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Large-scale circulation of the atmosphere in the Earth's extratropics is dominated by eddies, eastward (westerly) zonal winds, and their interaction. Eddies not only bring about weather variabilities but also help maintain the average state of climate. In recent years, our understanding of how large-scale eddies and mean flows interact in the extratropical atmosphere has advanced significantly due to new dynamical constraints on finite-amplitude eddies and the related eddy-free reference state. This article reviews the theoretical foundations for finite-amplitude Rossby wave activity and related concepts. Theory is then applied to atmospheric data to elucidate how angular momentum is redistributed by the generation, transmission, and dissipation of Rossby waves and to reveal how an anomalously large wave event such as atmospheric blocking may arise from regional eddy-mean flow interaction.
Stephen H. Davis (1939–2021) was an applied mathematician, fluid dynamicist, and materials scientist who lead the field in his contributions to interfacial dynamics, thermal convection, thin films, and solidification for over 50 years. Here, we briefly review his personal and professional life and some of his most significant contributions to the field.
Airtanker firefighting is the most spectacular tool used to fight wildland fires. However, it employs a rudimentary large-scale spraying technology operating at a high speed and a long distance from the target. This review gives an overview of the fluid dynamics processes that govern this practice, which are characterized by rich and varied physical phenomena. The liquid column penetration in the air, its large-scale fragmentation, and an intense surface atomization give shape to the rainfall produced by the airtanker and the deposition of the final product on the ground. The cloud dynamics is controlled by droplet breakup, evaporation, and wind dispersion. The process of liquid deposition onto the forest canopy is full of open questions of great interest for rainfall retention in vegetation. Of major importance, but still requiring investigation, is the role of the complex non-Newtonian viscoelastic and shear-thinning behavior of the retardant dropped to stop the fire propagation. The review describes the need for future research devoted to the subject.
This review highlights major developments and milestones during the early days of numerical simulation of turbulent flows and its use to increase our understanding of turbulence phenomena. The period covered starts with the first simulations of decaying homogeneous isotropic turbulence in 1971–1972 and ends about 25 years later. Some earlier history of the progress in weather prediction is included if relevant. Only direct simulation, in which all scales of turbulence are accounted for explicitly, and large-eddy simulation, in which the effect of the smaller scales is modeled, are discussed. The method by which all scales are modeled, Reynolds-averaged Navier–Stokes, is not covered.
Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities.
Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.
Bubble plumes are ubiquitous in nature. Instances in the natural world include the release of methane and carbon dioxide from the seabed or the bottom of a lake and from a subsea oil well blowout. This review describes the dynamics of bubble plumes and their various spreading patterns in the surrounding environment. We explore how the motion of the plume is affected by the density stratification in the external environment, as well as by internal processes of dissolution of the bubbles and chemical reaction. We discuss several examples, such as natural disasters, global warming, and fishing techniques used by some whales and dolphins.
We review some fundamentals of turbulent drag reduction and the turbulent drag reduction techniques using streamwise traveling waves of blowing/suction from the wall and wall deformation. For both types of streamwise traveling wave controls, their significant drag reduction capabilities have been well confirmed by direct numerical simulation at relatively low Reynolds numbers. The drag reduction mechanisms by these streamwise traveling waves are considered to be the combination of direct effects due to pumping and indirect effects of the attenuation of velocity fluctuations due to reduced receptivity. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts at experimental validation are also intensively ongoing toward their practical implementation.
Ventilation is central to human civilization. Without it, the indoor environment rapidly becomes uncomfortable or dangerous, but too much ventilation can be expensive. We spend much of our time indoors, where we are exposed to pollutants and can be infected by airborne diseases. Ventilation removes pollution and bioaerosols from indoor sources but also brings in pollution from outdoors. To determine an appropriate level of ventilation and an appropriate way of providing it, one must understand that the needs for ventilation extend beyond simple thermal comfort; the quality of indoor air is at least as important. An effective ventilation system will remove unwanted contaminants, whether generated within the space by activities or by the simple act of breathing, and ensure that the ventilation system does not itself introduce or spread contaminants from elsewhere. This review explores how ventilation flows in buildings influence personal exposure to indoor pollutants and the spread of airborne diseases.
In the last ten years, advances in experimental techniques have enabled remarkable discoveries of how the dynamics of thin gas films can profoundly influence the behavior of liquid droplets. Drops impacting onto solids can skate on a film of air so that they bounce off solids. For drop–drop collisions, this effect, which prevents coalescence, has been long recognized. Notably, the precise physical mechanisms governing these phenomena have been a topic of intense debate, leading to a synergistic interplay of experimental, theoretical, and computational approaches. This review attempts to synthesize our knowledge of when and how drops bounce, with a focus on (a) the unconventional microscale and nanoscale physics required to predict transitions to/from merging and (b) the development of computational models. This naturally leads to the exploration of an array of other topics, such as the Leidenfrost effect and dynamic wetting, in which gas films also play a prominent role.
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): J.M. Catalán, S. Olivieri, M. García-Villalba, O. Flores
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s):
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Ertiza Hossain Shopnil, Md. Nadeem Azad, Jahid Emon, A.K.M. Monjur Morshed
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Chen Chen, Yu Sun
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): Will Trojak, Tarik Dzanic
Publication date: 15 August 2024
Source: Computers & Fluids, Volume 280
Author(s): A. Navas-Montilla, J. Guallart, P. Solán-Fustero, P. García-Navarro
Publication date: Available online 25 July 2024
Source: Computers & Fluids
Author(s): Xiang Song, Linlin Fei, Haonan Peng, Xiaolong He
Publication date: Available online 25 July 2024
Source: Computers & Fluids
Author(s): Linfei Li, Tai Jin, Liyong Zou, Kun Luo, Jianren Fan
Publication date: Available online 11 July 2024
Source: Computers & Fluids
Author(s): Prakasha Chandra Sahoo, Jnana Ranjan Senapati, Basanta Kumar Rana
Publication date: Available online 10 July 2024
Source: Computers & Fluids
Author(s): Yong-Dong Liang, Zhi-Hui Li, Jie Liang, Jia-Zhi Hu
The staggered Legendre spectral element method is extended to the quasi-static magnetohydrodynamic (MHD) setting, which relative to hydrodynamics involves an additional Poisson-like problem for the electric potential. The proposed discretization is suitable for large-scale simulations involving three-dimensional geometries of arbitrary complexity that feature turbulent and/or transitional dynamics. The numerical solutions are shown to converge exponentially with polynomial order.
The classical staggered ℙN-ℙN−2$$ {\mathbb{P}}_N\hbox{-} {\mathbb{P}}_{N-2} $$ spectral element method (SEM) is revisited and extended to quasi-static magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the so-called consistent Poisson operator. The method is well suited for fully three-dimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density.
A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The scheme allows for CFL values up to 100, with reduced numerical diffusion compared to the original Godunov scheme. This plot shows a sample simulation for the 1D advection equation reported in the article.
A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, well-balanced discretisations of the geometric source term is acknowledged.
A novel interface reconstruction method is proposed to reconstruct the interface from volume fractions for use with Geometric Volume-of-Fluid algorithms. The algorithm uses a Marching Cube based isoAlpha method which uses a look-up-table based approach enabling fast and robust interface reconstruction. We highlight issues pertaining to the bracketability of the solution for certain interface configurations. These cases are isolated and handled using a Parker-Young based interface reconstruction method. Finally static and dynamic interface reconstruction cases are demonstrated.
In modelling two-phase flows, accurate representation of interfaces is crucial. A class of methods for interface reconstruction are based on isosurface extraction, which involves a non-iterative, interpolation based approach. These approaches have been shown to be faster by an order of magnitude than the conventional PLIC schemes. In this work, we present a new isosurface extraction based interface reconstruction scheme based on the Marching Cubes algorithm (MC), which is commonly used in computer graphics for visualizing isosurfaces. The MC algorithm apriori lists and categorizes all possible interface configurations in a single grid cell into a Look Up Table (LUT), which makes this approach fast and robust. We also show that for certain interface configurations, the inverse problem of obtaining the isovalue from the cell volume fraction is not surjective, and a special treatment is required while handling these cases. We then demonstrate the capabilities of the method through benchmark cases for 2D and 3D static/dynamic interface reconstruction.
This work proposes a modified forcing term in the Rothman–Keller (RK) model to minimize spurious velocities and provide more accurate results at lower capillary numbers. The current approach converges quickly and shows parallel flow accurately for all the capillary numbers as opposed to the traditional RK model (Guo approach). Leakage is also successfully captured by the current approach for most of the capillary numbers, which wasn't the case for Volume of Fluid and phase field methods.
The lattice-Boltzmann method (LBM) is becoming increasingly popular for simulating multi-phase flows on the microscale because of its advantages in terms of computational efficiency. Many applications of the method are restricted to relatively simple geometries. When a more complex geometry is considered—circular and inclined microchannels—some important physical phenomena may not be accurately captured, especially at low capillary numbers. A Y-Y micro-fluidic channel, widely used for a range of applications, is an example of a more complex geometry. This work aims to capture the various flow phenomena, with an emphasis on parallel flow and leakage, using the Rothman–Keller (RK) model of the LBM. To this purpose, we modify the forcing term to implement the surface tension for use at low capillary numbers. We compare the simulation results of the RK model with and without the force modification with experiments, Volume of Fluid and the phase field method and observe that the modified forcing term is an improvement over the current RK model at low capillary numbers, and it also captures parallel flow and leakage more accurately than the other simulation techniques.
This article develops a reduced smoothed integration (RSI) scheme of the cell-based finite element method for fluid-structure interaction. After introducing an hourglass control to the under-integrated formulation, the RSI scheme has an inbuilt advantage of its enormous tolerance towards negative-Jacobian elements. The proposed technique is tested, with good accuracy and higher efficiency, through various examples adopting fine and damaged meshes.
This article describes an inexpensive partitioned coupling strategy for computational fluid–structure interaction (FSI) admitting negative-Jacobian elements. The emphasis is very much on a reduced smoothed integration (RSI) scheme of the cell-based smoothed finite element method (CSFEM) using four-node quadrilateral (Q4) elements for a cost-effective solution to the Navier–Stokes (NS) equations. In the discrete fluid field, each Q4 element is considered as one single smoothing cell so as to diminish the smoothed integration loops substantially. However, the RSI scheme does not respect the stability condition of smoothed Galerkin weak-form integral in the CSFEM. To tackle this issue, a simple hourglass control is introduced to the under-integrated formulation of the NS solver. Importantly, the stabilized RSI scheme has an inbuilt advantage of its enormous tolerance towards negative-Jacobian elements. The developed technique is easy-to-implement and has been tested in various FSI examples adopting both fine and distorted meshes.
The paper describes an efficient co-design of a reactive GPGPU CFD flow solver for heterogeneous hardware architectures, that may lead to speedups up of an order of magnitude in reactive CFD computations using Direct Integration of finite-rate chemistry. Combustion simulations of Sustainable Aviation Fuels (SAFs) are used to test accuracy, performance and to validate the method.
The solution of reactive computational fluid dynamics (CFD) simulations is accelerated by the implementation of a hybrid central processing unit/graphics processing units (CPU/GPU) Finite Volume solver based on the operator-splitting strategy, where the chemistry integration is treated independently of the flow solution. The integration of ordinary differential equations (ODEs) describing the finite-rate chemical kinetics is solved by an adaptive multi-block explicit solver on GPUs, while the load of the fluid solution is distributed on a multicore CPU algorithm. The resulting speed-up for reactive CFD simulations is up to 10×$$ \times $$; the performance gain increases with the size of the mechanism. The proposed implementation is general and can be applied to any CFD problem where the governing equations for the fluid transport are coupled with an ODE system. Code validation is performed against reference solutions on a selection of test cases involving reacting flows.
In this work by Jakob Vandergrift* and Florian Kummer, “an extended discontinuous Galerkin shock tracking method” for PDEs with discontinuities is proposed and successfully applied to 2D problems showing promising results. At the heart of the method a level set is employed, implicitly enrichening the approximation space, allowing for accurate representation of solution discontinuities within cut-cells and without requiring additional stabilization. The shock-fitted level set and the PDE solution are computed simultaneously using an optimization approach.
In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso-contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two-dimensional problems, progressively increasing in complexity.
The MP-BP approximation model can improve hull form optimization efficiency. Numerical verification and hull form verification demonstrate the reliability of approximation. The optimization method can provide support for green design and manufacturing.
In 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.
Plot of cation concentration u at time t = 0.2.
In this work, we consider the Darcy scale precipitation–dissolution reactive transport 1D and 2D models in a porous medium and provide the adaptive mesh based numerical approximations for solving them efficiently. These models consist of a convection-diffusion-reaction PDE with reactions being described by an ODE having a nonlinear, discontinuous, possibly multi-valued right hand side describing precipitate concentration. The bulk concentration in the aqueous phase develops fronts and the precipitate concentration is described by a free and time-dependent moving boundary. The time adaptive moving mesh strategy, based on equidistribution principle in space and governed by a moving mesh PDE, is utilized and modified in the context of present problem for finite difference set up in 1D and finite element set up in 2D. Moreover, we use a predictor corrector based algorithm to solve the nonlinear precipitation–dissolution models. For equidistribution approach, we choose an adaptive monitor function and smooth it based on a diffusive mechanism. Numerical tests are performed to demonstrate the accuracy and efficiency of the proposed method by examples through finite difference approach for 1D and finite element approach in 2D. The moving mesh refinement accurately resolves the front location of Darcy scale precipitation–dissolution reactive transport model and reduces the computational cost in comparison to numerical simulations using a fixed mesh.
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Wei Jiang, Chunmei Su, Ganghui Zhang
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Liang Li, Jun Zhu, Yong-Tao Zhang
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Jin-Peng Liu, Lin Lin
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Zhaoyue Xu, Shizhao Wang, Xin-Lei Zhang, Guowei He
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Carlos A. Pereira, Brian C. Vermeire
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Sidi Wu, Aiqing Zhu, Yifa Tang, Benzhuo Lu
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Wonjun Lee, Li Wang, Wuchen Li
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): F. Clerici, P.R. Spalart, F. Alauzet
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Gian-Michele Cherchi, Alain Dequidt, Arnaud Guillin, Nicolas Martzel, Patrice Hauret, Vincent Barra
Publication date: 1 October 2024
Source: Journal of Computational Physics, Volume 514
Author(s): Robin Barta, Christian Bauer, Sebastian Herzog, Daniel Schiepel, Claus Wagner
The generation mechanism of wall heat flux is one of the fundamental problems in supersonic/hypersonic turbulent boundary layers. A novel heat decomposition formula under the curvilinear coordinate was proposed in this paper. The new formula has wider application scope and can be applied in the configurations with grid deformed. The new formula analyzes the wall heat flux of an interaction between a shock wave and a turbulent boundary layer over a compression corner. The results indicated good performance of the formula in the complex interaction region. The contributions of different energy transport processes were obtained. While the processes by the mean profiles such as molecular stresses and heat conduction, can be ignored, the contributions by the turbulent fluctuations, such as Reynolds stresses and turbulent transfer of heat flux, were greatly increased. Additionally, the pressure work is another factor that affects the wall heat flux. The pressure work in the wall-normal direction is concentrated close to the reattachment point, while the pressure work in the streamwise direction acts primarily in the shear layer and the reattachment point.
A previously developed numerical-multilayer modeling approach for systems of governing equations is extended so that unwanted terms, resulting from vertical variations in certain background parameters, can be removed from the dispersion-relation polynomial associated with the system. The new approach is applied to linearized anelastic and compressible systems of governing equations for gravity waves including molecular viscosity and thermal diffusion. The ability to remove unwanted terms from the dispersion-relation polynomial is crucial for solving the governing equations when realistic background parameters, such as horizontal velocity and temperature, with strong vertical gradients, are included. With the unwanted terms removed, previously studied dispersion-relation polynomials, for which methods for defining upgoing and downgoing vertical wavenumber roots already exist, are obtained. The new methods are applied to a comprehensive set of medium-scale time-wavepacket examples, with realistic background parameters, lower boundary conditions at 30 km altitude, and modeled wavefields extending up to 500 km altitude. Results from the compressible and anelastic model versions are compared, with compressible governing-equation solutions understood as the more physically accurate of the two. The new methods provide significantly less computationally expensive alternatives to nonlinear time-step methods, which makes them useful for comprehensive studies of the behavior of viscous/diffusive gravity waves and also for large studies of cases based on observational data. Additionally, they generalize previously existing Fourier methods that have been applied to inviscid problems while providing a theoretical framework for the study of viscous/diffusive gravity waves.
In this paper we present a numerical scheme based on spectral collocation methods to investigate the flow of a piezo-viscous fluid, i.e., a fluid in which the rheological parameters depend on the pressure. In particular, we consider an incompressible Navier–Stokes fluid with pressure dependent viscosity flowing in: (i) a two-dimensional non-symmetric planar channel; (ii) a three-dimensional axisymmetric non-straight conduit. For both cases we impose the Navier slip boundary conditions that can be reduced to the classical no-slip condition for a proper choice of the slip parameter. We assume that the dependence of the viscosity on the pressure is of exponential type (Barus law), even though the model can be replaced by any other viscosity function. We write the mathematical problem (stress based formulation) and discretize the governing equations through a spectral collocation scheme. The advantage of this numerical procedure, which to the authors’ knowledge has never been used before for this class of fluids, lies in in the ease of implementation and in the accuracy of the solution. To validate our model we compare the numerical solution with the one that can be obtained in the case of small aspect ratio, i.e., the leading order lubrication solution. We perform some numerical simulation to investigate the effects of the pressure-dependent viscosity on the flow. We consider different wall functions to gain insight also on the role played by the channel/duct geometry. In both cases (i), (ii) we find that the increase of the coefficient appearing in the viscosity function results in a global reduction of the flow, as physically expected.
The effects of inlet Mach number on the unsteadiness of shock-boundary layer interactions (SBLIs) over curved surfaces are investigated for a supersonic turbine cascade using wall-resolved large eddy simulations. Three inlet Mach numbers, 1.85, 2.00, and 2.15 are considered at a chord-based Reynolds number 395,000. The curved walls of the airfoils impact the SBLIs due to the state of the incoming boundary layers and local pressure gradients. On the suction side, due to the convex wall, the boundary layer entering the SBLI evolves under a favorable pressure gradient and bulk dilatation. On the other hand, the concave wall on the pressure side imposes an adverse pressure gradient and bulk compression. Variations in the inlet Mach number induce different shock impingement locations, enhancing these effects. A detailed characterization of the suction side boundary layers indicates that a higher Mach number leads to larger shape factors, favoring separation and larger bubbles, while the reverse holds for the pressure side. A time-frequency analysis reveals the presence of intermittent events in the separated flow occurring predominantly at low-frequencies on the suction side and at mid-frequencies on the pressure side. Increasing the inlet Mach number leads to an increase in the time scales of the intermittent events on the suction side, which are associated with instants when high-speed streaks penetrate the bubble, causing local flow reattachment and bubble contractions. Instantaneous flow visualizations show the presence of streamwise vortices developing on the turbulent boundary layers on both airfoil sides and along the bubbles. These vortices influence the formation of the large-scale longitudinal structures in the boundary layers, affecting the mass imbalance inside the separation bubbles.
We conduct a comprehensive analysis of two data assimilation methods: the first utilizes the discrete adjoint approach with a correction applied to the production term of the turbulence transport equation, preserving the Boussinesq approximation. The second is a state observer method that implements a correction in the momentum equations alongside a turbulence model, both applied to fluid dynamics simulations. We investigate the impact of varying computational mesh resolutions and experimental data resolutions on the performance of these methods within the context of a periodic hill test case. Our findings reveal the distinct strengths and limitations of both methods, which successfully assimilate data to improve the accuracy of a RANS simulation. The performance of the variational model correction method is independent of input data and computational mesh resolutions. The state observer method, on the other hand, is sensitive to the resolution of the input data and CFD mesh.
Two-dimensional free-surface flow past a submerged rectangular disturbance in an open channel is considered. The forced Korteweg–de Vries model of Binder et al. (Theor Comput Fluid Dyn 20:125–144, 2006) is modified to examine the effect of varying obstacle length and height on the response of the free-surface. For a given obstacle height and flow rate in the subcritical flow regime an analysis of the steady solutions in the phase plane of the problem determines a countably infinite set of discrete obstacle lengths for which there are no waves downstream of the obstacle. A rich structure of nonlinear behaviour is also found as the height of the obstacle approaches critical values in the steady problem. The stability of the steady solutions is investigated numerically in the time-dependent problem with a pseudospectral method.
An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input; for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval’s theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval’s theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform; and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow (Zhang et al. in Exp Fluids 61(226):1–12, https://doi.org/10.1007/s00348-020-03057-8, 2020) and high-fidelity large-eddy simulation (LES) data from a round jet (Brès et al. in J. Fluid Mech. 851:83–124, https://doi.org/10.1017/jfm.2018.476, 2018), with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage. The tonal frequencies associated with the Rossiter instability are accurately identified. For both the tonal cavity and the broadband jet flows, results comparable to or better than those from standard SPOD based on Welch’s overlapped segment averaging are obtained with up to 75% fewer snapshots, including similar convergence of the Rossiter modes and Kelvin-Helmholtz wavepacket structures for the cavity and jet examples, respectively. Drawing from these examples, we establish best practices.
This study explores coherent structures in a swirling turbulent jet. Stationary axisymmetric solutions of the Reynolds–Averaged Navier–Stokes equations at \(Re=200,000\) were obtained using an open source computational fluid dynamics code and the Spalart–Allmaras eddy viscosity model. Then, resolvent analysis with the same eddy viscosity field provided coherent structures of the turbulent fluctuations on the base flow. As in many earlier studies, a large gain separation is identified between the optimal and sub-optimal resolvent modes, permitting a focus on the most amplified response mode and its corresponding optimal forcing. At zero swirl, the results indicate that the jet’s coherent response is dominated by axisymmetric ( \(m=0\) ) structures, which are driven by the usual Kelvin–Helmholtz shear amplification mechanism. However, as swirl is increased, different coherent structures begin to dominate the response. For example, double and triple spiral ( \(|m|=2\) and \(|m|=3\) ) modes are identified as the dominant structures when the axial and azimuthal velocity maxima of the base flow are comparable. In this case, distinct co- and counter-rotating \(|m|=2\) modes experience vastly different degrees of amplification. The physics of this selection process involve several amplification mechanisms contributing simultaneously in different regions of the mode. This is analysed in more detail by comparing the alignment between the wavevector of the dominant response mode and the principal shear direction of the base flow. Additional discussion also considers the development of structures along the exterior of the jet nozzle.
In open flow simulations, the dispersion characteristics of disturbances near synthetic boundaries can lead to unphysical boundary scattering interactions that contaminate the resolved flow upstream by propagating numerical artifacts back into the domain interior. This issue is exacerbated in flows influenced by real or apparent body forces, which can significantly disrupt the normal stress balance along outflow boundaries and generate spurious pressure disturbances. To address this problem, this paper develops a zero-parameter, physics-based outflow boundary condition (BC) designed to minimize pressure scattering from body forces and pseudo-forces and enhance transparency of the artificial boundary. This “balanced outflow BC” is then compared against other common BCs from the literature using example axisymmetric and three-dimensional open swirling flow computations. Due to centrifugal and Coriolis forces, swirling flows are known to be particularly challenging to simulate in open geometries, as these apparent forces induce non-trivial hydrostatic stress distributions along artificial boundaries that cause scattering issues. In this context, the balanced outflow BC is shown to correspond to a geostrophic hydrostatic stress correction that balances the induced pressure gradients. Unlike the alternatives, the balanced outflow BC yields accurate results in truncated domains for both linear and nonlinear computations without requiring assumptions about wave characteristics along the boundary.
A combined data-assimilation and linear mean-flow analysis approach is developed to estimate coherent flow fluctuations from limited mean-flow measurements. It also involves Reynolds-Averaged Navier–Stokes (RANS) modelling to efficiently tackle turbulent flows. Considering time-averaged Particle Velocimetry Image (PIV) measurements of the near-stall flow past a NACA0012 airfoil at an angle of attack of \(10^{\circ }\) and in the chord-based Reynolds number range \(4.3 \cdot 10^4 \le Re \le 6.4 \cdot 10^4\) , data assimilation is first employed to correct RANS equations that are closed by the Spalart-Allmaras model. The outputs of this procedure are a full mean-flow description that matches the PIV data and a consistent turbulence model that provides not only a mean eddy-viscosity field but also the perturbations of the latter with respect to mean-flow modifications. Global stability and resolvent analyses are then performed based on the so-obtained mean flow and model to satisfactorily predict near-stall low-frequency phenomena, as confirmed through comparison with the Spectral Proper Orthogonal Decomposition (SPOD) of the PIV measurements. This comparison highlights the benefits in taking into account variations in the turbulent eddy-viscosity over a frozen approach for the correct estimation of the present coherent low-frequency oscillations.
