computational fluid dynamics (CFD) could provide the means for the calculation and interpretation of pressure and velocity fields, wall stresses, and important biomedical factors in such pathologies. Additionally, most of these pathological conditions are connected with geometric vessel changes. In this study, the numerical solution of the 2D flow in a branching artery and a multiscale model of 3D flow are presented utilizing CFD. In the 3D case, a multiscale approach (3D and 0D–1D) is pursued, in which a dynamically altered velocity parabolic profile is applied at the inlet of the geometry. The obtained waveforms are derived from a 0D–1D mathematical model of the entire arterial tree. The geometries of interest are patient-specific 3D reconstructed abdominal aortic aneurysms after fenestrated (FEVAR) and branched endovascular aneurysm repair (BEVAR). Critical hemodynamic parameters such as velocity, wall shear stress, time averaged wall shear stress, and local normalized helicity are presented, evaluated, and compared. Full article
(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)
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20 pages, 6400 KiB  
Article
Transfer Learning-Based Physics-Informed Convolutional Neural Network for Simulating Flow in Porous Media with Time-Varying Controls
by Jungang Chen, Eduardo Gildin and John E. Killough
Mathematics 2024, 12(20), 3281; https://doi.org/10.3390/math12203281 - 19 Oct 2024
Cited by 1 | Viewed by 1217
Abstract
A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state [...] Read more.
A physics-informed convolutional neural network (PICNN) is proposed to simulate two-phase flow in porous media with time-varying well controls. While most PICNNs in the existing literature worked on parameter-to-state mapping, our proposed network parameterizes the solutions with time-varying controls to establish a control-to-state regression. Firstly, a finite volume scheme is adopted to discretize flow equations and formulate a loss function that respects mass conservation laws. Neumann boundary conditions are seamlessly incorporated into the semi-discretized equations so no additional loss term is needed. The network architecture comprises two parallel U-Net structures, with network inputs being well controls and outputs being the system states (e.g., oil pressure and water saturation). To capture the time-dependent relationship between inputs and outputs, the network is well designed to mimic discretized state-space equations. We train the network progressively for every time step, enabling it to simultaneously predict oil pressure and water saturation at each timestep. After training the network for one timestep, we leverage transfer learning techniques to expedite the training process for a subsequent time step. The proposed model is used to simulate oil–water porous flow scenarios with varying reservoir model dimensionality, and aspects including computation efficiency and accuracy are compared against corresponding numerical approaches. The comparison with numerical methods demonstrates that a PICNN is highly efficient yet preserves decent accuracy. Full article
(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)
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15 pages, 337 KiB  
Article
Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions
by Evgenii S. Baranovskii and Olga Yu. Shishkina
Mathematics 2024, 12(5), 756; https://doi.org/10.3390/math12050756 - 3 Mar 2024
Cited by 5 | Viewed by 1077
Abstract
In this paper, we investigate the solvability of a boundary value problem for a heat and mass transfer model with the spatially averaged Rayleigh function. The considered model describes the 3D steady-state non-isothermal flow of a generalized Newtonian fluid (with shear-dependent viscosity) in [...] Read more.
In this paper, we investigate the solvability of a boundary value problem for a heat and mass transfer model with the spatially averaged Rayleigh function. The considered model describes the 3D steady-state non-isothermal flow of a generalized Newtonian fluid (with shear-dependent viscosity) in a bounded domain with Lipschitz boundary. The main novelty of our work is that we do not neglect the viscous dissipation effect in contrast to the classical Boussinesq approximation, and hence, deal with a system of strongly nonlinear partial differential equations. Using the properties of the averaging operation and d-monotone operators as well as the Leray–Schauder alternative for completely continuous mappings, we prove the existence of weak solutions without any smallness assumptions for model data. Moreover, it is shown that the set of all weak solutions is compact, and each solution from this set satisfies some energy equalities. Full article
(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)
18 pages, 320 KiB  
Article
Uniqueness of a Generalized Solution for a One-Dimensional Thermal Explosion Model of a Compressible Micropolar Real Gas
by Angela Bašić-Šiško and Ivan Dražić
Mathematics 2024, 12(5), 717; https://doi.org/10.3390/math12050717 - 28 Feb 2024
Cited by 2 | Viewed by 926
Abstract
In this paper, we analyze a quasi-linear parabolic initial-boundary problem describing the thermal explosion of a compressible micropolar real gas in one spatial dimension. The model contains five variables, mass density, velocity, microrotation, temperature, and the mass fraction of unburned fuel, while the [...] Read more.
In this paper, we analyze a quasi-linear parabolic initial-boundary problem describing the thermal explosion of a compressible micropolar real gas in one spatial dimension. The model contains five variables, mass density, velocity, microrotation, temperature, and the mass fraction of unburned fuel, while the associated problem contains homogeneous boundary conditions. The aim of this work is to prove the uniqueness theorem of the generalized solution for the mentioned initial-boundary problem. The uniqueness of the solution, together with the proven existence of the solution, makes the described initial-boundary problem theoretically consistent, which provides a basis for the development of numerical methods and the engineering application of the model. Full article
(This article belongs to the Special Issue Modeling of Multiphase Flow Phenomena)
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