Fluid Dynamics Problems Research Articles

Comparative Analysis of NURBS and Finite Element Method in Computational Fluid Dynamics Applications: Case Study on NACA 2412 Airfoil Aerodynamics

In this research, an attempt was made to employ the Non-Uniform Rational B-Splines (NURBS) method for a challenging computational fluid dynamics (CFD) problem of aerodynamics around NACA 2412 airfoils. The comparison was carried out thoroughly by using the same boundary conditions and geometry, comparing NURBS to standard FEM implementations. Our study was interested in demonstrating the foreseeable functionalities of NURBS for solving complex CFD problems and conducting a comparative effectiveness performance evaluation between them with traditional FEM methodologies.

Heat and mass transfer in MHD flow of SWCNT and graphene nanoparticles suspension in Casson fluid

AbstractThe exceptional mechanical properties of carbon nanotubes (CNTs) and graphene nanoparticles, particularly their high aspect ratio and flexibility, position them as highly promising materials for the next generation of armor technology. Their incorporation into protective wear, such as bullet‐proof vests, offers the potential for significant improvements in both performance and cost efficiency. By replacing traditional materials with CNTs and graphene, the durability and maintenance of these protective devices could be substantially enhanced, leading to more effective and sustainable solutions for personal safety. This study focuses on the complex phenomena of heat and mass transport within a suspension of CNTs and graphene nanoparticles dispersed in a Casson fluid, particularly under the influence of an applied magnetic field. The analysis begins by reformulating the governing equations using similarity variables to transform them into a dimensionless form to simplify the problem. The resulting dimensionless equations are then solved using the three‐stage Lobatto IIIa finite difference method, a robust numerical technique well‐suited for solving boundary value problems in fluid dynamics. The results of this investigation highlight a significant 78.41% reduction in skin friction when compared with traditional CNT‐water nanofluid systems. This considerable decrease in skin friction not only reveals the superior performance of the CNT‐graphene nanofluid suspension but also opens up new possibilities for the design and development of advanced protective materials. These findings contribute to the growing body of knowledge on nanofluid applications and offer valuable insights for future research in the field of advanced armor technology.

New and Modified Homotopy Perturbation Methods for Addressing Burger’s Non-linear Equation

Objectives: The aim of this study is to find a novel solution procedure for solving a fluid dynamical problem, especially to solve two-dimensional coupled Burger’s non-linear equation. Methods: New and Modified homotopy perturbation techniques are used to solve the two-dimensional coupled Burger’s equation. The methods intend to make homotopy perturbation method a more robust and trustworthy tool for fluid dynamics researchers by addressing convergence concerns, improving solution accuracy and allowing it to handle a broader range of problems. Findings: The solution for two-dimensional coupled Burger’s non-linear equation is obtained by constructing homotopies. Numerical results thus obtained are compared with the exact solution. The obtained results and the exact solutions to the stated problem are closely related. Novelty: The New and Modified Homotopy Perturbation Method proposed in this paper are effective mathematical tools for getting an exact solution to the coupled Burgers' equations. It is also a potential approach for solving various linear and nonlinear partial differential equations. Keywords: Perturbation, Homotopy, New homotopy perturbation, Modified homotopy perturbation, Two­dimension, Linear, Coupled burgers' equation

A comprehensive review of advances in physics-informed neural networks and their applications in complex fluid dynamics

Physics-informed neural networks (PINNs) represent an emerging computational paradigm that incorporates observed data patterns and the fundamental physical laws of a given problem domain. This approach provides significant advantages in addressing diverse difficulties in the field of complex fluid dynamics. We thoroughly investigated the design of the model architecture, the optimization of the convergence rate, and the development of computational modules for PINNs. However, efficiently and accurately utilizing PINNs to resolve complex fluid dynamics problems remain an enormous barrier. For instance, rapidly deriving surrogate models for turbulence from known data and accurately characterizing flow details in multiphase flow fields present substantial difficulties. Additionally, the prediction of parameters in multi-physics coupled models, achieving balance across all scales in multiscale modeling, and developing standardized test sets encompassing complex fluid dynamic problems are urgent technical breakthroughs needed. This paper discusses the latest advancements in PINNs and their potential applications in complex fluid dynamics, including turbulence, multiphase flows, multi-field coupled flows, and multiscale flows. Furthermore, we analyze the challenges that PINNs face in addressing these fluid dynamics problems and outline future trends in their growth. Our objective is to enhance the integration of deep learning and complex fluid dynamics, facilitating the resolution of more realistic and complex flow problems.

Exploring swirling flow dynamics: Unsupervised machine learning in Maxwell hybrid nanofluid convection over an exponentially stretching cylinder with non-linear radiation effects

This article analyses the flow of Maxwell hybrid nanofluid induced by an exponentially stretching and rotating cylinder. The presence of non-linear convection, non-linear radiation, and magnetic field is also assumed. The factors covered in the study has a wide spectrum of application in various disciplines, and therefore we analyse the influence of different flow parameters after numerically solving the set of modelled differential equations. A data-free physics-informed neural network using a wavelet activation function is used to approximate the numerical solution. The reliability of the used methodology is validated by comparing the results of the limiting case with the available results. The paper demonstrates the effectiveness of using PINN in an unsupervised fashion to tackle fluid flow problems, showcasing their ability to provide reliable and accurate solutions without the need for extensive datasets. This approach highlights the potential of PINN to address complex fluid dynamics problems by utilizing physical laws within the neural network framework. From the numerical study, it is observed that hybrid nanofluid has a better rate of heat transfer compared to the nanofluid. Furthermore, radiation parameter and maxwell flow parameter is seen to exhibit significant impact of the flow profiles.

MH-DCNet: An improved flow field prediction framework coupling neural network with physics solver

With the development of intelligent computing technology, deep learning methods have provided an efficient solution for rapid flow field prediction in computational fluid dynamics (CFD) problems. However, existing methods have limitations in handling interference among physical variables due to different data distributions, leading to a decline in prediction performance. In this paper, we propose MH-DCNet, an improved flow field prediction framework that couples a neural network with a physics solver. Specifically, to address the data distribution problem, we design a multi-head deep convolutional neural network that decouples the prediction of physical variables through multiple encoders and decoders. We also develop a hybrid loss function by introducing the mean structural similarity to better capture the complex spatial structures and distribution features of flow fields. We evaluate MH-DCNet with unseen geometries and various flow conditions. Experimental results show that MH-DCNet outperforms other advanced models in efficiency and generalization capability. It accelerates the prediction process by 2.35 times compared to the CFD method while meeting the convergence constraints.

Application of the iteratively regularized Gauss–Newton method to parameter identification problems in Computational Fluid Dynamics

Field Inversion and Machine Learning is an active field of research in Computational Fluid Dynamics (CFD). This approach can be leveraged to obtain a closed-form correction for a given turbulence model to improve the predictions. The fundamental approach is to insert a parameter into the system of RANS equations and determine it in a way such that, for example, a given pressure distribution is better approximated compared to the one obtained with the original set of equations. The goal of this article is twofold. Numerical arguments are presented that these kinds of problems can be severely ill-posed. In the second part, an approach is presented to directly reconstruct the turbulent viscosity field along with an example. The Iteratively Regularized Gauss-Newton Method (IRGNM) is used for a realization. The construction of a problem-adapted norm for a finite volume method is presented. Finally, an outlook is presented on how this approach can be used to possibly modify or improve turbulence models such that not only one, but a larger number of test cases are considered.

Deep Reinforcement Learning for Fluid Mechanics: Control, Optimization, and Automation

A comprehensive review of recent advancements in applying deep reinforcement learning (DRL) to fluid dynamics problems is presented. Applications in flow control and shape optimization, the primary fields where DRL is currently utilized, are thoroughly examined. Moreover, the review introduces emerging research trends in automation within computational fluid dynamics, a promising field for enhancing the efficiency and reliability of numerical analysis. Emphasis is placed on strategies developed to overcome challenges in applying DRL to complex, real-world engineering problems, such as data efficiency, turbulence, and partial observability. Specifically, the implementations of transfer learning, multi-agent reinforcement learning, and the partially observable Markov decision process are discussed, illustrating how these techniques can provide solutions to such issues. Finally, future research directions that could further advance the integration of DRL in fluid dynamics research are highlighted.

Reducing spatial discretization error on coarse CFD simulations using an openFOAM-embedded deep learning framework

AbstractWe propose a method for reducing the spatial discretization error of coarse computational fluid dynamics (CFD) problems by enhancing the quality of low-resolution simulations using deep learning. We feed the model with fine-grid data after projecting it to the coarse-grid discretization. We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values to produce velocities that approximate the down-sampled fine-grid data well. The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model. We automatically differentiate the CFD physics using a discrete adjoint code version. We present a fast communication method between TensorFlow (Python) and OpenFOAM (c++) that accelerates the training process. We applied the model to the flow past a square cylinder problem, reducing the error from 120% to 25% in the velocity for simulations inside the training distribution compared to the traditional solver using an x8 coarser mesh. For simulations outside the training distribution, the error reduction in the velocities was about 50%. The training is affordable in terms of time and data samples since the architecture exploits the local features of the physics.

Variable coefficient-informed neural network for PDE inverse problem in fluid dynamics

Variable-coefficient equations are crucial in the field of fluid dynamics as they accurately capture the spatial and temporal variations of fluid properties. In many cases, there exist some constraints among multiple coefficients and embedding these constraints into neural networks poses a challenge. In this paper, we design a variable coefficient-informed neural network (VCINN) to address the inverse problem of variable-coefficients partial differential equation in fluid dynamics. The VCINN framework integrates the physics-informed neural network (PINN) with the constraints among multiple coefficients, encoding both constraints and physics information into the neural networks. Compared to classical PINN, VCINN enjoys such several advantages as parallelization capacity, embedding constraint information and efficient hyperparameter adjustment. Through series of examples, the capability of the approach to recover coefficients from observations has been demonstrated. Numerical results indicate that the present method achieves higher accuracy and lower training error compared to classical PINN.

A comparative study of exact and neural network models for wave‐induced multiphase flow in nonuniform geometries: Application of Levenberg–Marquardt neural networks

AbstractMultiphase fluids exhibit immiscible, heterogeneous structures like emulsions, foams, and suspensions. Their complex rheology arises from relative phase proportions, interfacial interactions, and component properties. Consequently, they demonstrate nonlinear effects—shear‐thinning, viscoelasticity, and yield stress. Peristalsis generates fluid flow by propagating contraction waves along channel walls. This mechanism can effectively transport multiphase and non‐Newtonian fluids in microsystems. Accurate modeling requires considering evolving phase relations, variable viscosity, slip, and particle migration anomalies, using approaches like homogenization theory or volume‐averaging. Applications include peristaltic pumping of emulsified biopharmaceuticals, microscale mixing/separating of multiphase constituents, and enhancing porous media fluid flow in oil reservoirs. Analytical and computational approaches to modeling multiphase fluid flows in peristaltic conduits provide an enhanced understanding of their complex dynamics, toward innovating engineering systems. An analytical approach is taken to model non‐Newtonian Ree‐Eyring fluid flows in asymmetric, peristaltic systems. Governing differential equations incorporate key parameters and yield closed‐form solutions for velocity, flow rate, and permeability. Suitable assumptions of long wavelength, and low Reynolds number provide accuracy. In parallel, an artificial neural network (ANN) is developed using supervised learning to predict permeability. The inputs consist of channel asymmetry, Reynolds number, amplitude ratio, and other physical factors. Outcomes validate both methodologies—analytical equations derive precise relationships from first principles, while ANNs reliably learn the system patterns from input‐output data. Additionally, ANNs can tackle more complex fluid dynamics problems with speed and adaptability. Their promising role is highlighted in developing new fluid models, improving the efficiency of simulations, and designing control systems. Side‐by‐side analytical and ANN simulation plots will further highlight ANN capabilities in emulating the system characteristics. This paves the path for employing machine learning to investigate multifaceted flows in flexible, peristaltic systems at scale. Performing a graphical examination of the engineering skin friction coefficient across a range of parameters, encompassing volume fraction, first and second order slip, Ree–Eyring fluid attributes, and permeability.

Investigation on unsteady fluid flow around an oscillating sphere-A numerical and analytical approach

This article presents the Investigation on unsteady fluid flow around an oscillating sphere-A Numerical and Analytical approach. The analytical expressions for angular velocity and temperature of the fluid around an oscillating sphere have been obtained in form of Bessel functions with suitable assumed boundary conditions. The numerical results in terms of angular velocity, temperature and pressure distribution for various values of the material parameters have been obtained using R-K method of 6th order with shooting methods with the help of MATHEMATICA ND solver. The influence of thermo-viscous flow parameters on angular velocity, temperature, pressure and drag on the boundary have been presented in form of tables and graphs. It may be noticed that the thermo-viscous effects are more predominant in the flow region around the boundary of the oscillating sphere. The R-K method with shooting method is the most powerful and elegant method to solve the governing equations related to the fluid dynamics problems. This method gives the accurate and valid results of highly complex coupled governing equations. The analytical results obtained are validated with this method in the present problem. The results obtained by this method gives more accurate, stable and converging to the analytical results. The numerical solutions of governing equations of present work have been obtained are compared with the existing analytical results and are found to be in excellent agreement. The present theoretical work will be hope fully for the better understanding of researchers and scientists and also it is useful in chemical and nuclear industries.

Bifurcation tracking on moving meshes and with consideration of azimuthal symmetry breaking instabilities

We present a black-box method to numerically investigate the linear stability of arbitrary multi-physics problems. While the user just has to enter the system's residual in weak formulation, e.g. by a finite element method, all required discretized matrices are automatically assembled based on just-in-time generated and compiled C codes. Based on this method, entire phase diagrams in the parameter space can be obtained by bifurcation tracking and continuation at low computational costs. Particular focus is put on problems with moving domains, e.g. free surface problems in fluid dynamics, since a moving mesh introduces a plethora of complicated nonlinearities to the system. By symbolic differentiation before the code generation, however, these moving mesh problems are made accessible to bifurcation tracking methods. In a second step, our method is generalized to investigate symmetry-breaking instabilities of axisymmetric stationary solutions by effectively utilizing the symmetry of the base state. Each bifurcation type is validated on the basis of results reported in the literature on versatile fluid dynamics problems, for which we subsequently present novel results as well.

Asymmetrical suction and injection in laminar channels with porous walls: a fixed point approach

The problem of laminar flow in a rectangular channel with a pair of porous walls is considered. The porous walls allow fluid to be injected into or sucked out of the channel at constant velocities normal to the walls; the velocities at each wall are not necessarily of equal magnitude nor symmetrical in direction. In this article, a unique solution to this problem is shown to exist for sufficiently low Reynolds numbers through the application of Banach's fixed point theorem. This serves to further the discussion about the uniqueness of solutions for this problem, whilst also demonstrating the suitability of a fixed point approach to this family of fluid dynamics problems.

On the choice of physical constraints in artificial neural networks for predicting flow fields

The application of Artificial Neural Networks (ANNs) has been extensively investigated for fluid dynamic problems. A specific form of ANNs are Physics-Informed Neural Networks (PINNs). They incorporate physical laws in the training and have increasingly been explored in the last few years. In this work, the prediction accuracy of PINNs is compared with that of conventional Deep Neural Networks (DNNs). The accuracy of a DNN depends on the amount of data provided for training. The change in prediction accuracy of PINNs and DNNs is assessed using a varying amount of training data. To ensure the correctness of the training data, they are obtained from analytical and numerical solutions of classical problems in fluid mechanics. The objective of this work is to quantify the fraction of training data relative to the maximum number of data points available in the computational domain, such that the accuracy gained with PINNs justifies the increased computational cost. Furthermore, the effects of the location of sampling points in the computational domain and noise in training data are analyzed. In the considered problems, it is found that PINNs outperform DNNs when the sampling points are positioned in the Regions of Interest. PINNs for predicting potential flow around a Rankine oval have shown a better robustness against noise in training data compared to DNNs. Both models show higher prediction accuracy when sampling points are randomly positioned in the flow domain as compared to a prescribed distribution of sampling points. The findings reveal new insights on the strategies to massively improve the prediction capabilities of PINNs with respect to DNNs.

Numerical simulation for MHD slip flow with heat transfer over a stretching bullet‐shaped object

AbstractThis paper investigates magnetohydrodynamic (MHD) boundary layer slip flow with heat transfer over a bullet shaped object. The study addresses a significant problem in fluid dynamics and heat transport with applications in various engineering and industrial domains, including aerospace, material processing, and energy systems. The governing equations are resolved using the bvp4c, an inbuilt MATLAB tool, and the arithmetic computation for the momentum and thermotic equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted with the aid of velocity and temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The heat transfer processes and fluid flow are remarkably influenced by means of the ratio of surface thickness and stretching potential. The results obtained designated that the Mixed convection parameter λ increases momentum BL thickness, whereas the temperature profile diminishes. Furthermore, momentum and temperature profile improve for surface thickness parameter . The current investigation highlights the potential utility of heat transport rate and friction factor in the industrial divisions for regulating cooling rates and enhancing the quality of end products.

Reduced-order modeling of unsteady fluid flow using neural network ensembles

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at handling data that are spatially distributed, including solutions to partial differential equations. When applied to unsteady physics problems, ROMs also require a model for time-series prediction of the low-dimensional latent variables. Long short-term memory (LSTM) networks, a type of recurrent neural network useful for modeling sequential data, are frequently employed in data-driven ROMs for autoregressive time-series prediction. When making predictions at unseen design points over long time horizons, error propagation is a frequently encountered issue, where errors made early on can compound over time and lead to large inaccuracies. In this work, we propose using bagging, a commonly used ensemble learning technique, to develop a fully data-driven ROM framework referred to as the CAE-eLSTM ROM that uses CAEs for spatial reconstruction of the full-order model and LSTM ensembles for time-series prediction. When applied to two unsteady fluid dynamics problems, our results show that the presented framework effectively reduces error propagation and leads to more accurate time-series prediction of latent variables at unseen points.

Dynamics of ternary nanofluid through radiated sensor surface: Numerical investigation

Application: The impact of flow, heat transfer, and magneto hydrodynamics on sensor surfaces between two parallel compressing plates with porous walls has been examined in this study. This study focuses on understanding unsteady compressed flow in two dimensions, utilizing Aluminum oxide, copper oxide, and titanium dioxide with base fluid polymers as the base fluid. Nanofluids, known as nanometer suspensions in traditional nanoscale fluid transfer, are explored for their potential application in improving lubricative and cooling properties. Purpose and methodology: This study aims to investigate the behavior of a tri-hybrid nanofluid (Aluminum oxide, copper oxide, and titanium dioxide with base fluid polymers) in terms of flow dynamics, heat transfer, and magneto hydrodynamics. Energy and momentum equations, considering magneto hydrodynamic forms and heat transfer, are analyzed. The study employs numerical methods, including similarity transforms and a shooting approach, to solve the governing equations. Core findings: Several parameters, including permeable parameter, magnetic parameter, squeeze flow index parameter, volume fraction by nanoparticles, and radiation parameter, are investigated for their effects on temperature profile and velocity profile. The study illustrates these effects graphically and discusses the influence of these parameters on different components of velocity and temperature fields. Additionally, the impact of the radiation parameter ([Formula: see text] on temperature fields is examined for both positive. Future work: Future research may focus on further optimizing the tri-hybrid nanofluid composition for specific applications, exploring additional parameters that may affect flow behavior, heat transfer, and entropy generation. Additionally, experimental validation of the numerical findings and the development of more advanced numerical techniques for solving complex fluid dynamics problems could be the areas of interest for future work.

Molecular dynamics simulation of argon isochoric transition to supercritical state

AbstractThe effect of the initial atoms distribution on the molecular dynamics (MD) simulation of a model atomic fluid (argon) is investigated for the case of the isochoric phase transition to the supercritical state. In particular, the case of uniformly distributed atoms in the simulation domain is compared with the case of separated liquid and vapor atoms. The sensitivity of simulations to asymmetric nanoscale perturbations in the boundary is also studied. Despite its high computational cost, the MD approach has the potential to successfully address long‐standing problems in computational fluid dynamics (CFD), especially those associated with mathematical singularities, such as contact angles, vortices, phase transitions and so forth. Unlike conventional CFD simulations, where the initial condition is the pressure or velocity distribution in the simulation domain, MD simulations also require the initial position of each molecule. Thus, it is important to understand whether a judicious choice of the initial distribution of molecules can reduce the overall computation time of the simulation. The evolution of the model fluid system during the phase transition was simulated using a Lennard‐Jones interatomic potential, corrected with the Lorentz–Berthelot mixing rule for the interactions with the solid walls. The system was allowed to relax until equilibrium, and then a Heaviside temperature step was applied to the wall to bring the system to supercritical conditions. Results show the initial choice of the atoms distribution can significantly affect the computational time, while the effect of asymmetric perturbations on the boundary is negligible.

Step-like initial value problem and Whitham modulation in fluid dynamics to a generalized derivative nonlinear Schrödinger equation

Step-like initial value problem and Whitham modulation in fluid dynamics to a generalized derivative nonlinear Schrödinger equation