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Threedimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical setup, which restricts the development of intrinsic wake structure, leads to an overprediction of the onset point of the secondary wake instability (Re_{cr}). A best practice of the numerical setup is presented for the accurate prediction of Re_{cr} by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Re_{cr}, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical setup. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Re_{cr}, while the periodic boundary condition is recommended for simulating the wake structures above Re_{cr}. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.
This paper presents a best practice on the choices of the lateral boundary condition and cylinder span length for the prediction of the critical Reynolds number and wake transition of flow past a circular cylinder. A systematic comparison between the periodic and symmetry lateral boundary conditions is presented. The general conclusions are expected to be applicable to other bluff body configurations.
In complex applications, such as the analysis of hydraulic performance of blood pumps (ventricular assist devices or VADs), the NavierStokes equations have to be discretized on very anisotropic meshes. If stabilized finite element formulations are applied, standard definitions of the stabilization parameter are usually not appropriate to handle elements with a high aspect ratio. If, in addition, rotating objects, moving meshes or turbulence has to be considered in the simulation, further modifications of the stabilization procedure have to be applied.
In this paper, we present stabilized spacetime finite element formulations of the incompressible NavierStokes equations that show very good convergence properties on complex anisotropic meshes and lead to reasonable numerical accuracy in complex flows when compared to experimental data. This article is protected by copyright. All rights reserved.
In this article, we have devised a new reference smoothness indicator for thirdorder weighted essentially nonoscillatory (WENO) scheme to achieve desired order of convergence at critical points. In the context of the weighted essentially nonoscillatory scheme, reference smoothness indicator is constructed in such a way that it satisfies the sufficient condition on the weights for the thirdorder convergence. The goal is to construct a reference smoothness indicator such that the resulted scheme have to achieve the required order of accuracy even if the first two derivatives vanish but not the third derivative. The construction of such reference smoothness indicator is not possible through a linear combination of local smoothness indicators only. We have proposed a reference smoothness indicator to be of the fourth order of accuracy on threepoint stencil that contains the linear combination of the first derivative information of the local and global stencils. The performance enhancement of the WENO scheme through this reference smoothness indicator is verified through the standard numerical experiments. Numerical results indicate that the new scheme provides better results in comparison with the earlier thirdorder WENO schemes like WENOJS and WENOZ. Copyright © 2017 John Wiley & Sons, Ltd.
In this article, we have devised a new reference smoothness indicator for thirdorder weighted essentially nonoscillatory (WENO) scheme to achieve desired order of convergence at critical points. This reference smoothness indicator constructed through the linear combination of first derivative information of the local and global spatial stencils. The performance enhancement of the WENO scheme (WENOF3) through this reference smoothness indicator is verified by the standard numerical test cases. As shown in the figure, WENOF3 scheme is efficient than WENOJS and WENOZ schemes.
A new twodimensional interface reconstruction method that ensures continuity of the interface and preserves volume fractions is presented here. It is made of two steps, first, the minimization of a cost functional based on volume fractions least square errors by using dynamic programming, a fast and efficient scheme well known in image processing, and then a local correction phase. In each cell, the interface is made of two line segments joining two edges. This new interface reconstruction method, called Dynamic Programming Interface Reconstruction has been coupled with various advection schemes, among them the Lagrange + remap scheme. With a reasonable computational cost, it has been observed in various test cases that Dynamic Programming Interface Reconstruction is more accurate and less diffusive compared with other existing classical reconstruction methods. Copyright © 2017 John Wiley & Sons, Ltd.
A new interface reconstruction method for twodimensional multimaterial flows, which ensures continuity of the interface and preserves volumic fractions, is presented here. It is based on the minimization of a cost functional by using dynamic programming, a fast algorithm often used in image segmentation. With a reasonable cost, it has been observed on various advection test cases that this new method, called Dynamic Programming Interface Reconstruction, is more accurate and less diffusive than other existing ones, as the Youngs method.
Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semiimplicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.
In this paper, an improved moving particle semiimplicit model is used to simulate the propagation of progressive waves. A combined pressure gradient model that is deduced from the Taylor series expansion is put forward as well as a new pressure detection method for free surface particles. With the modifications, the energy conservation in the wave propagation is enhanced well and the wave damping is effectively reduced.
No abstract is available for this article.
The low Mach number performance of the MacCormack scheme is examined. The inherent dissipation in the scheme is found to suffer from the degradation in accuracy observed with traditional, densitybased methods for compressible flows. Two specific modifications are proposed, leading to the formation of the Generalized MacCormack Scheme within a dualtime framework (called GMCPC). The first modification involves reformulating the flux by splitting it into particle convection and acoustic parts, with the former terms treated using the traditional MacCormack discretization and the latter terms augmented by the addition of a pressurebased artificial dissipation. The second modification involves a reformulation of the traditional nonlinear fix introduced by MacCormack in 1971, which is found to be necessary to suppress pressure oscillations at low Mach numbers. The new scheme is demonstrated to have superior performance, independent of Mach number, compared to standard MacCormack implementations using several canonical test problems. This article is protected by copyright. All rights reserved.
A Gibbs phenomenon detector that is useful in damping numerical oscillations in hybrid solvers for compressible turbulence is proposed and tested. It is designed to function in regions away from discontinuities where commonly used discontinuity sensors are ineffective. Using this Gibbs phenomenon detector in addition to a discontinuity sensor for combining central and shock capturing schemes provides an integrated way of dealing with numerical oscillations generated by shock waves and contact lines that are normal to the flow. When complete suppression of numerical oscillations is not possible, they are sufficiently localized. Canonical tests and large eddy simulations show that inclusion of the proposed detector does not cause additional damping of ‘wellresolved’ physical oscillations. Copyright © 2017 John Wiley & Sons, Ltd.
The switching between central and dissipative flux splitting schemes in hybrid solvers based on discontinuity sensors may lead to Gibbs phenomenon characterized by twopoint numerical oscillations. Such oscillations may grow and contaminate the solution severely in some cases. A way to detect such oscillations and adjust the hybridization procedure as needed is proposed to remove such oscillations. In some cases, the adjustment prevents the formation of such oscillations, while in others, they are sufficiently localized near discontinuities where they originate.
In this paper, the circular functionbased gaskinetic scheme (CGKS), which was originally developed for simulation of flows on stationary grids, is extended to solve moving boundary problems on moving grids. Particularly, the unsteady flows through oscillating cascades are our major interests. The main idea of the CGKS is to discretize the macroscopic equations by the finite volume method while the fluxes at the cell interface are evaluated by locally reconstructing the solution of the continuous Boltzmann Bhatnagar–Gross–Krook equation. The present solver is based on the fact that the modified Boltzmann equation, which is expressed in a moving frame of reference, can recover the corresponding macroscopic equations with Chapman–Enskog expansion analysis. Different from the original Maxwellian functionbased gaskinetic scheme, in improving the computational efficiency, a simple circular function is used to describe the equilibrium state of distribution function. Considering that the concerned cascade oscillating problems belong to cases that the motion of surface boundary is known a priori, the dynamic mesh method is suitable and is adopted in the present work. In achieving the mesh deformation with high quality and efficiency, a hybrid dynamic mesh method named radial basic functionstransfinite interpolation is presented and applied for cascade geometries. For validation, several numerical test cases involving a wide range are investigated. Numerical results show that the developed CGKS on moving grids is well applied for cascade oscillating flows. And for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved by using the present method. Copyright © 2017 John Wiley & Sons, Ltd.
A recently developed circular functionbased gaskinetic scheme is extended into a version on moving grids for simulation of oscillation cascade problems. Because the dynamic mesh method is used to treat boundary movement, an efficient hybrid dynamic mesh method named radial basic functionstransfinite interpolation is presented and applied for cascade geometries. Numerical results prove that the developed circular functionbased gaskinetic scheme on moving grids is well applied, and for some cases where nonlinear effects are strong, the solution accuracy could be effectively improved.
In the context of High Energy Density Physics and more precisely in the field of laser plasma interaction, Lagrangian schemes are commonly used. The lack of robustness due to strong grid deformations requires the regularization of the mesh through the use of Arbitrary Lagrangian Eulerian methods. Theses methods usually add some diffusion and a loss of precision is observed. We propose to use Adaptive Mesh Refinement (AMR) techniques to reduce this loss of accuracy. This work focuses on the resolution of the anisotropic diffusion operator on Arbitrary Lagrangian EulerianAMR grids.
In this paper, we describe a secondorder accurate cellcentered finite volume method for solving anisotropic diffusion on AMR type grids. The scheme described here is based on local flux approximation which can be derived through the use of a finite difference approximation, leading to the CCLADNS scheme. We present here the 2D and 3D extension of the CCLADNS scheme to AMR meshes. Copyright © 2017 John Wiley & Sons, Ltd.
We are interested here in the resolution of anisotropic diffusion on nonconformal nonorthogonal 2D and 3D meshes. The numerical scheme used here is an extension of the CellCentered Lagrangian Diffusion CCLAD scheme, the NonSymmetric version of this diffusion scheme the CCLADNS scheme. The figure presented here corresponds to the isotropic linear solution of a diffusion problem on a randomly perturbed 3D AMR grid. Machine precision is reached with CCLADNS scheme.
This paper presents a twodimensional numerical study for mixed convection in a laminar crossflow with a pair of stationary equalsized isothermal cylinders in tandem arrangement confined in a channel. The governing equations are solved using the control volume method on a nonuniform orthogonal Cartesian grid, and the immersed boundary method is employed to identify the cylinders placed in the flow field. The numerical scheme is first validated against standard cases of symmetrically confined isothermal circular cylinders in plane channels, and grid convergence tests were also examined. The objective of the present study was to investigate the influence of buoyancy and the blockage ratio constraint on the flow and heat transfer characteristics of the immersed cylinder array. Using a fixed Reynolds number based on cylinder diameter of \(Re_{D} = 200\) , a fixed value of the Prandtl number of \(Pr = 7\) , and a blockage ratio of \(D/H = 0.2\) , all possible flow regimes are considered by setting the longitudinal spacing ratio ( \(\sigma = L/D\) ) between the cylinder axes to 2, 3, and 5 for values of the buoyancy parameter (Richardson number) in the range \(1\le Ri\le 4\) . The interference effects and complex flow features are presented in the form of mean and instantaneous velocity, vorticity, and temperature distributions. The results demonstrate how the buoyancy, spacing ratio, and wall confinement affect the wake structure and vortex dynamics. In addition, local and average heat transfer characteristics of both cylinders are comprehensively presented for a wide range in the parametric space.
The appearance of a ground surface can play an important role in the flow structures for the flows past a flat plate. We conduct twodimensional numerical simulations on viscous flows past a flat plate inclined at an angle of attack of \(20^\circ \) with ground effects using a finitevolume method. Results show that the effects on the separated flow from the ground are highly dependent on the gap (G) between the plate and the ground. As the gap decreases, the strength of vortices generated from the trailing edge is restrained, which is consistent with experimental observations. Further decrease in the gap even eliminates the vortex shedding and yields a steady flow. It is also found that the flow between the gap can either be accelerated at large gap ratios ( \({G/L >1}\) , G is the gap, L is the plate length), or be decelerated at small gap ratios ( \({G/L <1}\) ). Furthermore, the numerical results show that the wake flow behind the plate can significantly change the distribution of surface shear stress on the ground. Specifically, the mean shear stress on the ground in the downstream region at a gap ratio \(G/L = 2.0\) is one order of magnitude larger than that at a small gap ratio \(G/L = 0.3\) , and the length of the downstream region where the shear stress can be effectively changed is much larger than the plate length, which provides a guideline to manipulate the ground wall surface shear stress using an inclined plate in the vicinity of the wall.
This article addresses a classical fluid mechanics problem where the effect of capillary action on a column of viscous liquid is analyzed by quantifying its timedependent penetrated length in a narrow channel. Despite several past studies, a rigorous mathematical formulation of this inherently unsteady process is still unavailable, because these existing works resort to a crucial assumption only valid for mildly transient systems. The approximate theories use an integral approach where the penetration is described by equating total force acting on the domain to rate of change of total momentum. However, while doing so, the viscous resistance under temporally varying condition is assumed to be same as the resistance created by a quasisteady velocity profile. Thus, leading order error appears due to such approximation which can only be true when the variation in time is not strong enough causing negligible transient deviation in the hydrodynamic quantities. The present paper proposes a new way to solve this problem by considering the unsteady field itself as an unknown variable. Accordingly, the analysis applies an eigenfunction expansion of the flow with unknown timedependent amplitudes which along with the unsteady intrusion length are calculated from a system of ordinary differential equations. A comparative exploration identifies the situation for which the integral approach and the rigorous technique based on eigenfunction expansion deviate from each other. It also reveals that the two methods differ substantially in shorttime dynamics at the initial stage. Then, an asymptotic perturbation shows how the two sets of results should coincide in their longtime behavior. In this way, the findings will provide a comprehensive understanding of the physics behind the transport phenomenon.
This study aims to investigate effective slip arising from pressuredriven flow through a slit channel bounded by lubricantimpregnated grooved surfaces. The problem for flow over longitudinal grooves is solved analytically using the methods of domain decomposition and eigenfunction expansion, while that for flow over transverse grooves is solved numerically using the front tracking method. It is found that the effective slip length and the lubricant flow rate can depend strongly on the geometry of the microstructure, the direction of flow, and the lubricant viscosity. In particular, the effective slip can be effectively enhanced by increasing the thickness of a lubricating film atop the ribs. Under the same conditions, a flow that is parallel to the lubricantimpregnated grooves will have a larger effective slip, but also a larger lubricant flow rate, when compared with the case of flow normal to the grooves. It is also shown that, in the case of transverse grooves, because of the downward displacement of the interface between the working/lubricating fluids, the effective slip length and lubricant flow rate may vary nonmonotonically with the groove depth.
The effect of diffusive processes on the structure of passive vector and scalar gradient fields is investigated by analyzing the corresponding terms in the orientation and norm equations. Numerical simulation is used to solve the transport equations for both vectors in a twodimensional, parameterized model flow. The study highlights the role of molecular diffusion in the vector orientation process and shows its subsequent action on the geometric features of vector fields.
We present a lowdimensional Galerkin model with statedependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the threedimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier–Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limitcycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.
Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.
Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steadystates usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steadystates of unstable flows. Steady governing equations could be solved instead, by employing Newtontype methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steadystate to be reached. This approach does not require a good initial condition and works well for selfexcited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multistep schemes. A few chosen test cases shows that they enable convergence toward solutions that are unstable to stationary and oscillatory disturbances, with either a single or multiple frequency content. Finally, comparisons with SFD are also performed, showing significant reduction in computer cost for complex flows by using the implicit multistep MGM schemes.
Concentric, counterrotating vortex ring formation by transient jet ejection between concentric cylinders was studied numerically to determine the effects of cylinder gap ratio, \(\frac{\Delta R}{R}\) , and jet stroke lengthtogap ratio, \(\frac{L}{\Delta R}\) , on the evolution of the vorticity and the trajectories of the resulting axisymmetric vortex pair. The flow was simulated at a jet Reynolds number of 1000 (based on \(\Delta R\) and the jet velocity), \(\frac{L}{\Delta R} \) in the range 1–20, and \(\frac{\Delta R}{R}\) in the range 0.05–0.25. Five characteristic flow evolution patterns were observed and classified based on \(\frac{L}{\Delta R} \) and \(\frac{\Delta R}{R}\) . The results showed that the relative position, relative strength, and radii of the vortex rings during and soon after formation played a prominent role in the evolution of the trajectories of their vorticity centroids at the later time. The conditions on relative strength of the vortices necessary for them to travel together as a pair following formation were studied, and factors affecting differences in vortex circulation following formation were investigated. In addition to the characteristics of the primary vortices, the stopping vortices had a strong influence on the initial vortex configuration and effected the longtime flow evolution at low \(\frac{L}{\Delta R}\) and small \(\frac{\Delta R}{R}\) . For long \(\frac{L}{\Delta R} \) and small \(\frac{\Delta R}{R}\) , shedding of vorticity was sometimes observed and this shedding was related to the Kelvin–Benjamin variational principle of maximal energy for steadily translating vortex rings.
We report the findings from a theoretical analysis of optimally growing disturbances in an initially turbulent boundary layer. The motivation behind this study originates from the desire to generate organized structures in an initially turbulent boundary layer via excitation by disturbances that are tailored to be preferentially amplified. Such optimally growing disturbances are of interest for implementation in an active flow control strategy that is investigated for effective jet noise control. Details of the optimal perturbation theory implemented in this study are discussed. The relevant stability equations are derived using both the standard decomposition and the triple decomposition. The chosen test case geometry contains a convergent nozzle, which generates a Mach 0.9 round jet, preceded by a circular pipe. Optimally growing disturbances are introduced at various stations within the circular pipe section to facilitate disturbance energy amplification upstream of the favorable pressure gradient zone within the convergent nozzle, which has a stabilizing effect on disturbance growth. Effects of temporal frequency, disturbance input and output plane locations as well as separation distance between output and input planes are investigated. The results indicate that optimally growing disturbances appear in the form of longitudinal counterrotating vortex pairs, whose size can be on the order of several times the input plane mean boundary layer thickness. The azimuthal wavenumber, which represents the number of counterrotating vortex pairs, is found to generally decrease with increasing separation distance. Compared to the standard decomposition, the triple decomposition analysis generally predicts relatively lower azimuthal wavenumbers and significantly reduced energy amplification ratios for the optimal disturbances.