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Mathematics
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Numerical Simulation and Methods in Computational Fluid Dynamics
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Numerical Simulation and Methods in Computational Fluid Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: closed (31 March 2025) | Viewed by 6236

Special Issue Editor

Dr. Sebastian A. Altmeyer

E-Mail Website
Guest Editor
Castelldefels School of Telecom and Aerospace Engineering (EETAC), Universitat Politècnica de Catalunya (UPC), 08034 Barcelona, Spain
Interests: computational fluid dynamics; nonlinear dynamics; computational and mathematical physics; numerical simulation; numerical modeling

Special Issue Information

Dear Colleagues,

We are pleased to announce this Special Issue of the journal Mathematics entitled “Numerical Simulation and Methods in Computational Fluid Dynamics”. Computational fluid dynamics (CFD) is a branch of fluid mechanics that utilizes numerical simulations and modeling to study the behavior of fluids in various engineering and scientific applications. It plays a crucial role in understanding complex fluid dynamics, optimizing designs, and predicting the performance of fluid systems. Currently, many researchers make use of numerical simulation to investigate fluid flow phenomena such as turbulence, transition to turbulence, fluid–structure interactions, multiphase flows, and heat transfer to further analyze fluid behavior, the prediction of flow patterns, and the optimization of system. This Special Issue welcomes papers focusing on innovative numerical methods and simulation techniques in computational fluid dynamics. Topics of interest include but are not limited to numerical schemes for solving ferrofluids, nanofluids, binary fluids, fluid flow equations, turbulence modeling, and novel approaches for handling complex fluid flow problems. We invite contributions from authors on these topics.

Dr. Sebastian A. Altmeyer
Guest Editor

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Keywords

  • computational fluid dynamics
  • Taylor–Couette system
  • mathematical modeling
  • numerical simulation
  • nonlinear dynamics
  • dynamical system theory
  • pattern formation
  • transition to turbulence
  • turbulent flow
  • Navier–Stokes equations
  • computational approaches
  • ferrofluids
  • nanofluids
  • computational and mathematical physics

 

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Published Papers (6 papers)

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Research

26 pages, 11860 KiB  
Article
Convection in a Rapidly Rotating Spherical Shell: Newton’s Method Using Implicit Coriolis Integration
by Juan Cruz Gonzalez Sembla, Camille Rambert, Fred Feudel and Laurette S. Tuckerman
Mathematics 2025, 13(13), 2113; https://doi.org/10.3390/math13132113 - 27 Jun 2025
Viewed by 150
Abstract
Geophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by the implicit integration of the terms that are most responsible for destabilizing the numerical scheme. We have implemented [...] Read more.
Geophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by the implicit integration of the terms that are most responsible for destabilizing the numerical scheme. We have implemented an implicit treatment of the Coriolis force in a rotating spherical shell driven by a radial thermal gradient. We modified the resulting timestepping code to carry out steady-state solving via Newton’s method, which has no timestepping error. The implicit terms have the effect of preconditioning the linear systems, which can then be rapidly solved by a matrix-free Krylov method. We computed the branches of rotating waves with azimuthal wavenumbers ranging from 4 to 12. As the Ekman number (the non-dimensionalized inverse rotation rate) decreases, the flows are increasingly axially independent and localized near the inner cylinder, in keeping with well-known theoretical predictions and previous experimental and numerical results. The advantage of the implicit over the explicit treatment also increases dramatically with decreasing Ek, reducing the cost of computation by as much as a factor of 20 for Ekman numbers of order of 10−5. We carried out continuation for both the Rayleigh and Ekman numbers and obtained interesting branches in which the drift velocity remained unchanged between pairs of saddle–node bifurcations. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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21 pages, 13453 KiB  
Article
Buoyant Flow and Thermal Analysis in a Nanofluid-Filled Cylindrical Porous Annulus with a Circular Baffle: A Computational and Machine Learning-Based Approach
by Pushpa Gowda, Sankar Mani, Ahmad Salah and Sebastian A. Altmeyer
Mathematics 2025, 13(12), 2027; https://doi.org/10.3390/math13122027 - 19 Jun 2025
Viewed by 1027
Abstract
Control of buoyancy-assisted convective flow and the associated thermal behavior of nanofluids in finite-sized conduits has become a great challenge for the design of many types of thermal equipment, particularly for heat exchangers. This investigation discusses the numerical simulation of the buoyancy-driven convection [...] Read more.
Control of buoyancy-assisted convective flow and the associated thermal behavior of nanofluids in finite-sized conduits has become a great challenge for the design of many types of thermal equipment, particularly for heat exchangers. This investigation discusses the numerical simulation of the buoyancy-driven convection (BDC) of a nanofluid (NF) in a differently heated cylindrical annular domain with an interior cylinder attached with a thin baffle. The annular region is filled with non-Darcy porous material saturated-nanofluid and both NF and the porous structure are in local thermal equilibrium (LTE). Higher thermal conditions are imposed along the interior cylinder as well as the baffle, while the exterior cylinder is maintained with lower or cold thermal conditions. The Darcy–Brinkman–Forchheimer model, which accounts for inertial, viscous, and non-linear drag forces was adopted to model the momentum equations. An implicit finite difference methodology by considering time-splitting methods for transient equations and relaxation-based techniques is chosen for the steady-state model equations. The impacts of various pertinent parameters, such as the Rayleigh and Darcy numbers, baffle dimensions, like length and position, on flow, thermal distributions, as well as thermal dissipation rates are systematically estimated through accurate numerical predictions. It was found that the baffle dimensions are very crucial parameters to effectively control the flow and associated thermal dissipation rates in the domain. In addition, machine learning techniques were adopted for the chosen analysis and an appropriate model developed to predict the outcome accurately among the different models considered. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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26 pages, 3650 KiB  
Article
Geometrical Optics Stability Analysis of Rotating Visco-Diffusive Flows
by Oleg Kirillov
Mathematics 2025, 13(3), 382; https://doi.org/10.3390/math13030382 - 24 Jan 2025
Viewed by 931
Abstract
Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, encompassing both compressible and incompressible fluids. The method models perturbations as high-frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving [...] Read more.
Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, encompassing both compressible and incompressible fluids. The method models perturbations as high-frequency wavelets, evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and amplitude of the wavelet envelope along streamlines, with coefficients derived from the background flow. While viscosity and diffusivity were traditionally regarded as stabilizing factors, recent extensions of the geometrical optics framework have revealed their destabilizing potential in visco-diffusive and multi-diffusive flows. This review highlights these advancements, with a focus on their application to the azimuthal magnetorotational instability in magnetohydrodynamics and the McIntyre instability in lenticular vortices and swirling differentially heated flows. It introduces new analytical instability criteria, applicable across a wide range of Prandtl, Schmidt, and magnetic Prandtl numbers, which still remains beyond the reach of numerical methods in many important physical and industrial applications. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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18 pages, 16053 KiB  
Article
Modelling the Transition from Shear-Driven Turbulence to Convective Turbulence in a Vertical Heated Pipe
by Shijun Chu, Elena Marensi and Ashley P. Willis
Mathematics 2025, 13(2), 293; https://doi.org/10.3390/math13020293 - 17 Jan 2025
Viewed by 790
Abstract
Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and [...] Read more.
Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length L=5D and L=25D. Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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23 pages, 5357 KiB  
Article
Convective Heat Transfer in Uniformly Accelerated and Decelerated Turbulent Pipe Flows
by Ismael Essarroukh and José M. López
Mathematics 2024, 12(22), 3560; https://doi.org/10.3390/math12223560 - 14 Nov 2024
Viewed by 1053
Abstract
This study presents a detailed investigation of the temporal evolution of the Nusselt number (Nu) in uniformly accelerated and decelerated turbulent pipe flows under a constant heat flux using direct numerical simulations. The influence of different acceleration and deceleration rates [...] Read more.
This study presents a detailed investigation of the temporal evolution of the Nusselt number (Nu) in uniformly accelerated and decelerated turbulent pipe flows under a constant heat flux using direct numerical simulations. The influence of different acceleration and deceleration rates on heat transfer is systematically studied, addressing a gap in the previous research. The simulations confirm several key experimental findings, including the presence of three distinct phases in the Nusselt number temporal response—delay, recovery, and quasi-steady phases—as well as the characteristics of thermal structures in unsteady pipe flow. In accelerated flows, the delay in the turbulence response to changes in velocity results in reduced heat transfer, with average Nu values up to 48% lower than those for steady-flow conditions at the same mean Reynolds number. Conversely, decelerated flows exhibit enhanced heat transfer, with average Nu exceeding steady values by up to 42% due to the onset of secondary instabilities that amplify turbulence. To characterize the Nu response across the full range of acceleration and deceleration rates, a new model based on a hyperbolic tangent function is proposed, which provides a more accurate description of the heat transfer response than previous models. The results suggest the potential to design unsteady periodic cycles, combining slow acceleration and rapid deceleration, to enhance heat transfer compared to steady flows. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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14 pages, 13879 KiB  
Article
Effect of an Applied Magnetic Field on Joule Heating-Induced Thermal Convection
by Anupam M. Hiremath, Harunori N. Yoshikawa and Innocent Mutabazi
Mathematics 2024, 12(21), 3395; https://doi.org/10.3390/math12213395 - 30 Oct 2024
Viewed by 1202
Abstract
Thermal convection induced by internal heating appears in different natural situations and technological applications with different internal sources of heat (e.g., radiation, electric or magnetic fields, chemical reactions). Thermal convection due to Joule heating in weak electrical conducting liquids such as molten salts [...] Read more.
Thermal convection induced by internal heating appears in different natural situations and technological applications with different internal sources of heat (e.g., radiation, electric or magnetic fields, chemical reactions). Thermal convection due to Joule heating in weak electrical conducting liquids such as molten salts with symmetric thermal boundary conditions is investigated using linear stability analysis. We show that, in the quasi-static approximation where the induced magnetic field is negligible, the effect of the external magnetic field consists of the delay in the threshold of thermal convection and the increase in the size of thermoconvective rolls for an intense magnetic field. Analysis of the budget of the perturbations’ kinetic energy reveals that the Lorentz force contributes to the dissipation of the kinetic energy. Full article
(This article belongs to the Special Issue Numerical Simulation and Methods in Computational Fluid Dynamics)
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