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Advances in Numerical Simulations of Fluid Flow, Heat Transfer, and Turbulence Modeling

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 November 2026 | Viewed by 1532

Editor

Dr. Watit Pakdee

E-Mail Website
Guest Editor
Department of Mechanical Engineering, Thammasat School of Engineering, Faculty of Engineering, Thammasat University, Bangkok, Thailand
Interests: numerical simuation; fluid mechanics; heat transfer

Special Issue Information

Dear Colleagues,

Fluid flow, heat transfer, and turbulence are fundamental phenomena encountered in a wide range of natural processes and engineering applications. Their inherent nonlinearity, multiscale nature, and strong coupling with physical and mathematical principles make accurate modeling and prediction particularly challenging.

In recent decades, significant progress in this area has been achieved through the development of advanced numerical methods, mathematical models, and high-performance computing techniques. Numerical simulations now play a crucial role in improving our understanding of complex flow and heat transfer mechanisms, enabling the design and optimization of systems in aerospace, energy, environmental, and industrial applications.

This Special Issue, entitled “Advances in Numerical Simulations of Fluid Flow, Heat Transfer, and Turbulence Modeling”, aims to showcase recent developments regarding the use of mathematical modeling, numerical analysis, and computational techniques applied to fluid mechanics and heat transfer. We invite researchers and professionals to submit original research articles and high-quality review papers that present novel methodologies, theoretical insights, or significant applications in this area.

Topics of interest include, but are not limited to, the following:

  • Numerical methods for fluid flow and heat transfer;
  • Turbulence modeling and simulation (RANS, LES, DNS, hybrid approaches);
  • Mathematical modeling of complex and multiphysics flows;
  • Heat and mass transfer in laminar and turbulent regimes;
  • Stability, bifurcation, and nonlinear phenomena in fluid systems;
  • High-performance and parallel computing for CFD;
  • Validation, verification, and uncertainty quantification in numerical simulations.

We warmly invite you to contribute to this Special Issue and share your latest research findings with the scientific community.

Dr. Watit Pakdee
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • numerical simulation
  • computational fluid dynamics
  • heat transfer modeling
  • turbulence modeling

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Published Papers (3 papers)

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Research

25 pages, 4293 KB  
Article
Numerical Simulation of Droplet Impact, Spreading and Penetration onto Curved Porous Media
by Zhenqiang Ma and Min Wei
Mathematics 2026, 14(16), 2891; https://doi.org/10.3390/math14162891 - 10 Aug 2026
Viewed by 307
Abstract
Droplet impact on curved porous media involves coupled spreading, wrapping, recoiling, and penetration. A three-dimensional level set model was developed in COMSOL and validated using high-speed imaging experiments to quantify axial and circumferential spreading lengths, central liquid film height, penetration depth, and energy [...] Read more.
Droplet impact on curved porous media involves coupled spreading, wrapping, recoiling, and penetration. A three-dimensional level set model was developed in COMSOL and validated using high-speed imaging experiments to quantify axial and circumferential spreading lengths, central liquid film height, penetration depth, and energy partitioning at maximum spreading. As the We increased from 10 to 40, the maximum axial and circumferential spreading factors increased by 15.58% and 25.80%, respectively, while viscous dissipation increased by 17.32% and the recoiling-stage peak central liquid film height decreased by 16.70%. Increasing porosity from 0.4 to 0.6 had little effect on macroscopic spreading but raised the penetration peak and reduced the recoiling-stage liquid film height by 18.25%; similarly, increasing particle diameter from 0.15 to 0.25 mm increased the penetration depth at 20 ms by 49.75%, by reducing Darcy–Forchheimer resistance. Increasing surface tension from 0.0273 to 0.1092 N/m reduced the peak axial and circumferential spreading factors by 26.08% and 36.49%, respectively, whereas increasing viscosity from 0.003 to 0.009 Pa·s reduced the peak axial spreading factor and penetration peak by 15.96% and 45.95%. These results demonstrate that pore-scale parameters and liquid properties jointly regulate droplet impact on curved porous media, with pore structure affecting penetration and liquid properties controlling spreading and recoiling. Full article
(This article belongs to the Special Issue Advances in Numerical Simulations of Fluid Flow, Heat Transfer, and Turbulence Modeling)
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30 pages, 10099 KB  
Article
Simulation Study of Micro-Natural Circulation in the Reactor Pressure Vessel During Cold Shutdown Maintenance
by Fulong Tang, Yuqing Chen, Wei Wang and Hongguang Xiao
Mathematics 2026, 14(14), 2630; https://doi.org/10.3390/math14142630 - 20 Jul 2026
Viewed by 426
Abstract
To investigate the micro-natural circulation phenomenon within the pressure vessel of a small nuclear reactor during cold shutdown maintenance, a comprehensive reactor pressure vessel model was developed utilizing the RELAP5 3D program. A sensitivity analysis was performed on the node division of critical [...] Read more.
To investigate the micro-natural circulation phenomenon within the pressure vessel of a small nuclear reactor during cold shutdown maintenance, a comprehensive reactor pressure vessel model was developed utilizing the RELAP5 3D program. A sensitivity analysis was performed on the node division of critical control components, including the reactor core, descent section, chamber, and bypass flow channel, to assess the efficacy of the improved modeling scheme. The thermohydraulic characteristics of micro-natural circulation at varying power levels were examined. Furthermore, the Collier formula was employed to refine the low-flow heat-exchange model. The results indicate that the node division in core areas, such as the reactor core and the descending section, is highly sensitive to simulation outcomes. The optimized model effectively addresses the issues of overestimating circulation flow and underestimating the temperature difference in heat exchange present in the original model. Within the pressure vessel, three parallel flow paths exist: the main circulation, local short circulation, and bypass circulation, with the main circulation flow rate comprising nearly 69%. Power significantly influences micro-natural circulation. At a power level of 25 kW, the steady-state flow rate of natural circulation reaches 0.95 kg/s, while the steady-state temperature difference between the inlet and outlet of the reactor core is 3.7 K. Conversely, at a power level of 5 kW, the microcirculation flow rate is approximately 0.53 kg/s, and the temperature difference between the inlet and outlet of the reactor core is about 1.3 K. Compared to the original heat-exchange model of the RELAP5 program, the Collier formula more accurately characterizes the heat-exchange behavior under low-flow micro-natural circulation conditions. These research findings provide a theoretical basis and modeling reference for the thermal simulation of cold shutdown conditions in pressurized water reactors, as well as for nuclear safety assessments during maintenance. Full article
(This article belongs to the Special Issue Advances in Numerical Simulations of Fluid Flow, Heat Transfer, and Turbulence Modeling)
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40 pages, 4376 KB  
Article
Memory-Driven Anomalous Heat Transport in Heterogeneous Media: A Two-Dimensional Time-Fractional Porous Medium Approach
by Mashael Bander Alshammari, Norazrizal Aswad Abdul Rahman and Abdullah Haif Alshammari
Mathematics 2026, 14(13), 2251; https://doi.org/10.3390/math14132251 - 24 Jun 2026
Viewed by 367
Abstract
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical [...] Read more.
Heat transport in heterogeneous materials can deviate markedly from classical Fourier behavior when microstructural disorder, trapping effects, nonlinear mobility, and long-range temporal correlations interact across multiple spatial and temporal scales. These mechanisms may produce delayed relaxation, persistent thermal footprints, front deformation, and non-classical spreading patterns that are not adequately represented by conventional integer-order diffusion models. In this study, a modeling and simulation framework is developed for anomalous heat transport in heterogeneous media using a two-dimensional time-fractional porous medium equation. The model combines a Caputo fractional time derivative, which represents thermal memory, with nonlinear degenerate porous-medium diffusion, spatially heterogeneous conductivity, localized volumetric heating, and Robin-type convective boundary exchange. A conservative fully discrete numerical scheme is constructed using flux-based finite differences for the heterogeneous nonlinear diffusion operator and an L1 approximation for the Caputo derivative. The nonlinear algebraic system at each time level is solved using an under-relaxed Picard frozen-coefficient iteration with non-negativity enforcement and sparse direct solution of the resulting linear systems. The numerical implementation is verified through a manufactured-solution convergence study, and additional analyses are performed to examine computational cost, Picard iteration behavior, coefficient-regularization sensitivity, strong-source effects, heterogeneous conductivity structures, and long-time thermal-footprint persistence. The results show that heterogeneous conductivity mainly redirects heat through preferential pathways and enlarges the spatial footprint while producing negligible changes in global heat content. Stronger fractional memory, represented by smaller fractional order, increases the persistence and spatial reach of moderate heating, whereas larger porous-medium exponents confine heat near the source and preserve higher local peaks. Source amplitude increases the thermal burden and footprint monotonically over the tested range, including strong forcing, without producing an abrupt localization-spreading transition. Boundary exchange remains secondary in the short-time interior-heating regime considered. These findings demonstrate that the proposed two-dimensional time-fractional porous medium framework provides a verified and physically interpretable model for non-Fourier heat transport in heterogeneous materials, where local intensity, global heat retention, and spatial thermal exposure must be assessed jointly. Full article
(This article belongs to the Special Issue Advances in Numerical Simulations of Fluid Flow, Heat Transfer, and Turbulence Modeling)
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