Large-eddy-simulation of 3-dimensional Rayleigh-Taylor instability in incompressible fluids

The 3-dimensional incompressible Rayleigh-Taylor instability is numerically studied through the large-eddy-simulation ( LES) approach based on the passive scalar transport model. Both the instantaneous velocity and the passive scalar fields excited by sinusoidal perturbation and random perturbation are simulated. A full treatment of the whole evolution process of the instability is addressed. To verify the reliability of the LES code, the averaged turbulent energy as well as the flux of passive scalar are calculated at both the resolved scale and the subgrid scale. Our results show good agreement with the experimental and other numerical work. The LES method has proved to be an effective approach to the Rayleigh-Taylor instability.     

THE GENERALIZED RIEMANN PROBLEM FOR A SCALAR NONCONVEX COMBUSTION MODEL-THE PERTURBATION ON INITIAL BINDING ENERGY

In this article,we study the generalized Riemann problem for a scalar nonconvex Chapman-Jouguet combustion model in a neighborhood of the origin (t ＞ 0) on the (x,t) plane.We focus our attention to the...     

Algorithm for a general discrete k-out-of-n: G system subject to several types of failure with an indefinite number of repairpersons

A discrete k-out-of-n: G system with multi-state components is modelled by means of block-structured Markov chains. An indefinite number of repairpersons are assumed and PH distributions for the lifetime of the units and for the repair time are considered. The units can undergo two types of failures, repairable or non-repairable. The repairability of the failure can depend on the time elapsed up to failure. The system is modelled and the stationary distribution is built by using matrix analytic methods. Several performance measures of interest, such as the conditional probability of failure for the units and for the system, are built into the transient and stationary regimes. Rewards are included in the model. All results are shown in a matrix algorithmic form and are implemented computationally with Matlab. A numerical example of an optimization problem shows the versatility of the model.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

Lagrangian coherent structures,transport and chaotic mixing in simple kinematic ocean models

Methods of dynamical system’s theory are used for numerical study of transport and mixing of passive particles (water masses, temperature, salinity, pollutants, etc.) in simple kinematic ocean models composed with the main Eulerian coherent structures in a randomly fluctuating ocean—a jet-like current and an eddy. Advection of passive tracers in a periodically-driven flow consisting of a background stream and an eddy (the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere) is analyzed as an example of chaotic particle’s scattering and transport. A numerical analysis reveals a non-attracting chaotic invariant set Λ that determines scattering and trapping of particles from the incoming flow. It is shown that both the trapping time for particles in the mixing region and the number of times their trajectories wind around the vortex have hierarchical fractal structure as functions of the initial particle’s coordinates. Scattering functions are singular on a Cantor set of initial conditions, and this property should manifest itself by strong fluctuations of quantities measured in experiments. The Lagrangian structures in our numerical experiments are shown to be similar to those found in a recent laboratory dye experiment at Woods Hole. Transport and mixing of passive particles is studied in the kinematic model inspired by the interaction of a current (like the Gulf Stream or the Kuroshio) with an eddy in a noisy environment. We demonstrate a non-trivial phenomenon of noise-induced clustering of passive particles and propose a method to find such clusters in numerical experiments. These clusters are patches of advected particles which can move together in a random velocity field for comparatively long time. The clusters appear due to existence of regions of stability in the phase space which is the physical space in the advection problem.     

Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves

The goal of this article is to develop a new technique to obtain better asymptotic estimates for scalar conservation laws. General convex flux, f″(u)?0, is considered with an assumption . We show that, under suitable conditions on the initial value, its solution converges to an N-wave in L¹ norm with the optimal convergence order of O(1/t). The technique we use in this article is to enclose the solution with two rarefaction waves. We also show a uniform convergence order in the sense of graphs. A numerical example of this phenomenon is included.     

Folding characterization in conservative chaotic fluid flows

We study transport of passive scalar fields in a bidimensional incompressible chaotic fluid flow. For a spatially smooth velocity field with impulsive perturbations, the model is described by a randomized standard mapping. We numerically investigate passive scalar field transport for given initial concentration distributions and their dependence on the nonlinearity and noise amplitude. We show that space and time concentration histograms are determined by the underlying mechanism of stretching and folding. Moreover, to characterize this process we introduce a parameter, the average derivative of a tracer line length, which shows interesting scale properties.     

Time harmonic wave diffraction problems in materials with sign-shifting coefficients

Some electromagnetic materials present, in a given frequency range, an effective dielectric permittivity and/or magnetic permeability which are negative. We are interested in the reunion of such a “negative” material and a classical one. More precisely, we consider here a scalar model problem for the simulation of a wave transmission between two such materials. This model is governed by a Helmholtz equation with a weight function in the Δ principal part which takes positive and negative real values. Introducing additional unknowns, we have already proposed in Bonnet-Ben Dhia et al. (2006) [1] some new variational formulations of this problem, which are of Fredholm type provided the absolute value of the contrast of permittivities is large enough, and therefore suitable for a finite element discretization. We prove here that, under similar conditions on the contrast, the natural variational formulation of the problem, although not “coercive plus compact”, is nonetheless suitable for a finite element discretization. This leads to a numerical approach which is straightforward, less costly than the previous ones, and very accurate.     

MUSTA: A multi-stage numerical flux

Numerical methods for conservation laws constructed in the framework of finite volume and discontinuous Galerkin finite elements require, as the building block, a monotone numerical flux. In this paper we present some preliminary results on the MUSTA approach [E.F. Toro, Multi-stage predictor–corrector fluxes for hyperbolic equations, Technical Report NI03037-NPA, Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK, 17th June, 2003] for constructing upwind numerical fluxes. The scheme may be interpreted as an un-conventional approximate Riemann solver that has simplicity and generality as its main features. When used in its first-order mode we observe that the scheme achieves the accuracy of the Godunov method used in conjunction with the exact Riemann solver, which is the reference first-order method for hyperbolic systems. At least for the scalar model hyperbolic equation, the Godunov scheme is the best of all first-order monote schemes, it has the smallest truncation error. Extensions of the scheme of this paper are realized in the framework of existing approaches. Here we present a second-order TVD (TVD for the scalar case) extension and show numerical results for the two-dimensional Euler equations on non-Cartesian geometries. The schemes find their best justification when solving very complex systems for which the solution of the Riemann problem, in the classical sense, is too complex, too costly or is simply unavailable.     

Improved T − ψ nodal finite element schemes for eddy current problems

The aim of this paper is to propose improved T − ψ finite element schemes for eddy current problems in the three-dimensional bounded domain with a simply-connected conductor. In order to utilize nodal finite elements in space discretization, we decompose the magnetic field into summation of a vector potential and the gradient of a scalar potential in the conductor; while in the nonconducting domain, we only deal with the gradient of the scalar potential. As distinguished from the traditional coupled scheme with both vector and scalar potentials solved in a discretizing equation system, the proposed decoupled scheme is presented to solve them in two separate equation systems, which avoids solving a saddle-point equation system like the traditional coupled scheme and leads to an important saving in computational effort. The simulation results and the data comparison of TEAM Workshop Benchmark Problem 7 between the coupled and decoupled schemes show the validity and efficiency of the decoupled one.     

Space-time discontinuous galerkin method for maxwell equations in dispersive media

In this paper, a unified model for time-dependent Maxwell equations in dispersive media is considered. The space-time DG method developed in [29] is applied to solve the underlying problem. Unconditional L²-stability and error estimate of order O(τ^r+1+h^k+1/2) are obtained when polynomials of degree at most r and k are used for the temporal discretization and spatial discretization respectively. 2-D and 3-D numerical examples are given to validate the theoretical results. Moreover, numerical results show an ultra-convergence of order 2r+1 in temporal variable t.     

Development of the parametric tolerance modeling and optimization schemes and cost-effective solutions

Most of previous research on tolerance optimization seeks the optimal tolerance allocation with process parameters such as fixed process mean and variance. This research, however, differs from the previous studies in two ways. First, an integrated optimization scheme is proposed to determine both the optimal settings of those process parameters and the optimal tolerance simultaneously which is called a parametric tolerance optimization problem in this paper. Second, most tolerance optimization models require rigorous optimization processes using numerical methods, since closed-form solutions are rarely found. This paper shows how the Lambert W function, which is often used in physics, can be applied efficiently to this parametric tolerance optimization problem. By using the Lambert W function, one can express the optimal solutions to the parametric tolerance optimization problem in a closed-form without resorting to numerical methods. For verification purposes, numerical examples for three cases are conducted and sensitivity analyses are performed.     

Simulation of mass transfer in liquid/liquid slug flow

The mass transport for a liquid/liquid extraction system is examined using a numerical concept following the idea of the interface-tracking method. Separate, body-fitted, static computational domains are arranged around an imported steady-state interface topology. The domains are coupled at the free interface to capture the behaviour of the conjugated system. The steady-state hydrodynamics are the basis for the simulation of the transient mass transport, which is calculated as a passive scalar concentration or one-way coupling. The investigation is restricted to the extraction from the disperse to the continuous phase. Simulation results for an extraction from the disperse to the continuous phase show that most of the mass is transferred through the wall-film region into the continuous phase. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A 3D non-linear k–ε turbulent model for prediction of flow and mass transport in channel with vegetation

The results from a 3D non-linear k–ε turbulence model with vegetation are presented to investigate the flow structure, the velocity distribution and mass transport process in a straight compound open channel and a curved open channel. The 3D numerical model for calculating flow is set up in non-orthogonal curvilinear coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLEC algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k–ε turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The water level of this model is determined from 2D Poisson equation derived from 2D depth-averaged momentum equations. For concentration simulation, an expression for dispersion through vegetation is derived in the present work for the mixing due to flow over vegetation. The simulated results are in good agreement with available experimental data, which indicates that the developed 3D model can predict the flow structure and mass transport in the open channel with vegetation.     

Numerical stability analysis of differential equations with piecewise constant arguments with complex coefficients

In this paper we consider the analytical and numerical stability regions of Runge-Kutta methods for differential equations with piecewise continuous arguments with complex coefficients. It is shown that the analytical stability region contained in the numerical one is violated for a∉R by the geometric technique. And we give the conditions under which the analytical stability region is contained in the union of the numerical stability regions of two Runge-Kutta methods. At last, some experiments are given.     

Order h4 difference methods for a class of singular two space elliptic boundary value problems

In this article, we derive difference methods of O(h⁴) for solving the system of two space nonlinear elliptic partial differential equations with variable coefficients having mixed derivatives on a uniform square grid using nine grid points. We obtain two sets of fouth-order difference methods; one in the absence of mixed derivatives, second when the coefficients of u_xy are not equal to zero and the coefficients of u_xx and u_yy are equal. There do not exist fourth-order schemes involving nine grid points for the general case. The method having two variables has been tested on two-dimensional viscous, incompressible steady-state Navier-Stokes' model equations in polar coordinates. The proposed difference method for scalar equation is also applied to the Poisson's equation in polar coordinates. Some numerical examples are provided to illustrate the fourth-order convergence of the proposed methods.     

Periodic solutions for second order differential inclusions with the scalar p-Laplacian

We study periodic problems driven by the scalar p-Laplacian with a multivalued right-hand side nonlinearity. We prove two existence theorems. In the first, we assume nonuniform nonresonance conditions between two successive eigenvalues of the negative p-Laplacian with periodic boundary conditions. In the second, we employ certain Landesman-Lazer type conditions. Our approach is based on degree theory.     

l-solutions and stability analysis of difference equations using the Kummer’s test

We address the p-summability and asymptotic stability properties in nonautonomous linear difference equations. We focus our discussion on two kind of difference equations. The first one is a first order system of linear nonautonomous difference equations, and our discussion involves the use of Kummer’s convergence test. The second one is a linear nonautonomous scalar higher order difference equation. In this case our discussion is based on a recently introduced transformation of a higher order system into a first-step recursion, where the companion matrices are well treatable from our point of view. We give insight on our ideas that are behind our methods, prove new results, and show applications.     

A fuzzy algorithm for continuous capacitated location allocation model with risk consideration

This paper presents a continuous capacitated location-allocation model with fixed cost as a risk management model. In the presented model, the fixed cost consists of production and installation costs. The model considers risk as percent of unsatisfied demands. The fixed cost is assigned to a zone with a predetermined radius from its center. Because of uncertain environment, demand in each zone is investigated as a fuzzy number. The model is solved by a fuzzy algorithm based on α-cut method. After solving the model based on different α-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved based on different α-values to determine best allocation values. Also, this paper proposes a Cross Entropy (CE) algorithm considering multivariate normal and multinomial density functions for solving large scale instances and is compared with GAMS. Finally, a numerical example is expressed to illustrate the proposed model.     

The degree of a typical vertex in generalized random intersection graph models

In this paper we consider the degree of a typical vertex in two models of random intersection graphs introduced in [E. Godehardt, J. Jaworski, Two models of random intersection graphs for classification, in: M. Schwaiger, O. Opitz (Eds.), Exploratory Data Analysis in Empirical Research, Proceedings of the 25th Annual Conference of the Gesellschaft für Klassifikation e.V., University of Munich, March 14-16, 2001, Springer, Berlin, Heidelberg, New York, 2002, pp. 67-81], the active and passive models. The active models are those for which vertices are assigned a random subset of a list of objects and two vertices are made adjacent when their subsets intersect. We prove sufficient conditions for vertex degree to be asymptotically Poisson as well as closely related necessary conditions. We also consider the passive model of intersection graphs, in which objects are vertices and two objects are made adjacent if there is at least one vertex in the corresponding active model “containing” both objects. We prove a necessary condition for vertex degree to be asymptotically Poisson for passive intersection graphs.