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In this paper, we propose a new evolvethenfilter reduced order model (EFROM). This is a regularized ROM (RegROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convectiondominated flows. We also consider the Leray ROM (LROM). These two RegROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four RegROM/filter combinations are tested in the numerical simulation of the threedimensional flow past a circular cylinder at a Reynolds number Re=1000. Overall, the most accurate RegROM/filter combination is EFROMDF. Furthermore, the spatial filter has a higher impact on the RegROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EFROM and LROM. Finally, the CPU times of the four RegROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd.
In this paper, we propose a new evolvethenfilter reduced order model (EFROM), which is a regularized ROM (RegROM) that increases the numerical stability of ROMs for convectiondominated flows. This new RegROM uses two explicit ROM spatial filters (a differential filter and a projection) to smooth (regularize) various terms in the ROMs. The new EFROM produces accurate and efficient numerical approximations of a threedimensional flow past a circular cylinder at a Reynolds number Re = 1000.
Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in Computational Fluid Dynamics. Due to 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.
We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the secondorder upwind method with proper slope limiter. Our scheme is locally conservative and has only cellcentered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost secondorder accuracy. Copyright © 2017 John Wiley & Sons, Ltd.
We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. Our scheme is locally conservative and has only cellcentered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost secondorder accuracy.
A new 2D interface reconstruction method which 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 DPIR (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 DPIR is more accurate and less diffusive compared to other existing classical reconstruction methods. This article is protected by copyright. All rights reserved.
This paper presents new linearitypreserving nodal limiters for enforcing discrete maximum principles in continuous (linear or bilinear) finite element approximations to transport problems with steep fronts. In the process of algebraic flux correction, the oscillatory antidiffusive part of a highorder base discretization is decomposed into a set of internodal fluxes and constrained to be local extremum dim inishing. The proposed nodal limiter functions are designed to be continuous and satisfy the principle of linearity preservation that implies the preservation of secondorder accuracy in smooth regions. The use of limited nodal gradients makes it possible to circumvent angle conditions and guarantee that the discrete maximum principle holds on arbitrary meshes. A numerical study is performed for linear convection and anisotropic diffusion problems on uniform and distorted meshes in two space dimensions. Copyright © 2017 John Wiley & Sons, Ltd.
Edgebased limiting techniques are proposed for enforcing local maximum principles in continuous finite element schemes for transport equations. Different generalizations of a onedimensional jump and average limiter are considered and improved step by step. The use of limited nodal gradients makes it possible to circumvent angle conditions that apply to other local extremum diminishing and linearitypreserving limiters.
In [1], a viscous regularization technique, based on the local entropy residual, was proposed to stabilize the nonequilibriumdiffusion Grey RadiationHydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, the work in [1] was only based on the hyperbolic parts of the Grey RadiationHydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here, we extend the theoretical grounds for the method and derive an entropy minimum principle for the full set of nonequilibriumdiffusion Grey Radiation Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiationhydrodynamic shock simulations. Radiative shock calculations using constant and temperaturedependent opacities are compared against semianalytical reference solutions and we present a procedure to perform spatial convergence studies of such simulations. This article is protected by copyright. All rights reserved.
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 BGK 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 ChapmanEnskog (CE) expansion analysis. Different from the original Maxwellian functionbased GKS, in order to improve 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 prior, the dynamic mesh method is suitable and is adopted in the present work. To achieve the mesh deformation with high quality and efficiency, a hybrid dynamic mesh method named RBFsTFI 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.
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Motivated by the need to efficiently obtain loworder models of fluid flows around complex geometries for the purpose of feedback control system design, this paper considers the effect on system dynamics of basing plant models on different formulations of the linearised NavierStokes equations. We consider the dynamics of a single computational node formed by spatial discretisation of the governing equations in both primitive variables (momentum equation & continuity equation) and pressure Poisson equation (PPE) formulations. This reveals fundamental numerical differences at the nodal level, whose effects on the system dynamics at the full system level are exemplified by considering the corresponding formulations of a twodimensional (2D) channel flow, subjected to a variety of different boundary conditions. This article is protected by copyright. All rights reserved.
In the context of High Energy Density Physics (HEDP) 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 (ALE) 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 focus on the resolution of the anisotropic diffusion operator on ALEAMR grids. redIn this paper, we describe a secondorder accurate cellcentered finite volume method for solving anisotropic diffusion on AMR type grids. The scheme describe here is based on local flux approximation which can be derived through the use of a finite difference approximation, leading to the CCLADNS scheme. In this paper, we discuss the 2D and 3D extension of the CCLADNS scheme to AMR meshes. This article is protected by copyright. All rights reserved.
The forces acting on a solid body just at the time of impact on the surface of a medium with very low compressibility, such as water, can be quantified at acoustic time scales. This is necessary in wide range of applications varying from largescale ship designs to the walking or running mechanisms of small creatures such as the basilisk lizard. In order to characterize such forces, a numerical model is developed in this study and is validated using analytical expressions of pressure as a function of the speed of soundwave propagation in water. The computational results not only accurately match the analytical values but are also able to effectively capture the propagation of acoustic waves in water. The model is further applied to a case study wherein the impact impulse required by the basilisk lizard to assist in its walking on the water surface is evaluated. The numerical results are found to be in agreement with the closest available experimental data. The model and approach are thus proposed to evaluate impact forces for wide range of applications.
We compare results from a spectral model for nonstationary, inhomogeneous turbulence (Besnard et al. in Theor Comp Fluid Dyn 8:1–35, 1996) with direct numerical simulation (DNS) data of a shearfree mixing layer (SFML) (Tordella et al. in Phys Rev E 77:016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physicalspace transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of meanflow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long times, including the evolution of the mixinglayer width and turbulent kinetic energy. At shorttimes, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We propose two possible causes for the discrepancies. The first is the local approximation to the pressuretransport and the second is the a priori spherical averaging used to reduce the dimensionality of the solution space of the model, from wavevector to wavenumber space. DNS data are then used to gauge the relative importance of both possible deficiencies in the model.
Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate science in particular, they are important for helping the community improve our ability to predict the effect of climate change on the earth system. Climate models are large computer codes based on the discretization of the fluid dynamics equations on grids of horizontal resolution in the order of 100 km, whereas unresolved processes are handled by subgrid models. For instance, simple models are routinely used to help understand the interactions between smallscale processes due to atmospheric moist convection and largescale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solved numerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to represent free tropospheric circulation and is coupled to a bulk atmospheric boundary layer (ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are represented through a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarily hyperbolic. This makes the design of a numerical method for the solution of this system particularly difficult. Here, we develop a numerical scheme based on the operator timesplitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity since it avoids the Riemann problem by design. One of the advective parts is a hyperbolic diagonal matrix, which is easily handled by classical methods for hyperbolic equations, while the other advective part is a nilpotent matrix, which is solved via the method of lines. Validation tests using a synthetic exact solution are presented, and formal secondorder convergence under grid refinement is demonstrated. Moreover, the model is tested under realistic monsoon conditions, and the ability of the model to simulate key features of the monsoon circulation is illustrated in two distinct parameter regimes.
The dynamics of oblique shock wave/turbulent boundary layer interactions is analyzed by mining a largeeddy simulation (LES) database for various strengths of the incoming shock. The flow dynamics is first analyzed by means of dynamic mode decomposition (DMD), which highlights the simultaneous occurrence of two types of flow modes, namely a lowfrequency type associated with breathing motion of the separation bubble, accompanied by flapping motion of the reflected shock, and a highfrequency type associated with the propagation of instability waves past the interaction zone. Global linear stability analysis performed on the mean LES flow fields yields a single unstable zerofrequency mode, plus a variety of marginally stable lowfrequency modes whose stability margin decreases with the strength of the interaction. The least stable linear modes are grouped into two classes, one of which bears striking resemblance to the breathing mode recovered from DMD and another class associated with revolving motion within the separation bubble. The results of the modal and linear stability analysis support the notion that lowfrequency dynamics is intrinsic to the interaction zone, but some continuous forcing from the upstream boundary layer may be required to keep the system near a limit cycle. This can be modeled as a weakly damped oscillator with forcing, as in the early empirical model by Plotkin (AIAA J 13:1036–1040, 1975).
Leadingedge modifications based on designs inspired by the protrusions on the pectoral flippers of the humpback whale (tubercles) have been the subject of research for the past decade primarily due to their flow control potential in ameliorating stall characteristics. Previous studies have demonstrated that, in the transitional flow regime, fullspan wings with tubercled leading edges outperform unmodified wings at high attack angles. The flow mechanism associated with such enhanced loading traits is, however, still being investigated. Also, the performance of fullspan tubercled wings in the turbulent regime is largely unexplored. The present study aims to investigate Reynolds number effects on the flow mechanism induced by a fullspan tubercled wing with the NACA0021 crosssectional profile in the transitional and nearturbulent regimes using computational fluid dynamics. The analysis of the flow field suggests that, with the exception of a few different flow features, the same underlying flow mechanism, involving the presence of transverse and streamwise vorticity, is at play in both cases. With regard to liftgeneration characteristics, the numerical simulation results indicate that in contrast to the transitional flow regime, where the unmodified NACA0021 undergoes a sudden loss of lift, in the turbulent regime, the baseline foil experiences gradual stall and produces more lift than the tubercled foil. This observation highlights the importance of considerations regarding the Reynolds number effects and the stall characteristics of the baseline foil, in the industrial applications of tubercled lifting bodies.
The presence of a finite tangential velocity on a hydrodynamically slipping surface is known to reduce vorticity production in bluff body flows substantially while at the same time enhancing its convection downstream and into the wake. Here, we investigate the effect of hydrodynamic slippage on the convective heat transfer (scalar transport) from a heated isothermal circular cylinder placed in a uniform crossflow of an incompressible fluid through analytical and simulation techniques. At low Reynolds ( \({\textit{Re}}\ll 1\) ) and high Péclet ( \({\textit{Pe}}\gg 1\) ) numbers, our theoretical analysis based on Oseen and thermal boundary layer equations allows for an explicit determination of the dependence of the thermal transport on the nondimensional slip length \(l_s\) . In this case, the surfaceaveraged Nusselt number, Nu transitions gradually between the asymptotic limits of \(Nu \sim {\textit{Pe}}^{1/3}\) and \(Nu \sim {\textit{Pe}}^{1/2}\) for noslip ( \(l_s \rightarrow 0\) ) and shearfree ( \(l_s \rightarrow \infty \) ) boundaries, respectively. Boundary layer analysis also shows that the scaling \(Nu \sim {\textit{Pe}}^{1/2}\) holds for a shearfree cylinder surface in the asymptotic limit of \({\textit{Re}}\gg 1\) so that the corresponding heat transfer rate becomes independent of the fluid viscosity. At finite \({\textit{Re}}\) , results from our twodimensional simulations confirm the scaling \(Nu \sim {\textit{Pe}}^{1/2}\) for a shearfree boundary over the range \(0.1 \le {\textit{Re}}\le 10^3\) and \(0.1\le {\textit{Pr}}\le 10\) . A gradual transition from the lower asymptotic limit corresponding to a noslip surface, to the upper limit for a shearfree boundary, with \(l_s\) , is observed in both the maximum slip velocity and the Nu. The local timeaveraged Nusselt number \(Nu_{\theta }\) for a shearfree surface exceeds the one for a noslip surface all along the cylinder boundary except over the downstream portion where unsteady separation and flow reversal lead to an appreciable rise in the local heat transfer rates, especially at high \({\textit{Re}}\) and Pr. At a Reynolds number of \(10^3\) , the formation of secondary recirculating eddy pairs results in appearance of additional local maxima in \(Nu_{\theta }\) at locations that are in close proximity to the mean secondary stagnation points. As a consequence, Nu exhibits a nonmonotonic variation with \(l_s\) increasing initially from its lowermost value for a noslip surface and then decreasing before rising gradually toward the upper asymptotic limit for a shearfree cylinder. A nonmonotonic dependence of the spanwiseaveraged Nu on \(l_s\) is observed in three dimensions as well with the threedimensional wake instabilities that appear at sufficiently low \(l_s\) , strongly influencing the convective thermal transport from the cylinder. The analogy between heat transfer and singlecomponent mass transfer implies that our results can directly be applied to determine the dependency of convective mass transfer of a single solute on hydrodynamic slip length in similar configurations through straightforward replacement of Nu and \({\textit{Pr}}\) with Sherwood and Schmidt numbers, respectively.
A combined theoretical and numerical analysis of an experiment devoted to the excitation of Görtler vortices by localized stationary or vibrating surface nonuniformities in a boundary layer over a concave surface is performed. A numerical model of generation of smallamplitude disturbances and their downstream propagation based on parabolic equations is developed. In the framework of this model, the optimal and the modal parts of excited disturbance are defined as solutions of initialvalue problems with initial values being, respectively, the optimal disturbance and the leading local mode at the location of the source. It is shown that a representation of excited disturbance as a sum of the optimal part and a remainder makes it possible to describe its generation and downstream propagation, as well as to predict satisfactorily the corresponding receptivity coefficient. In contrast, the representation based on the modal part provides only coarse information about excitation and propagation of disturbance in the range of parameters under investigation. However, it is found that the receptivity coefficients estimated using the modal parts can be reinterpreted to preserve their practical significance. A corresponding procedure was developed. The theoretical and experimental receptivity coefficients are estimated and compared. It is found that the receptivity magnitudes grow significantly with the disturbance frequency. Variation of the spanwise scale of the nonuniformities affects weakly the receptivity characteristics at zero frequency. However, at high frequencies, the efficiency of excitation of Görtler vortices depends substantially on the spanwise scale.
The pressure drag of blunt bluff bodies is highly relevant in many practical applications, including to the aerodynamic drag of road vehicles. This paper presents theory revealing that a mean drag reduction can be achieved by manipulating wake flow fluctuations. A linear feedback control strategy then exploits this idea, targeting attenuation of the spatially integrated base (back face) pressure fluctuations. Largeeddy simulations of the flow over a Dshaped blunt bluff body are used as a testbed for this control strategy. The flow response to synthetic jet actuation is characterised using system identification, and controller design is via shaping of the frequency response to achieve fluctuation attenuation. The designed controller successfully attenuates integrated base pressure fluctuations, increasing the timeaveraged pressure on the body base by 38%. The effect on the flow field is to push the rollup of vortices further downstream and increase the extent of the recirculation bubble. This control approach uses only bodymounted sensing/actuation and input–output model identification, meaning that it could be applied experimentally.
The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closedloop control framework addresses a key issue of modelbased control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a clusterbased discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames highdimensional, nonlinear dynamics into lowdimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The datadriven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a controldependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the longterm behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the openloop actuation in a separating flow dominated by Kelvin–Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.
An analysis of pressuregradientdriven flows in channels with walls modified by transverse ribs has been carried out. The ribs have been introduced intentionally in order to generate streamwise vortices through centrifugally driven instabilities. The cost of their introduction, i.e. the additional pressure losses, have been determined. Linear stability theory has been used to determine conditions required for the formation of the vortices. It has been demonstrated that there exists a finite range of rib wave numbers capable of creating vortices. Within this range, there exists an optimal wave number which results in the minimum critical Reynolds number for the specified rib amplitude. The optimal wave numbers marginally depend on the rib positions and amplitudes. As the formation of the vortices can be interfered with by viscositydriven instabilities, the critical conditions for the onset of such instabilities have also been determined. The rib geometries which result in the vortex formation with the smallest drag penalty and without interference from the viscositydriven instabilities have been identified.