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Publication date: Available online 1 February 2023
Source: Computers & Fluids
Author(s): Shiying Xiong, Xingzhe He, Yunjin Tong, Yitong Deng, Bo Zhu
Publication date: Available online 1 February 2023
Source: Computers & Fluids
Author(s): Hongmin Su, Jinsheng Cai, Kun Qu, Shucheng Pan
Publication date: Available online 2 February 2023
Source: Computers & Fluids
Author(s): Agustín Villa Ortiz, Lilla Koloszar
Publication date: 15 March 2023
Source: Computers & Fluids, Volume 253
Author(s):
Publication date: Available online 1 February 2023
Source: Computers & Fluids
Author(s): Tingyun Yin, Giorgio Pavesi, Shouqi Yuan
Publication date: Available online 1 February 2023
Source: Computers & Fluids
Author(s): Bradley Boyd, Yue Ling
Publication date: Available online 19 November 2022
Source: Computers & Fluids
Author(s): Boris Chetverushkin, Andrey Saveliev, Valeri Saveliev
Publication date: Available online 20 January 2023
Source: Computers & Fluids
Author(s): Néstor Ramos-García, Aliza Abraham, Thomas Leweke, Jens Nørkær Sørensen
Publication date: Available online 30 January 2023
Source: Computers & Fluids
Author(s): Satoshi Saito, Masato Yoshino, Kosuke Suzuki
Publication date: Available online 30 January 2023
Source: Computers & Fluids
Author(s): Marcel Blind, Ali Berk Kahraman, Johan Larsson, Andrea Beck
It was asserted that no multistep method with more than two steps is A-stable (Altunkaya et al. 2017). However, this article proposes a third-order multistep method that is always stable for time-dependent partial differential equations. A third-order numerical scheme has been proposed for solving parabolic equations. The scheme is linear and unconditionally stable. The comparison showed less error than the existing backward Euler scheme with fourth-order spatial discretization. The proposed scheme solves the nonlinearized partial differential equation due to the compact scheme implementation technique.
This work proposes an unconditionally stable third-order multistep technique for time-dependent partial differential equations. Its unconditional stability is proved by employing von Neumann stability analysis, and constructed Matlab code is another solid proof of the existence of the such scheme. The scheme is constructed on three consecutive time levels, and a compact fourth-order scheme is considered for spatial discretization. The convergence conditions are found when applied to the system of parabolic equations. The scheme is tested on two examples of flow between parallel plates. The mathematical model of heat and mass transfer of flow between parallel plates under the effects of viscous dissipation, thermal radiations, and chemical reaction is given and solved by the proposed scheme. The impact of some parameters, including radiation and reaction rate parameters, on velocity, temperature, and concentration profiles is also illustrated by graphs. The proposed scheme is also compared with the existing scheme, providing faster convergence than an existing one. The fundamental benefit of the proposed scheme is that it can give a compact fourth-order solution to parabolic equations.
In computational fluid dynamics of compressible fluid flow, the simple low-dissipation advection upstream (SLAU) scheme formulated with multidimensional velocity components (normal and parallel to a cell interface) is a widely employed all-speed scheme. As a variant of SLAU, the mSLAU scheme, which adopts only a velocity component normal to the cell interface instead of multidimensional velocity components, is used for rotorcraft calculations. However, although mSLAU has been claimed to be empirically stable, it has been pointed out that using only the cell-interface-normal velocity component instead of the multidimensional velocity components causes numerical instability. Therefore, to clarify the roles of the multidimensional velocity components for computational stability, we solved some benchmark problems associated with using SLAU or mSLAU. We discovered that the multidimensional velocity components contributed to stability against poor-quality grids by isotropically producing a larger amount of numerical dissipation, especially in low-subsonic and hypersonic flows. Although mSLAU could practically treat moderate Mach number flows (approximately 0.1 < M < 1.0) when coupled with the minmod limiter, using only the cell-interface-normal velocity component can deteriorate convergence of calculations and lead to susceptibility in the grid geometry.
This article is protected by copyright. All rights reserved.
The basic idea of this article is to investigate the numerical solutions of Gardner Kawahara equation, a particular case of extended Korteweg-de Vries (KdV) equation, by means of finite element method. For this purpose, a collocation finite element method based on trigonometric quintic B-spline basis functions is presented. The standard finite difference method is used to discretize time derivative and Crank-Nicolson approach is used to obtain more accurate numerical results. Then, von Neumann stability analysis is performed for the numerical scheme obtained using collocation finite element method. Several numerical examples are presented and discussed to exhibit the feasibility and capability of the finite element method and trigonometric B-spline basis functions. More specifically, the error norms L 2 and L ∞ are reported for numerous time and space discretization values in tables. Graphical representations of the solutions describing motion of wave are presented.
The Volume-Averaged Navier-Stokes equations are used to study fluid flow in the presence of fixed or moving solids such as packed or fluidized beds. We develop a high-order finite element solver using both forms A and B of these equations. We introduce tailored stabilization techniques to prevent oscillations in regions of sharp gradients, to relax the Ladyzhenskaya-Babuska-Brezzi inf-sup condition, and to enhance the local mass conservation and the robustness of the formulation. We calculate the void fraction using the Particle Centroid Method. Using different drag models, we calculate the drag force exerted by the solids on the fluid. We implement the method of manufactured solution to verify our solver. We demonstrate that the model preserves the order of convergence of the underlying finite element discretization. Finally, we simulate gas flow through a randomly packed bed and study the pressure drop and mass conservation properties to validate our model.
The unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming mesh. On the other hand, the efficient solution of the resultant system is a challenging task because of the numerical ill-conditioning that typically entails from the formulation of such methods. We use an adaptive geometric multigrid solver for the solution of the mixed finite cell formulation of saddle-point problems and investigate its convergence in the context of the Stokes and Navier-Stokes equations. We present two smoothers for the treatment of cutcells in the finite cell method and analyze their effectiveness for the model problems using a numerical benchmark. Results indicate that the presented multigrid method is capable of solving the model problems independently of the problem size and is robust with respect to the depth of the grid hierarchy.
New Findings Applying the models to practical datasets, statistics from the error analysis shows classical POD algorithm seems to be more preferred for LRA. However, since non-negativity of permeability datasets is a priority, the constrained POD (non-negative POD) algorithm described in this article is more appropriate. Results shows that the NPOD model has the capability of using minimal number of modes to reconstruct the permeability image while still retaining the geological details from the original data as opposed to the POD model.
Reservoir modeling and simulation are vital components of modern reservoir management processes. Despite the advances in computing power and the advent of smart technologies, the implementation of model-based operational/control strategies has been limited by the inherent complexity of reservoir models. Thus, reduce order models that not only reduce the cost of the implementation but also provide geological consistent prediction are essential. This article introduces reduced-order models based on the proper orthogonal decomposition (POD) coupled with linear interpolation for upscaling. First, using POD-based models, low rank approximate (LRA) are obtained by projecting the high dimensional permeability dataset to a low dimensional subspace spanned by its trajectories to decorrelate the dataset. Next, the LRA is integrated into the interpolation algorithm to generate upscaled values. This technique is highly scalable since low-rank approximations are achieved by the variation in the number of modes used for reconstruction. To test the validity and reliability of the model, we show its application to the practical dataset from SPE10 benchmark case2. From statistics of the error analysis, the classical POD algorithm seems to be more preferred for LRA; however, since non-negativity of the permeability data set is a priority, the constrained POD (non-negative POD) algorithm described in this article is more appropriate. Finally, we compared the POD-based models to a traditional industry-standard upscaling technique (e.g., arithmetic mean) to highlight our model benefits/performance. Results show that the POD-based models, particularly the non-negative POD model, produce considerably less error than the arithmetic mean model in the upscaling process.
A simple and efficient dry-wet boundary treatment method is proposed. We also improve difference scheme to solve the problem of distortion of left and right traveling waves propagating in the dry bed.
To solve shallow water equation, this paper proposes a simple and easy-to-operate dry-wet boundary treatment method based on the total variation diminishing (TVD)- MacCormack scheme. The method requires to judge dry and wet nodes before the calculation of prediction step and correction step, respectively. Then, the dry nodes are fictitiously celled and the topographic variables are reset. Moreover, previous researches show that when the same differential scheme was used, the left and right traveling waves showed over predicted computational fluxes during the downstream dry bed flow evolution, which led to distorted values and non-real physical phenomena. To solve the problem, the difference scheme for prediction step and correction step is modified, and a new finite difference scheme improvement method is proposed. Finally, the numerical solutions are compared with the analytical solution results by five classical cases to verify the rationality of the proposed method in this paper.
The pressure-free two-fluid model is a model for stratified incompressible flow in ducts, in which the pressure is eliminated through intricate use of the constraints. This article proposes a modification to the model based on the requirement of energy conservation, which makes it consistent with the original pressure-including two-fluid model. An energy-conserving discretization is applied to the improved model, and is extended with an energy-conserving discretization of the source terms due to gravity acting in the streamwise direction.
The pressure-free two-fluid model (PFTFM) is a recent reformulation of the one-dimensional two-fluid model (TFM) for stratified incompressible flow in ducts (including pipes and channels), in which the pressure is eliminated through intricate use of the volume constraint. The disadvantage of the PFTFM was that the volumetric flow rate had to be specified as an input, even though it is an unknown quantity in case of periodic boundary conditions. In this work, we derive an expression for the volumetric flow rate that is based on the demand for energy (and momentum) conservation. This leads to PFTFM solutions that match those of the TFM, justifying the validity and necessity of the derived choice of volumetric flow rate. Furthermore, we extend an energy-conserving spatial discretization of the TFM, in the form of a finite volume scheme, to the PFTFM. We propose a discretization of the volumetric flow rate that yields discrete momentum and energy conservation. The discretization is extended with an energy-conserving discretization of the source terms related to gravity acting in the streamwise direction. Our numerical experiments confirm that the discrete energy is conserved for different problem settings, including sloshing in an inclined closed tank, and a traveling wave in a periodic domain. The PFTFM solutions and the volumetric flow rates match the TFM solutions, with reduced computation time, and with exact momentum and energy conservation.
A unified Discontinuous Galerkin Time, Space-Time Finite Element scheme is developed and is applied for discretizing time dependent viscous shear-thinning p-power law fluid flow models. A stability bound is given. The efficiency of the method is investigated by solving associated benchmark problems.
In this work, a stabilized time Discontinuous Galerkin, Space-Time Finite Element (tDG-ST-FE) scheme is presented for discretizing time-dependent viscous shear-thinning fluid flow models, which exhibit a usual power-law stress strain relation. The development of the proposed numerical scheme based mainly on a unified weak space-time formulation, where simple streamline-upwind terms have been added in the numerical scheme, for stabilizing the discretization of the associated temporal and convective terms. The original time interval is partitioned into time subintervals, resulting in a subdivision of the space-time cylinder into space-time subdomains. Discontinuous Galerkin techniques are applied for the time discretization between the space-time subdomain interfaces. A stability bound is given for the derived ST-FE scheme. In the last part numerical examples on benchmark problems are presented for testing the efficiency of the proposed method.
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Zhenming Wang, Jun Zhu, Chunwu Wang, Ning Zhao
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Seth Taylor, Jean-Christophe Nave
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Dongfang Li, Xiaoxi Li, Zhimin Zhang
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Maxim Sukharev
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Yiming Ren, Shan Zhao
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Michael Penwarden, Shandian Zhe, Akil Narayan, Robert M. Kirby
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Ashesh Chattopadhyay, Ebrahim Nabizadeh, Eviatar Bach, Pedram Hassanzadeh
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Spencer H. Bryngelson, Rodney O. Fox, Tim Colonius
Publication date: 15 March 2023
Source: Journal of Computational Physics, Volume 477
Author(s): Yuze Zhang, Xuguang Yang, Lei Zhang, Yiteng Li, Tao Zhang, Shuyu Sun
A freely moving elastic ring is used to enhance mixed convection heat transfer in a two-dimensional square cavity with three different Richardson (Ri) numbers of 0.1, 1.0, and 10. The multiple-relaxation time lattice Boltzmann method combined with the immersed boundary method is employed to simulate the mixed convection heat transfer and its interaction with the elastic ring in the cavity. Two different thermal conditions for the elastic ring, i.e., with and without thermal interaction, are considered. The results are given in terms of streamlines, isotherms, temperature distribution, and Nusselt (Nu) number. It was found that at the steady state, the ring accords to one of the streamlines in the cavity. In addition, for each investigated case, the Nu number decreases as the Ri number increases. Besides, the presence of the ring leads to a much higher heat transfer (Nu number) and a much earlier steady state as compared to the case with no ring. Finally, the values of the Nu number for both thermal conditions of the ring are about the same being slightly higher for the ring with thermal interaction.
The separation of two-phase flow is essential for many fluid systems in microgravity environments. The passive cyclonic separator is a prominent technology for this task. In the absence of gravity, the separators can operate in different parametric ranges than in normal gravity. The objective of the present investigation is to better understand the fluid physics involved in two-phase flow separation in microgravity by deriving the basic scaling laws for various important parameters. Combined approaches of control-volume analysis and numerical simulations are used to construct a system of equations that can accurately predict the gas core size under various conditions. The predictions are found to be in good agreement with the experimental data, both for pure liquid injection and two-phase flow injection cases. The control-volume equations are modified to include capillary effects and predict the critical condition for the collapse of the liquid layer in microgravity as the surface tension overcomes the centrifugal acceleration at the interface. It is shown that the results of the control-volume analysis can also be used to construct the operational map and to study the separation of a single bubble in microgravity.
High-speed boundary layer transition is dominated by the modal, exponential amplification of the oblique Mack’s first mode waves in two-dimensional boundary layers from Mach 1 up to freestream Mach numbers of 4.5 to 6.5 depending on the wall-to-adiabatic temperature ratio. At higher Mach numbers, the acoustic, planar Mack’s second mode waves become dominant. Although many theoretical, computational and experimental studies have focused on the supersonic boundary layer transition due to the oblique Mack’s first mode, several fundamental questions about the source of this instability and the reasons for its obliqueness remain unsolved. Here, we perform an inviscid energetics investigation and classify disturbances based on their energetics signature on a Blasius boundary layer for a range of Mach numbers. This approach builds insight into the fundamental mechanisms governing various types of instability. It is shown that first mode instability is distinct from Tollmien–Schlichting instability, being driven by a phase shifting between streamwise velocity and pressure perturbations in the vicinity of the generalized inflection point and insensitive to the viscous no-slip condition. Further, it is suggested that the obliqueness of the first mode is associated with an inviscid flow invariant.
A novel surface tracking, and advection algorithm for incompressible fluid flows in two and three dimensions is presented. This method based on the volume-of-fluid (VOF) method, is named VOF-with-center-of-mass-and-Lagrangian-particles (VCLP), and it uses spatially and temporally localized Lagrangian particles (LPs) inside a finite volume framework. The fluid surface is recaptured and reconstructed piecewise using the mean slope and curvature. The fluid mass inside each cell is discretized spatially by LPs and distributed as blue noise. LPs are then advected cell by cell with a choice of two different advection schemes in time using interpolated velocity and approximated acceleration fields. VCLP continuously tracks the center of mass of the fluid parcels in the Lagrangian way and this helps to reduce the errors due to numerical acceleration that results from lack of information to reconstruct the interface accurately. VCLP’s performance is evaluated using standard benchmark tests in 2D and 3D such as translation, single vortex, deformation, and Zalesak’s tests from the literature. VCLP is applied to TSUNAMI2D, a 2D Navier–Stokes model to simulate shoaling and breaking of waves.
The influence of turbulence inflow generation on direct numerical simulations (DNS) of high-speed turbulent boundary layers at Mach numbers of 2 and 5.84 is investigated. Two main classes of inflow conditions are considered, based on the recycling/rescaling (RR) and the digital filtering (DF) approach, along with suitably modified versions. A series of DNS using very long streamwise domains is first carried out to provide reliable data for the subsequent investigation. A set of diagnostic parameters is then selected to verify achievement of an equilibrium state, and correlation laws for those quantities are obtained based on benchmark cases. Simulations using shorter domains, with extent comparable with that used in the current literature, are then carried out and compared with the benchmark data. Significant deviations from equilibrium conditions are found, to a different extent for the various flow properties, and depending on the inflow turbulence seeding. We find that the RR method yields superior performance in the evaluation of the inner-scaled wall pressure fluctuations and the turbulent shear stress. DF methods instead yield quicker adjustment and better accuracy in the prediction of wall friction and of the streamwise Reynolds stress in supersonic cases. Unrealistically high values of the wall pressure variance are obtained by the baseline DF method, while the proposed DF alternatives recover a closer agreement with respect to the benchmark. The hypersonic test case highlights that similar distribution of wall friction and heat transfer are obtained by both RR and DF baseline methods.
Global instability analysis of flows is often performed via time-stepping methods, based on the Arnoldi algorithm. When setting up these methods, several computational parameters must be chosen, which affect intrinsic errors of the procedure, such as the truncation errors, the discretization error of the flow solver, the error associated with the nonlinear terms of the Navier–Stokes equations and the error associated with the limited size of the approximation of the Jacobian matrix. This paper develops theoretical equations for the estimation of optimal balance between accuracy and cost for each case. The 2D open cavity flow is used both for explaining the effect of the parameters on the accuracy and the cost of the solution, and for verifying the quality of the predictions. The equations demonstrate the impact of each parameter on the quality of the solution. For example, if higher-order methods are used for approaching a Fréchet derivative in the procedure, it is shown that the solution deteriorates more rapidly for larger grids or less accurate flow solvers. On the other hand, lower-order approximations are more sensitive to the initial disturbance magnitude. Nevertheless, for accurate flow solvers and moderate grid dimensions, first-order Fréchet derivative approximation with optimal computational parameters can provide 5 decimal place accurate eigenvalues. It is further shown that optimal parameters based on accuracy tend to also lead to the most cost-effective solution. The predictive equations, guidelines and conclusions are general, and, in principle, applicable to any flow, including 3D ones.
Avoiding aliasing in time-resolved flow data obtained through high-fidelity simulations while keeping the computational and storage costs at acceptable levels is often a challenge. Well-established solutions such as increasing the sampling rate or low-pass filtering to reduce aliasing can be prohibitively expensive for large datasets. This paper provides a set of alternative strategies for identifying and mitigating aliasing that are applicable even to large datasets. We show how time-derivative data, which can be obtained directly from the governing equations, can be used to detect aliasing and to turn the ill-posed problem of removing aliasing from data into a well-posed problem, yielding a prediction of the true spectrum. Similarly, we show how spatial filtering can be used to remove aliasing for convective systems. We also propose strategies to prevent aliasing when generating a database, including a method tailored for computing nonlinear forcing terms that arise within the resolvent framework. These methods are demonstrated using a nonlinear Ginzburg–Landau model and large-eddy simulation data for a subsonic turbulent jet.
Wavenumber-frequency spectra of the forcing component for the streamwise momentum computed on the lipline near the jet nozzle.
Natural convection heat transfer from a porous cylinder put at various positions in a square, cooled enclosure, with air as the working fluid, is investigated in this work. The following setups are taken into account: The hot cylinder is placed in the middle of the enclosure, near the bottom, top, right sides, along diagonal as top-diagonal and bottom-diagonal. The cylinder and the enclosure walls are kept hot and cold, respectively. The lattice Boltzmann method is used to perform a numerical analysis for Rayleigh number \(10^{4}\le \) Ra \(\le 10^{6}\) and Darcy number \(10^{-6}\le \) Da \(\le 10^{-2}\) . The results are plotted as streamlines, isotherms, and local and mean Nusselt number values. The amount of heat transported from the heated porous cylinder is determined by varying Ra, Da, and the cylinder location. Even at a lower Rayleigh number ( \(10^{4}\) ), the average Nusselt number grows by nearly 70 % as the cylinder moves from the centre to the bottom and 105% as it moves to bottom-diagonal location when \({Da}=10^{-2}\) . At Ra \(=10^{6}\) and Da \(=10^{-2}\) , the heat transfer rate of the cylinder located near the corner of the enclosure at the bottom wall increases by approximately 33% when compared to the case of the cylinder in the centre. Convective effects are more noticeable when the cylinder is positioned towards the enclosure’s bottom wall. This research is applicable to electronic cooling applications in which a collection of electronic components is arranged in a circular pattern inside a cabinet.
The dispersion of respiratory saliva droplets by indoor wake structures may enhance the transmission of various infectious diseases, as the wake spreads virus-laden droplets across the room. Thus, this study analyzes the interaction between vortical wake structures and exhaled multi-component saliva droplets. A self-propelling analytically described dipolar vortex is chosen as a model wake flow, passing through a cloud of micron-sized evaporating saliva droplets. The droplets’ spatial location, velocity, diameter, and temperature are traced, coupled to their local flow field. For the first time, the wake structure decay is incorporated and analyzed, which is proved essential for accurately predicting the settling distances of the dispersed droplets. The model also considers the nonvolatile saliva components, adequately capturing the essence of droplet–aerosol transition and predicting the equilibrium diameter of the residual aerosols. Our analytic model reveals non-intuitive interactions between wake flows, droplet relaxation time, gravity, and transport phenomena. We reveal that given the right conditions, a virus-laden saliva droplet might translate to distances two orders of magnitude larger than the carrier-flow characteristic size. Moreover, accounting for the nonvolatile contents inside the droplet may lead to fundamentally different dispersion and settling behavior compared to non-evaporating particles or pure water droplets. Ergo, we suggest that the implementation of more complex evaporation models might be critical in high-fidelity simulations aspiring to assess the spread of airborne respiratory droplets.
Evolution of three-dimensional body motion within surrounding three-dimensional fluid motion is addressed, each motion affecting the other significantly in a dynamic fluid–body interaction. This unsteady problem is set near a wall. The spatial three-dimensionality present is a new feature. For inviscid incompressible fluid, a basic nonlinear formulation is described, followed by a linearised form as a first exploration of parameter space and solution responses. The problem reduces to solving Poisson’s equation within the underbody planform, subject to mixed boundary conditions and to coupling with integral equations. Numerical and analytical properties show dependence mainly on the normal and pitch motions, as well as instability or bounded oscillations depending on the position of the centre of mass of the body, and a variety of three-dimensional shapes is examined.
