Axisymmetric flow over a backward-facing step in an annular pipe

The incompressible flow of a Newtonian fluid over a backward-facing step is investigated numerically. The geometry is an annular pipe in which the radius of the inner cylinder decreases suddenly. Keeping the radial expansion ratio fixed axisymmetric flows are computed for outlet radius ratios from 0.1 to 1 (ratio of the inner to the outer outlet radius). The Reynolds number at which the flow separates from the outer cylinder decreases as the outlet radius ratio decreases for constant inlet geometry. The growth with Reynolds number of the recirculation zone on the inner outlet cylinder just behind the step is strongly reduced when the recirculation zone on the outer cylinder is established. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of vortical evolution in a backward-facing step expansion flow

A numerical investigation of laminar flow over a backward-facing step is presented for the Reynolds number in the range of 50Re2500. The objective of this numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the expansion flow structure. We proceed with the analysis by verifying the computer code through the Pearson vortex problem. We then perform a parametric study by varying the Reynolds number, with the aim of determining whether or not there exists a critical Reynolds number, above which reattachment length on the channel floor decreases. We also concentrate on subjects that have been little explored in the flow, examples of which are the onset of a single vortex in the primary eddy and how the recirculating bubble containing flow reversals is torn into smaller eddies. Eddy distortion, leading to mobile saddle points, and the merging of eddies are also discussed in this study.     

Low-Reynolds-number modelling of flows over a backward-facing step

The complex turbulent flow behind a backward-facing step is modelled using a full Reynolds stress closure. In order to develop a closure model that can resolve the complex near-wall flow in the recirculation region and in the recovery region downstream of the reattachment point, the performance of a low and a high Reynolds number version of the full Reynolds stress closure is examined and compared. Furthermore, the effects of redistribution modelling on the calculated flow is studied by comparing the performance of three redistribution models: one return-to-isotropy model and two with mean-strain effects. The results are grid independent and show that the flow downstream of the step is best described by a low-Reynolds-number model that does not depend on the conventional wall function assumption. However, the skin friction behavior is correctly predicted by the stipulation of a wall function. Of the three redistribution models examined, the return-to-isotropy model gives results that are in excellent agreement with measurements. Finally, the calculated results are adversely affected by refining the redistribution models to include meanstrain effects.     

Dynamics of reattachment region behind backward-facing step in a narrow channel

Dynamics of the flow reattachment behind the backward-facing step in a narrow channel is studied experimentally using the PIV technique. Reattachment region is detected by statistical characteristics of the flow velocity close to the channel bottom. Two methods of reattachment definition are applied. The reattachment region structure and extent is shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Comparison of isotropic and anisotropic subgrid scale models in Large Eddy Simulations of a backward-facing step and square duct flow

The present paper employs the anisotropic explicit algebraic subgrid-stress model (EASM), proposed by Marstorp et al. J. Fluid. Mech. 639, 403 - 432 (2009), developed in the spirit of an earlier explicit algebraic RANS-model for statistical closures. The EASM in its elementary, computationally efficient non-dynamic version is used for Large Eddy Simulation of three-dimensional flows over a backward-facing step at a bulk Reynolds number of 4805 and a square duct at 2205. Its performance is assessed by comparison with experimental data and an own Direct Numerical Simulation. Furthermore, a set of eddy-viscosity models, including the recent σ-model, is employed for comparison. Various statistical quantities are evaluated to assess the respective performance of the different models showing, that the anisotropic EASM compares favorably to the other models. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct Numerical Simulation of turbulent heat transfer behind a backward-facing step at low Prandtl number

The paper presents Direct Numerical Simulations of the turbulent flow of a low Prandtl number fluid over a backward-facing step with heat transfer. The backward-facing step flow is investigated as a generic configuration for sudden changes in cross section. Several simulations are reported: for isothermal conditions, for heat transfer with the Prandtl number of air, and for heat transfer with the Prandtl number of liquid sodium. The simulation for air is compared to results from literature. The differences induced by reduction of the Prandtl number are then assessed by comparison of the two cases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

CFD of turbulent transport of particles behind a backward-facing step using a new model—k-ε-Sp

The k-ε-S_p model, describing two-dimensional gas–solid two-phase turbulent flow, has been developed. In this model, the diffusion flux and slip velocity of solid particles are introduced to represent the particle motion in two-phase flow. Based on this model, the gas–solid two-phase turbulent flow behind a vertical backward-facing step is simulated numerically and the turbulent transport velocities of solid particles with high density behind the step are predicted. The numerical simulation is validated by comparing the results of the numerical calculation with two other two-phase turbulent flow models (k-ε-A_p, k-ε-k_p) by Laslandes and the experimental measurements. This model, not only has the same virtues of predicting the longitudinal transport of the solid particles as the present practical two-phase flow models, but also can predict the lateral transport of the solid particles correctly.     

Analytical and numerical Riemann solutions of the Saint Venant equations for forward- and backward-facing step flows

Analytical solutions of the Saint Venant equations for five typical Riemann problems over a forward- or backward-facing step are constructed. These analytical solutions are used as reference ones to estimate the accuracy of simulated discontinuous solutions based on the regularized shallow water equations.     

Reconstructing obstacles by the enclosure method using the far field measurements in one step

In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the far field measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the far field pattern to the reflected solutions corresponding to the used complex geometrical optics solutions. Second, we use layer potential techniques to derive the needed estimates of the reflected solutions. No condition on the geometry of the obstacle or on the used frequency is needed.     

Diffraction of a sinusoidal impulse by a rigid strip

The diffraction of a sinusoidal impulse by an absolutely rigid strip is considered. Approximate formulas are obtained for the field measured at large distances from the strip in the direction of the incident impulse (the case of location). The results are expressed in terms of Fresnel integrals. The possibility of determining the width of the strip and the angle between it and the direction of the incident impulse or the basis of the envelope of the location field is discussed. Graphs of the envelopes for certain specific cases are presented.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 62, pp. 39–47, 1976.The author is grateful to D. P. Kouzov for his attention to the work.     

Fluctuation measurements in the boundary layer of a supersonic flow

Fluctuation measurements were carried out via constant-temperature hot-wire anemometry inside the turbulent boundary layer of a flat plate and a compression ramp (deflexion angle: 11.5). The free-stream Mach number was M = 2.54. Fluctuation profiles of the alternating quantities temperature, density and velocity were obtained under the assumption of low pressure fluctuations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaotic behavior of earthquakes induced by a nonlinear magma up flow

This paper considers the dynamics of a modified 1D nonlinear spring-block model for earthquake subjected to the strengths induced by the motion of the tectonic plates and the up flow of magma during volcanism. Based on the multiple time scales method, we establish that after the slip, the fault remains active and the frictions increase with the power of the earthquake. We also obtain in the non-resonance case that the appearing probability of an event decreases with these frictions. In the resonance case, the dynamics of harmonic oscillations show that the rocks constituting the block will fracture or resist to the effects induced by the magma motion. Our analytical investigations are complemented by numerical simulations from which it appears that, for given values of the magma thrust strength magnitude, the friction coefficient, the quadratic and cubic nonlinear parameters, the system exhibits chaotic behavior.     

Delayed reflection of the energy flow at a potential step for dispersive wave packets

We study Klein–Gordon equations with constant coefficients and different dispersion relations on two one‐dimensional semi‐infinite media coupled with transmission conditions. We obtain lower and upper bounds of the reflected part of the energy flow at the connecting point when the frequency band involved in the initial signal is sufficiently narrow. We detect a phenomenon of delayed reflection for low frequency wave packets, which is in accordance with the recent experiments of Haibel and Nimtz. The result is then generalized for a star‐shaped network of n semi‐infinite branches connected at one point. Copyright © 2004 John Wiley & Sons, Ltd.     

Limiting behavior of a controlled system at infinite time

The system of Lotka–Volterra equations with transport is generalized to the case of a controlled system. The limiting behavior is investigated depending on initial values and control options.     

On the computational behavior of a polynomial-time network flow algorithm

A variation on the Edmonds-Karp scaling approach to the minimum cost network flow problem is examined. This algorithm, which scales costs rather than right-hand sides, also runs in polynomial time. Large-scale computational experiments indicate that the computational behavior of such scaling algorithms may be much better than had been presumed. Within several distributions of square, dense, capacitated transportation problems, a cost scaling code, SCALE, exhibits linear growth in average execution time with the number of edges, while two network simplex codes, RNET and GNET, exhibit greater than linear growth.Our experiments reveal that median and mean execution times are predictable with surprising accuracy for all of the three codes and all three distributions from which test problems were generated. Moreover, for fixed problem size, individual execution times appear to behave as though they are approximately lognormally distributed with constant variance. The experiments also reveal sensitivity of the parameters in the models, and in the models themselves, to variations in the distribution of problems. This argues for caution in the interpretation of such computational studies beyond the realm in which the computations were performed.This work has been supported in part by NSF grants ENG-7910807, ECS-8313853, DMS-8706133, and DDM-8813054, and by AFOSR, NSF, and ONR under NSF grant DMS-8920550 to Cornell University, and by a Sloan Foundation research fellowship held by the first author.     

Mathematical analysis of a continuous version of statistical model for criminal behavior

This paper is concerned with a reaction-advection-diffusion system, which is a continuous version of statistical model for criminal activity proposed by Short et al (Math. Models Methods Appl. Sci., 8 (2008), 1249-1267). From very recently results, it is known that the classical solution of the corresponding initial-boundary value problem exists globally. On the other hand, Rodriguez (Phys. D, 260 (2013), 191-200) asserted the uniform-in-time boundedness of classical solution; however, there is a gap in the proof. In this work, we first solve this open problem by establishing some crucial a priori estimates. Then, invoking the uniform boundedness, we present that the classical solution converges exponentially to the steady state. Our results are consistent with the experiment observation and numerical simulation in the existing literatures.     

One-sided approximation of a step by algebraic polynomials in the mean

An asymptotically sharp estimate is obtained for the best one-sided approximation of a step by algebraic polynomials in the space L ₁:     

Phase transition and critical behavior in a model of organized criticality

We study a model of organized criticality, where a single avalanche propagates through an a priori static (i.e., organized) sandpile configuration. The latter is chosen according to an i.i.d. distribution from a Borel probability measure on [0,1]. The avalanche dynamics is driven by a standard toppling rule, however, we simplify the geometry by placing the problem on a directed, rooted tree. As our main result, we characterize which are critical in the sense that they do not admit an infinite avalanche but exhibit a power-law decay of avalanche sizes. Our analysis reveals close connections to directed site-percolation, both in the characterization of criticality and in the values of the critical exponents.Mathematics Subject Classification (2000): 60K35, 82C20, 82C44     

Progress on asymptotic behavior of the Yang-Mills-Higgs flow

In this note we will introduce our recent work on the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles, and the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity.