Fluid Dynamics Problems Research Articles

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

On the BEM solution of convection–diffusion type equations involving variable convective coefficients

In this study, numerical solutions of the unsteady convection–diffusion type equations of variable convective coefficients are investigated by two effective techniques alternative to direct boundary element method (BEM). That is, the domain boundary element and the dual reciprocity BEMs with the fundamental solution of convection–diffusion equation are used in space to transform the governing differential equations into equivalent integral equations while a backward finite difference scheme is utilized in time discretization. The fruitfulness of these combined techniques are shown by the implementation of the techniques for some widely investigated fluid dynamics problems. In fact, the lid-driven cavity flow is solved, and precise results are attained as benchmarks for assessing the accuracy of the aforementioned methods. Further, the application of the methods is extended for the natural convection flow which is governed mainly by the convection–diffusion type equations accompanied by the velocity components as variable convective coefficients. The obtained numerical results reveal that the domain BEM which uses the fundamental solution of convection–diffusion equation captures the characteristics and physical advancement of the fluid flow quite well at various combined values of the problem physical parameters.

Feeding rate in adult Manduca sexta is unaffected by proboscis submersion depth.

Adult moths from framily Spingidae (i.e. hawkmoths or sphinx moths) commonly feed on flower nectar through an extended proboscis, often several centimeters in length and longer than the body of the moth. Feeding on a viscous liquid (nectar) through a long and narrow tube is a challenging fluid dynamic problem and the subject of long-running scientific investigation. Here we characterized the relationship between proboscis submergence depth and nectar drinking rate in Manduca sexta hawkmoths. Video recordings of moth feeding bouts were collected and neural networks were used to extract data by object localization, tracking the location of the nectar meniscus and moths' proboscis tips. We found that although feeding rates vary among bouts, the variation was not associated with proboscis submergence depth. These results show that despite the theoretical possibility of fluid uptake through the walls of the proboscis, such effects do not have a substantial effect on nectar uptake rate, and suggest that nectar must traverse the full length of the proboscis.

The Schwarzian Approach in Sturm–Liouville Problems

A novel method for finding the eigenvalues of a Sturm–Liouville problem is developed. Following the minimalist approach, the problem is transformed to a single first-order differential equation with appropriate boundary conditions. Although the resulting equation is nonlinear, its form allows us to find the general solution by adding a second part to a particular solution. This splitting of the general solution into two parts involves the Schwarzian derivative: hence, the name of the approach. The eigenvalues that correspond to acceptable solutions can be found by requiring the second part to correct the asymptotically diverging behavior of the particular solution. The method can be applied to many different areas of physics, such as the Schrödinger equation in quantum mechanics and stability problems in fluid dynamics. Examples are presented.

SYNTHETIC DATA GENERATION FOR ANN MODELING OF THE HYDRODYNAMIC PROCESSES OF IN-SITU LEACHING

The work presents an approach to enhance the forecasting capabilities of In-Situ Leaching processes during both the production stage and early prognosis. ISL, a crucial method for resource extraction, demands rapid on-site forecasting to guide the deployment of new technological blocks. Traditional modeling techniques, though effective, are hindered by their computational demands and network throughput requirements, particularly when dealing with substantial datasets or remote computing needs. The integration of AI technologies, specifically neural networks, offers a promising opportunity for expedited calculations by leveraging the power of forward propagation through pretrained neural models. However, a critical challenge lies in transforming conventional numerical datasets into a format suitable for neural modeling. Furthermore, the scarcity of training data during the production phase, where vital parameters are concealed underground, poses an additional challenge in training AI models for In-Situ Leaching processes. This research addresses these challenges by proposing a methodology for generating training data tailored to the most resource-intensive Computational Fluid Dynamics problems encountered during modeling. Traditional numerical modeling techniques are harnessed to construct training datasets comprising input and corresponding expected output data, with a particular focus on varying well network patterns. Subsequent efforts are directed at the conversion of the acquired data into a format compatible with neural networks. The data is normalized to align with the data ranges stipulated by the activation functions employed within the neural network architecture. This preprocessing step ensures that the neural model can effectively learn from the generated data, facilitating accurate forecasting of In-Situ Leaching processes. An advantage of proposed technique lies in provision of large, reliable datasets to train neural network to predict hydrodynamic properties based on technological regimes currently active or expected on ISL site. A major implication of this approach lies in applicability of pre-trained AI technologies to forecast future or determine current hydrodynamic regime in the stratum circumventing cost deterministic simulations currently deployed at mining sites. Hence, innovative approach outlined in this paper holds promise for optimizing forecasting, allowing for quicker and more efficient decision-making in resource extraction operations while getting around the computational barriers associated with traditional methods.

Leapfrogging vortex rings for the three‐dimensional incompressible Euler equations

AbstractA classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three‐dimensional fluid. In 1858, Helmholtz observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3D Euler equations exhibiting this motion pattern.

Application of the Fibonacci wavelet approach to the MHD boundary layer analysis of a Casson fluid past a stretching sheet

The current work investigates the MHD boundary layer flow of Casson fluid over a stretching sheet with the help of Fibonacci wavelet approach. The stable laminar MHD flow, mass and heat transport properties of a nanofluid over a stretching sheet in the presence of a fluctuating magnetic field has been under scrutiny. By choosing relevant non-dimensional parameters, the governing boundary layer equation undergoes transformation into a dimensionless Falkner-Skan equation. The Fibonacci integral operational matrix is used to solve the achieved nonlinear equation and it has been used for the first time to solve stretching sheet problem in fluid dynamics. The nature of the boundary layer flow are analyzed graphically for a range of distinct values of physical parameters. Impact of parameters on axial and transverse velocity has been investigated. It can be observed that local skinfriction coefficient grows for larger values of Casson parameter for ϵ = 0.3 and decreases for higher values of Casson parameter and decreases for higher values of magnetic parameter, angle of inclination and pressure gradient parameter. To ensure the accuracy of the findings, local skin friction is recorded and contrasted with various approaches that are already documented in research.

Geometrically parametrised reduced order models for studying the hysteresis of the Coanda effect in finite element-based incompressible fluid dynamics

This article presents a general reduced order model (ROM) framework for addressing fluid dynamics problems involving time-dependent geometric parametrisations. The framework integrates Proper Orthogonal Decomposition (POD) and Empirical Cubature Method (ECM) hyper-reduction techniques to effectively approximate incompressible computational fluid dynamics simulations. To demonstrate the applicability of this framework, we investigate the behaviour of a planar contraction-expansion channel geometry exhibiting bifurcating solutions known as the Coanda effect. By introducing time-dependent deformations to the channel geometry, we observe hysteresis phenomena in the solution.The paper provides a detailed formulation of the framework, including the stabilised finite elements full order model (FOM) and ROM, with a particular focus on the considerations related to geometric parametrisation. Subsequently, we present the results obtained from the simulations, analysing the solution behaviour in a phase space for the fluid velocity at a probe point, considered as the Quantity of Interest (QoI). Through qualitative and quantitative evaluations of the ROMs and hyper-reduced order models (HROMs), we demonstrate their ability to accurately reproduce the complete solution field and the QoI.While HROMs offer significant computational speedup, enabling efficient simulations, they do exhibit some errors, particularly for testing trajectories. However, their value lies in applications where the detection of the Coanda effect holds paramount importance, even if the selected bifurcation branch is incorrect. Alternatively, for more precise results, HROMs with lower speedups can be employed.

Hull form optimization research based on multi‐precision back‐propagation neural network approximation model

AbstractIn order to shorten the optimization cycle of ship design optimization and solve the time‐consuming problem of computational fluid dynamics (CFD) numerical calculation, this paper proposes a multi‐precision back‐propagation neural network (MP‐BP) approximation technology. Fewer high‐precision ship samples and more low‐precision ship samples were used to construct an approximate model, back‐propagation (BP) neural network was used to train multi‐precision samples. So that the approximate model is as close as possible to the real model, and achieving the effect of high‐precision approximation model. Subsequently, numerical verification and typical hull form verification are given. Based on CFD and Rankine theory, the multi‐objective design optimization framework for ship comprehensive navigation performance is constructed. The multi‐objective approximation model of KCS ship is constructed by MP‐BP approximation technology, and optimized by particle swarm optimization (PSO) algorithm. The results show that the multi‐objective optimization design framework using the MP‐BP approximation model can capture the global optimal solution and improve the efficiency of the entire hull form design optimization. It can provide a certain degree of technical support for green ship and low‐carbon shipping.

A data–driven sensibility tool for flow control based on resolvent analysis

This study presents a novel application of data-driven resolvent analysis algorithm for flow control. The objective is to identify key coherent structures connected to regions of the flow that are highly sensitive to structural changes. Modifying such regions, i.e., including momentum source terms, flow stabilizers, or changing the shape of the body under study, we can control the appearance of flow instabilities. The method is tested in two different applications: the laminar flow behind a two-dimensional circular cylinder and a turbulent channel flow including heat transfer to the endwall. In the first test case, the flow unsteadiness is controlled by including two stabilizers (formed by two small cylinders) in the areas suggested by resolvent analysis. This is a benchmark problem in fluid dynamics that serves to validate the idea of using this tool for flow control. In the second test case, data-driven resolvent analysis is applied as a mean to control, enhance or reduce, convective heat transfer. Modifications in the geometry, in the form of cavities and ribs included in the areas pointed by resolvent analysis, show the possibility of enhancing heat transfer while reducing drag. The findings highlight the importance of resolvent analysis in understanding flow dynamics and designing effective flow control strategies.

Application of lattice Boltzmann method to solution of viscous incompressible fluid dynamics problems

Application of lattice Boltzmann method to solution of viscous incompressible fluid dynamics problems

Investigating the new perspectives of Caudrey–Dodd–Gibbon equation arising in quantum field theory

The main purpose of the paper is obtaining the analytical results for beta fractional Caudrey–Dodd–Gibbon equation which is used to resolve complex problems in fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics by using auxiliary method. Beta derivative is a useful fractional operator due to satisfying basic properties of integer order derivative and also, allows us using chain rule and wave transform to turn nonlinear fractional partial differential equations into integer order ordinary differential equations. By the way many analytical methods can be applied to these equations. In order to understand the physical features of the solutions, 3D and 2D graphical illustrations are given. Finally, authors expect that the obtained solutions may give a deep insight for the explanation of physical phenomena in the fluid dynamics, chemical kinetics, plasma physics, quantum field theory, crystal dislocations, and nonlinear optics.

A Multi-Fidelity Uncertainty Propagation Model for Multi-Dimensional Correlated Flow Field Responses

Given the randomness inherent in fluid dynamics problems and limitations in human cognition, Computational Fluid Dynamics (CFD) modeling and simulation are afflicted with non-negligible uncertainties, casting doubts on the credibility of CFD. Scientifically and rigorously quantifying the uncertainty of CFD is paramount for assessing its credibility and informing engineering decisions. In order to quantify the uncertainty of multidimensional flow field responses stemming from uncertain model parameters, this paper proposes a method based on Gappy Proper Orthogonal Decomposition (POD) for supplementing high-fidelity flow field data within a framework that leverages POD and surrogate models. This approach enables the generation of corresponding high-fidelity flow fields from low-fidelity ones, significantly reducing the cost of high-fidelity flow field computation in uncertainty propagation modeling. Through an analysis of the impact of uncertainty in the coefficients of the Spalart–Allmaras (SA) turbulence model on the distribution of wall friction coefficients for the NACA0012 airfoil and pressure coefficients for the M6 wing, the proposed multi-fidelity modeling approach is demonstrated to offer significant advancements in both accuracy and efficiency compared to single-fidelity methods, providing a robust and efficient prediction model for large-scale random sampling.

XLB: A differentiable massively parallel lattice Boltzmann library in Python

The lattice Boltzmann method (LBM) has emerged as a prominent technique for solving fluid dynamics problems due to its algorithmic potential for computational scalability. We introduce XLB library, a Python-based differentiable LBM library based on the JAX platform. The architecture of XLB is predicated upon ensuring accessibility, extensibility, and computational performance, enabling scaling effectively across CPU, TPU, multi-GPU, and distributed multi-GPU or TPU systems. The library can be readily augmented with novel boundary conditions, collision models, or multi-physics simulation capabilities. XLB's differentiability and data structure is compatible with the extensive JAX-based machine learning ecosystem, enabling it to address physics-based machine learning, optimization, and inverse problems. XLB has been successfully scaled to handle simulations with billions of cells, achieving giga-scale lattice updates per second. XLB is released under the permissive Apache-2.0 license and is available on GitHub at https://github.com/Autodesk/XLB. Program summaryProgram Title: XLBCPC Library link to program files:https://doi.org/10.17632/n25h65vw59.1Developer's repository link:https://github.com/Autodesk/XLBLicensing provisions: Apache-2.0Programming language: PythonNature of problem: XLB is a scalable Lattice Boltzmann simulation library based on JAX. It is designed to be accessible, extensible, and high performance. The library can be readily augmented with novel boundary conditions, collision models, or simulation capabilities. Moreover, XLB is differentiable, offering the unique advantage of integration with JAX's extensive machine learning ecosystem, and tackling physics-based machine learning, optimization, and inverse problems.Solution method: XLB utilizes the JAX library for just-in-time (JIT) compilation and distributed computing, enabling it to scale effectively across distributed multi-GPU/multi-TPU systems. XLB's programming model combines an object-oriented interface for easy extensibility. The library can be readily augmented with novel boundary conditions, collision models, or other simulation capabilities.

Thermal Analysis of a Casson Boundary Layer Flow over a Penetrable Stretching Porous Wedge

This work aims to analyze the Casson thermal boundary layer flow over an expanding wedge in a porous medium with convective boundary conditions and ohmic heating. Moreover, the effects of porosity and viscous dissipation are studied in detail and included in the analysis. The importance of this study is due to its applications in biomedical engineering where the analysis of behavior of non-Newtonian blood flow in arteries and veins is desired. Within the context of blood flow, it is also applicable to many other fields, for instance, radiative therapy, MHD generators, soil machines, melt-spinning, and insulation processes. The modeled problem is a set of PDEs, which is nondimensionalized to derive a nonlinear boundary value problem (BVP). The obtained BVP is solved using the shooting technique, endowed with the order four Runge-Kutta and Newton methods. The impact of different parameters on the momentum and temperature fields is investigated along with two important parameters of physical significance, i.e., the Nusselt number and the surface drag force. Results are validated, and an excellent agreement is seen for the parameters of interest using MATLAB built-in function bvp4c. A significant finding is that by increasing the Casson liquid parameter, the velocity decreases as the wedge expands quicker than the free stream velocity at R=2. However, the velocity increases for the case when R=0.1. A decrease in the Darcy number increases the temperature profile. Furthermore, the convective parameter accelerated the heat transmission rate, and a rise in the Prandtl number thickens the thermal boundary layer. The findings of this investigation contribute to problems in fluid dynamics and heat transfer that involve studying the behavior of a non-Newtonian fluid with Casson rheological properties near a solid porous wedge surface.

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .

A fast, matrix-based method to perform omnidirectional pressure integration

Experimentally-measured pressure fields play an important role in understanding many fluid dynamics problems. Unfortunately, pressure fields are difficult to measure directly with non-invasive, spatially resolved diagnostics, and calculations of pressure from velocity have proven sensitive to error in the data. Omnidirectional line integration methods are usually more accurate and robust to these effects as compared to implicit Poisson equations, but have seen slower uptake due to the higher computational and memory costs, particularly in 3D domains. This paper demonstrates how omnidirectional line integration approaches can be converted to a matrix inversion problem. This novel formulation uses an iterative approach so that the boundary conditions are updated each step, preserving the convergence behavior of omnidirectional schemes while also keeping the computational efficiency of Poisson solvers. This method is implemented in Matlab and also as a GPU-accelerated code in CUDA-C++. The behavior of the new method is demonstrated on 2D and 3D synthetic and experimental data. Three-dimensional grid sizes of up to 125 million grid points are tractable with this method, opening exciting opportunities to perform volumetric pressure field estimation from 3D PIV measurements.

Flow2Mesh: A flow-guided data-driven mesh adaptation framework

Mesh adaptation is crucial in numerical simulation, providing optimal resource allocation for accurately capturing physical phenomena. However, when applied to Computational Fluid Dynamics (CFD) problems with complex multi-scale properties, existing adaptation methods face huge challenges due to the high computational cost of solving auxiliary partial differential equations (PDEs) and the difficulty in aligning the flow features with mesh geometric features. In this work, an end-to-end data-driven mesh adaptation framework, Flow2Mesh, is proposed to address these challenges by adopting a hybrid modeling strategy to construct the mapping from pixelated flow-fields to graph-based meshes. It achieves a rapid and accurate one-step mesh adaptation via a perceptual feature network (PFN) and a mesh movement network (MMN). PFN extracts the global perceptual features from flow-fields to enhance flow feature representation and mesh resolution independence. In MMN, these features are utilized to deform the initial mesh to a topology-invariant adaptive mesh by a proposed physically driven mesh convolutional network. It considers the inherent mesh geometric information for efficient node feature aggregation and alignment of mesh density with a flow-field structure. To generate high-quality adaptive meshes, various mesh-related losses are designed to regularize the mesh movement and alleviate the mesh tangling. Experiments in CFD scenarios demonstrate the generalization of our model to different design parameters and mesh configurations. It takes three orders of magnitude less time to generate similar meshes than the PDE-based method. The results exhibit the potential of Flow2Mesh to be a flexible and reliable tool for rapid mesh adaptation in scientific and industrial fields.

Emulator of PR‐DNS: Accelerating Dynamical Fields With Neural Operators in Particle‐Resolved Direct Numerical Simulation

AbstractParticle‐resolved direct numerical simulations (PR‐DNS) play an increasing role in investigating aerosol‐cloud‐turbulence interactions at the most fundamental level of processes. However, the high computational cost associated with high resolution simulations poses considerable challenges for large domain or long duration simulation using PR‐DNS. To address these issues, here we present an emulator of the complex physics‐based PR‐DNS developed by use of the data‐driven Fourier Neural Operator (FNO) method. The effectiveness of the method is showcased by presenting turbulence and temperature fields in a two‐dimensional space. The results demonstrate high accuracy at various resolutions and the emulator is two orders of magnitude cheaper in terms of computational demand compared to the physics‐based PR‐DNS model. Furthermore, the FNO emulator exhibits strong generalization capabilities for different initial conditions and ultra‐high‐resolution without the need to retrain models. These findings highlight the potential of the FNO method as a promising tool to simulate complex fluid dynamics problems with high accuracy, computational efficiency, and generalization capabilities, enhancing our understanding of the aerosol‐cloud‐precipitation system.