This study evaluates the generalization performance and representation efficiency (parsimony) of a previously introduced Tensor Basis Kolmogorov-Arnold Network (TBKAN) architecture for data-driven turbulence modeling. The TBKAN framework replaces the multi-layer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov-Arnold network (KAN), which significantly reduces the model complexity while providing a structure that potentially can be used with symbolic regression to provide a physical interpretability that is not available in a 'black box' MLP. While some prior work demonstrated TBKAN's feasibility for modeling a 'simple' flat plate boundary layer flow, this study extends the TBKAN architecture to model more complex benchmark flows, in particular, square duct and periodic hills flows which exhibit strong turbulence anisotropy, secondary motion, and flow separation and reattachment. A realizability-informed loss function is employed to constrain the model predictions, and, for the first time, TBKAN predictions are stably injected into the Reynolds-averaged Navier-Stokes equations to provide it a posteriori predictions of the mean velocity field.

A k , and A v2 .For any tensor A, the first invariant is given by I 1 ðAÞ ¼ trðAÞ and the second invariant is given by I 2 ðAÞ ¼

Despite well-known limitations of Reynolds-averaged Navier–Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows due to computational efficiency. Machine learning is a promising approach to improve the accuracy of RANS simulations. One major area of improvement is using machine learning models to represent the complex relationship between the mean flow field gradients and the Reynolds stress tensor. In the present work, modifications to improve the stability of previous optimal eddy viscosity approaches for RANS simulations are presented and evaluated. The optimal eddy viscosity is reformulated with a non-negativity constraint, which promotes numerical stability. We demonstrate that the new formulation of the optimal eddy viscosity improves conditioning of RANS equations for a periodic hills test case. To demonstrate the suitability of this proportional/orthogonal tensor decomposition for use in a physics-informed data-driven turbulence closure, we use two neural networks (structured on this specific tensor decomposition, which is incorporated as an inductive bias into the network design) to predict the newly reformulated linear and non-linear parts of the Reynolds stress tensor. Injecting these network model predictions for the Reynolds stresses into RANS simulation improves predictions of the velocity field, even when compared to a sophisticated (state of the art) physics-based turbulence closure model. Finally, we apply shapley additive explanations values to obtain insights from the learned representation for inner workings of the neural network used to predict the optimal eddy viscosity from the input feature data.

In this paper, we present a Cartesian grid-based numerical framework for the direct simulation of dense particulate flow under explosive dispersal. This numerical framework is established through the integration of the following numerical techniques: (1) operator splitting for partitioned fluid–solid interaction in the time domain, (2) the second-order SSP Runge–Kutta method and third-order WENO scheme for temporal and spatial discretization of governing equations, (3) the front-tracking method for evolving phase interfaces, (4) a field function proposed for low-memory-cost multimaterial mesh generation and fast collision detection, (5) an immersed boundary method developed for treating arbitrarily irregular and changing boundaries, and (6) a deterministic multibody contact and collision model. Employing the developed framework, this paper further studies particle jet formation under explosive dispersal by considering the effects of particle properties, particulate payload morphologies, and burster pressures. By the simulation of the dispersal processes of dense particle systems driven by pressurized gas, in which the driver pressure reaches \(1.01325\times 10^{10}\,\,\mathrm {Pa}\) (\(10^5\) times the ambient pressure) and particles are impulsively accelerated from stationary to a speed that is more than \(12000\,\,\mathrm {m/s}\) within \(15\,\,\mathrm {\upmu s}\), it is demonstrated that the presented framework is able to effectively resolve coupled shock–shock, shock–particle, and particle–particle interactions in complex fluid–solid systems with shocked flow conditions, arbitrarily irregular particle shapes, and realistic multibody collisions.

SUMMARY This paper makes the first attempt of extending implicit AUSM‐family schemes to multiphase flow simulations. Water faucet, air–water shock tube and oscillating manometer problems are used as benchmark tests with the generic four‐equation two‐fluid model. For solving the equations implicitly, Newton's method along with a sparse matrix solver (UMFPACK solver) is employed, and the numerical Jacobian matrix is calculated. Comparison between implicit and explicit AUSM‐family schemes is presented, indicating that similarly accurate results are obtained with both schemes. Furthermore, the water faucet problem is solved using both staggered and collocated grids. This investigation helps integrate high‐resolution schemes into staggered‐grid‐based computational algorithms. The influence of the interface pressure correction on the simulation results is also examined. Results show that the interfacial pressure correction introduces numerical dissipation. However, this dissipation cannot eliminate the overshoots because of the incompatibility of numerical discretization of the conservative and non‐conservative terms in the governing equations. The comparison of CPU time between implicit and explicit schemes is also studied, indicating that the implicit scheme is capable of improving the computational efficiency over its explicit counterpart. Copyright © 2014 John Wiley & Sons, Ltd.

Large-eddy simulations (LES) of high Reynolds number flows are performed using a non-body conformal method in conjunction with a wall model. We use a simple wall function to model the wall-shear stress and the truncation error of the numerical discretization to model the sub-grid scale turbulence (implicit LES), although these can be easily replaced if necessary. The validation cases are: turbulent flow through an inclined channel, turbulent flow over a wavy surface, and supersonic flow over a circular cylinder. Since the near-wall grids are naturally coarse, the key is to use a method that is capable of capturing the flow dynamics accurately in the vicinity of the interface. Towards the purpose, we develop a Cartesian cut-cell method, referred to as the ghost-cell based cut-cell method (GC-CCM), in the context of fully compressible solutions of Navier-Stokes equations. This method employs ghost-cells inside the solid interface such that the local spatial reconstruction remains consistent everywhere including in the vicinity of the boundary. In order to capture the near-wall flow behavior more accurately with coarse grids, this method decomposes cell faces of merged cells and computes fluxes through each decomposed segment separately. The objective of this work is to qualify whether the proposed method can accurately represent the high Reynolds number flows in the vicinity of immersed interfaces. To analyze the performance of the proposed method, we compare the results to the corresponding numerical results from the two other non-body conformal methods, namely the ghost-cell based immersed boundary method (GCIBM) and standard cut-cell method (S-CCM), that are implemented in the same numerical solver. The comparison demonstrates that the proposed method is capable of capturing near-wall flows relatively accurately with coarse grids. (C) 2015 Elsevier Inc. All rights reserved.

A methodology to perform a ghost-cell-based immersed boundary method (GCIBM) is presented for simulating compressible turbulent flows around complex geometries. In this method, the boundary condition on the immersed boundary is enforced through the use of 'ghost cells' that are located inside the solid body. The computations of variables on these ghost cells are achieved using linear interpolation schemes. The validity and applicability of the proposed method is verified using a three-dimensional (3D) flow over a circular cylinder, and a large-eddy simulation of fully developed 3D turbulent flow in a channel with a wavy surface. The results agree well with the previous numerical and experimental results, given that the grid resolution is reasonably fine. To demonstrate the capability of the method for higher Mach numbers, supersonic turbulent flow over a circular cylinder is presented. While more work still needs to be done to demonstrate higher robustness and accuracy, the present work provides interesting insights using the GCIBM for the compressible flows.

A dense, solid particle flow is numerically studied at a mesoscale level for a cylindrical shock tube problem. The shock tube consists of a central high pressure gas driver section and an annular solid powder bed with air in void regions as a driven section with its far end adjacent to ambient air. Simulations are conducted to explore the fundamental phenomena, causing clustering of particles and formation of coherent particle jet structures in such a dense solid flow. The influence of a range of parameters is investigated, including driver pressure, particle morphology, particle distribution and powder bed configuration. The results indicate that the physical mechanism responsible for this phenomenon is twofold: the driver gas jet flow induced by the shock wave as it passes through the initial gaps between the particles in the innermost layer of the powder bed, and the chaining of solid particles by inelastic collision. The particle jet forming time is determined as the time when the motion of the outermost particle layer of the powder bed is first detected. The maximum number of particle jets is bounded by the total number of particles in the innermost layer of the powder bed. The number of particle jets is mainly a function of the number of particles in the innermost layer and the mass ratio of the powder bed to the gas in the driver section, or the ratio of powder bed mass (in dimensionless form) to the pressure ratio between the driver and driven sections.

The k c v--7model has been investigated to quantify its predictive performance on two high-lift configurations: 2D flow over a single-element aerofoil, involving closedtype separation; 3D flow over a prolate spheroid, involving open-type separation. A 'code-friendly' modification has been proposed which enhances the numerical stability, in particular, for explicit and uncoupled flow solvers. As a result of introducing Reynolds-number dependence into a coefficient of the e-equation, the skin-friction distribution for the by-pass transitional flow over a flat plate is better predicted. In order to improve deficiencies arising from the Boussinesq approximation, a nonlinear stress-strain constitutive relation was adopted, in which the only one free constant is calibrated on the basis of DNS data, and the Reynolds-stress anisotropy near the wall is fairly well represented.

In this paper the Navier-Stokes- (NS-) model is considered within a large-eddy simulation framework. An investigation is carried out using fully developed turbulent channel flow at a fairly low Reynolds number. This is a flow where diffusion plays a prominent role, and presents a challenge to the nonlinear model investigated here. It is found that when 2k is based on the mesh spacing, the NS- model has a tendency to tilt spanwise vorticity in the streamwise direction, leading to high skin friction. This is due to interaction between the spanwise vorticity, the model, and the streamwise streaks. To overcome this problem 2k is damped in the streak-affected region. The overall results demonstrate the potential of the model to reproduce some features of the DNS (helicity statistics and small-scale features), but more work is required before the full potential of the model can be achieved. In addition to the channel flow investigation, a derivation of the governing using Hamilton's principle is given. The derivation is intended to be clear and accessible to a wide audience, and contains a new interpretation of the model parameter.

Isolating the source of an unknown contaminant emission is a challenging problem when provided with only a limited and noisy set of mean concentration measurements. A Bayesian approach to this inverse problem yields estimates for the source parameters (location and strength) which depend directly on the quality of the information obtained from an array of detectors. If the data are of poor quality, uncertainties associated with the source parameter estimates may be large, necessitating further exploration (e.g., using mobile detection) in order to better isolate the putative source. We employ Bayesian experimental design with the goal of strategically placing an additional detector in order to maximize the ‘expected information’ contained in subsequent posterior distributions for the source parameters. The methodology is demonstrated using synthetic data from detectors lying in a horizontally homogeneous, neutrally-stratified atmospheric surface layer. Markov chain Monte Carlo and a posterior sampling technique are used to calculate the expected information over a grid of potential detector locations, and an auxiliary detector measuring both mean concentration and turbulent scalar fluxes is added where the expected information reaches a maximum. The updated posterior distribution (calculated based on the additional measurements) yields significantly improved estimates for the source location and strength.

The present study focuses on the development of the methodology necessary for the study of fluid-structure interactions between a square cross-section cylinder and a turbulent cross-flow. The square cylinder is simulated in three configurations: 1) stationary, 2) undergoing prescribed vertical motion, and 3) undergoing autonomous vertical motion. Motion of the square cylinder through the computational domain is facilitated through a method of localized mesh deformation, which deforms the control volumes immediately above and below the square cylinder as it moves. Results for prescribed vertical motion of the cylinder, governed by sinusoidal equations of motion, are compared to those from published literature and a substantial agreement is achieved. In order to simulate autonomous motion, a vibration model is implemented providing direct application of the shear and pressure balance around the square cylinder to the motion of the cylinder.

In this paper we investigate a subgrid model based on an anisotropic version of the NS-α model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-α model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic equations (Holm, Physica D 133:215, 1999). It was found that when α 2 was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices and a ‘mixing out’ of the velocity profile. This is analogous to the Craik–Leibovich mechanism, with the difference being that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in α 2 encountered when α 2 = 0 on the endwalls. A definition of α 2 based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the model show a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region, in qualitative agreement with DNS results.

Models for momentum and heat exchange have been derived from the results of previous 3D mesoscale simulations of detonation in packed aluminum particles saturated with nitromethane, where the shock interaction timescale was resolved. In these models, particle acceleration and heating within the shock and detonation zone are expressed in terms of velocity and temperature transmission factors, which are a function of the metal to explosive density ratio, solid volume fraction and ratio of particle size to detonation zone thickness. These models are incorporated as source terms in the governing equations for continuum dense two-phase flow, and then applied to macroscopic simulation of detonation of nitromethane/aluminum in lightly-cased cylinders. Heterogeneous detonation features such as velocity deficit, enhanced pressure, and critical diameter effects are demonstrated. Various spherical particle diameters from 3 - 350 mu m are utilized where most of the particles react in the expanding detonation products. Results for detonation velocity, pressure history, failure and U-shaped critical diameter behavior are compared to existing experiments.

Among many presumed-shape pdf approaches for modeling non-premixed turbulent combustion, the presumed β-function pdf is widely used in the literature. However, numerical integration of the β-function pdf may encounter singularity difficulties at mixture fraction values of Z = 0 or 1. To date, this issue has been addressed by few publications. The present study proposes the Piecewise Integration Method (PIM), an efficient, robust and accurate algorithm to overcome these numerical difficulties with the added benefit of improving computational efficiency. Comparison of this method to the existing numerical integration methods shows that the PIM exhibits better accuracy and greatly increases computational efficiency. The PIM treatment of the β-function pdf integration is first applied to the Burke–Schumann solution in conjunction with the k − ε turbulence model to simulate a CH4/H2 bluff-body turbulent flame. The proposed new method is then applied to the same flow using a more complex combustion model, the laminar flamelet model. Numerical predictions obtained by using the proposed β-function pdf integration method are compared to experimental values of the velocity field, temperature and species mass fractions to illustrate the efficiency and accuracy of the present method.

The conventional volume-of-fluid method has the potential to deal with large free surface deformation on a fixed Cartesian grid. However, when free-surface flows are within or over complex geometries of industrial relevance, such as free-surface flows over offshore oil platforms, it is advantageous to extend the method originally written in Cartesian forms into non-Cartesian forms. In the present study, an algorithm similar to the algorithm described by Rudman in 1997 is proposed for use with curvilinear co-ordinates. This extension results in the ability to model complex geometries which could not be modelled using the original algorithm. Excellent agreement between the solutions obtained on both orthogonal and non-orthogonal meshes is achieved, although in general the L1 error, based on the exact solution, on the non-orthogonal mesh is slightly higher than that on the orthogonal mesh. The extended fluid flow solving capacity of the present method is demonstrated through its application to a non-orthogonal Rayleigh-Taylor instability problem.

The present study is focused on large eddy simulations (LES) that use a statistical (RANS) turbulence model near solid walls, and on the artificial buffer layer that is formed at the interface between these two modeling regions. Additional forcing is used to trigger resolved motions in the LES region more quickly, and leads to improved results in several ways. The study investigates the artificial buffer layer and how it changes with the use of forcing in an in-depth manner, with the purpose of increased understanding of the increasingly popular hybrid LES/RANS group of methods.The artificial buffer layer is shown to extend from below the modeling interface to well above it, in fact up to 20% of the boundary layer thickness for the cases studied here. The artificial buffer layer is found to be similar to the true buffer layer in many aspects, including a high correlation between the streamwise and wall normal velocity components in the 'superstreaks'. This indicates that while the superstreaks are highly anisotropic and have unphysical length scales, they still contribute to the resolved shear stress. The forcing does not remove the artificial buffer layer, but it does reduce its extent and increases the resolved shear stress. This increase is mainly associated with increased fluctuations of the wall normal velocity.A simple, low-dimensional forcing model is proposed and tested, with favorable results. The model is simple to implement and easily generalized to more complex geometries. (C) 2007 Elsevier Inc. All rights reserved.

Early experimental work, conducted at Defence R&D Canada — Suffield, measured and characterized the personal and environmental contamination associated with the simulated opening of anthrax-tainted letters under a number of different scenarios. A better understanding of the physical and biological processes is considerably significant for detecting, assessing, and formulating potential mitigation strategies for managing these risks. These preliminary experimental investigations have been extended to simulate the contamination from the opening of anthrax-tainted letters in an Open-Office environment using Computational Fluid Dynamics (CFD). Bacillus globigii (BG) was used as a biological simulant for anthrax, with 0.1 gram of the simulant released from opened letters in the experiments conducted. The accuracy of the model for prediction of the spatial distribution of BG spores in the office is first assessed quantitatively by comparison with measured SF6 concentrations (the baseline experiment), and then qualitatively by comparison with measured BG concentrations obtained under a number of scenarios, some involving people moving within various offices.