Oscillation of Confined Jets in Continuous Casting Mold Flow

In continuous slab casting, the liquid steel is introduced into the mould via a submergered entry nozzle. This nozzle usually has two opposed orifices on its side walls, generating two diametrically opposed turbulent jets that are declined about 20° to the horizontal axis. These jets interact with the surrounding walls of the mould, which leads to an unstable flow situation and a self induced oscillation of the jets. Although both mould and nozzle geometry have two perpendicular symmetry planes, the oscillations are asymmetric. The fluid flow inside the mold is calculated with a 3D finite volume solver using turbulence models based on Reynolds-averaging. The massflow of the jets and the mould extensions are varied, and the numerical results are partially compared with PIV-measurements at a 1:1 scaled watermodel of the mould. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the implementation of WENO schemes for a class of polydisperse sedimentation models

The sedimentation of a polydisperse suspension of small rigid spheres of the same density, but which belong to a finite number of species (size classes), can be described by a spatially one-dimensional system of first-order, nonlinear, strongly coupled conservation laws. The unknowns are the volume fractions (concentrations) of each species as functions of depth and time. Typical solutions, e.g. for batch settling in a column, include discontinuities (kinematic shocks) separating areas of different composition. The accurate numerical approximation of these solutions is a challenge since closed-form eigenvalues and eigenvectors of the flux Jacobian are usually not available, and the characteristic fields are neither genuinely nonlinear nor linearly degenerate. However, the flux vectors associated with the widely used models by Masliyah, Lockett and Bassoon (MLB model) and Höfler and Schwarzer (HS model) give rise to Jacobians that are low-rank perturbations of a diagonal matrix. This property allows to apply a convenient hyperbolicity criterion that has become known as the “secular equation” [J. Anderson, A secular equation for the eigenvalues of a diagonal matrix perturbation, Lin. Alg. Appl. 246 (1996) 49–70]. This criterion was recently applied [R. Bürger, R. Donat, P. Mulet, C.A. Vega, Hyperbolicity analysis of polydisperse sedimentation models via a secular equation for the flux Jacobian, SIAM J. Appl. Math. 70 (2010) 2186–2213] to prove that the MLB and HS models are strictly hyperbolic under easily verifiable conditions, that their eigenvalues interlace with the velocities of the species that form the flux vector (so the velocities are good starting values for a root finder), and that the corresponding eigenvectors can be calculated with acceptable effort. In the present work, the newly available characteristic information is exploited for the implementation of characteristic-wise (spectral) weighted essentially non-oscillatory (WENO) schemes for the MLB and HS models. Numerical examples illustrate that WENO schemes which use this spectral information are superior in resolution, and even in efficiency for the same overall resolution, to component-wise WENO schemes.     

On the difficulty of triangulating three-dimensional Nonconvex Polyhedra

A number of different polyhedraldecomposition problems have previously been studied, most notably the problem of triangulating a simple polygon. We are concerned with thepolyhedron triangulation problem: decomposing a three-dimensional polyhedron into a set of nonoverlapping tetrahedra whose vertices must be vertices of the polyhedron. It has previously been shown that some polyhedra cannot be triangulated in this fashion. We show that the problem of deciding whether a given polyhedron can be triangulated is NP-complete, and hence likely to be computationally intractable. The problem remains NP-complete when restricted to the case of star-shaped polyhedra. Various versions of the question of how many Steiner points are needed to triangulate a polyhedron also turn out to be NP-hard.This work was supported by National Science Foundation Grant CCR-8809040.     

Calculating 3D stresses in layered composite plates and shells

Advanced failure criteria for fiber composites account for all six components of the stress tensor. Plate and shell analysis, however, is sensibly performed by assuming the plane state of stress, which results in global displacements, cross-sectional membrane forces, and bending moments of suitable accuracy. Based on these results, equilibrium conditions can be applied to locally determine the stress components in the transverse direction. Therewith, the transverse shear stresses require first derivatives and transverse normal stresses even second derivatives of the membrane stresses. Higher-order finite elements would be necessary if these stress components are to be determined on the element level. To ease this deficiency, a procedure is proposed based on neglecting the in-plane derivatives of the membrane forces and twisting moments as well as the mixed derivatives of the bending moments. This allows us to reduce the order of differentiation by one. Applicability of this procedure is demonstrated by calculating the transverse shear and normal stresses for layered composite structures of different geometric dimensions and various stacking orders under mechanical as well as thermal loads. Comparison with results from 3D analyses shows excellent accuracy and efficiency of the proposed procedure.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Deutsches Zentrum für Luft- und Raumfahrt e.V. (German Aerospace Center), Institute of Structural Mechanics, D-38022 BRAUNSCHWEIG, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 491–500, July–August, 1998.     

Routing of Railway Carriages

In the context of organizing timetables for railway companies the following railway carriage routing problem occurs. Given a timetable containing rail links with departure and destination times/stations and the composition of the trains, find a routing of railway carriages such that the required carriages are always available when a train departs. The problem is formulated as an integer multi-commodity network flow problem with nonlinear objective function. We will present a local search approach for this NP-hard problem. The approach uses structural properties of the integer multi-commodity network flow formulation of the problem. Computational results for a real world instance are given.     

On second-order antidiffusive Lagrangian-remap schemes for multispecies kinematic flow models

This paper focuses on the numerical approximation of the solutions of multi-species kinematic flow models. These models are strongly coupled nonlinear first-order conservation laws with various applications like sedimentation of a polydisperse suspension in a viscous fluid, or traffic flow modeling. Since the eigenvalues and eigenvectors of the corresponding flux Jacobian matrix have no closed algebraic form, this is a challenging issue. A new class of simple schemes based on a Lagrangian- Eulerian decomposition (the so-called Lagrangian-remap (LR) schemes) was recently advanced in [4] for traffic flow models with nonnegative velocities, and extended to models of polydisperse sedimentation in [5]. These schemes are supported by a partial numerical analysis when one species is considered only, and turned out to be competitive in both accuracy and efficiency with several existing schemes. Since they are only first-order accurate, it is the purpose of this contribution to propose an extension to second-order accuracy using quite standard MUSCL and Runge-Kutta techniques. Numerical illustrations are proposed for both applications and involving eleven species (sedimentation) and nine species (traffic) respectively.     

N-K electron energy-loss near-edge structures for TiN/VN layers: an ab initio and experimental study

We study N-K-edge electron energy-loss near-edge structures for well-defined TiN/VN bilayers grown on a MgO(100) substrate by both calculations and experiments. The structural relaxations and the electronic structure of TiN/VN multilayers are calculated using the Vienna Ab Initio Simulation Package computer code, which uses density functional theory to describe the electronic interaction. The effects of the core hole created in the excitation process are included in the calculations. For VN, off-stoichiometric effects due to nitrogen vacancies are modelled. The partial density of states (PDOS) for the N-K edge of atoms in the vicinity of the TiN/MgO interface revealed that two new peaks appear between 7 and 9 eV instead of a broad shoulder typical for the bulk. For the VN/TiN interface, the PDOS is modified only slightly, owing to similar bonding on both sides of the interface, and is thus very similar to the respective bulk spectra. An experimental spectrum taken at the VN/TiN interface is, however, well described by an average of the simulated spectra for VN and TiN bulk (interface). Such a finding is characteristic of an intermixed interface.      

Antidiffusive Lagrangian‐remap schemes for models of polydisperse sedimentation

One‐dimensional models of gravity‐driven sedimentation of polydisperse suspensions with particles that belong to N size classes give rise to systems of N strongly coupled, nonlinear first‐order conservation laws for the local solids volume fractions. As the eigenvalues and eigenvectors of the flux Jacobian have no closed algebraic form, characteristic‐wise numerical schemes for these models become involved. Alternative simple schemes for this model directly utilize the velocity functions and are based on splitting the system of conservation laws into two different first‐order quasi‐linear systems, which are solved successively for each time iteration, namely, the Lagrangian and remap steps (so‐called Lagrangian‐remap [LR] schemes). This approach was advanced in (Bürger, Chalons, and Villada, SIAM J Sci Comput 35 (2013), B1341–B1368) for a multiclass Lighthill–Whitham‐Richards traffic model with nonnegative velocities. By incorporating recent antidiffusive techniques for transport equations a new version of these Lagrangian‐antidiffusive remap (L‐AR) schemes for the polydisperse sedimentation model is constructed. These L‐AR schemes are supported by a partial analysis for N = 1. They are total variation diminishing under a suitable CFL condition and therefore converge to a weak solution. Numerical examples illustrate that these schemes, including a more accurate version based on MUSCL extrapolation, are competitive in accuracy and efficiency with several existing schemes. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1109–1136, 2016     

DAE-index monitoring for semi-discretized viscous Cosserat rod models

The dynamics of viscous jets due to external forces like gravity and aerodynamics can be described by Cosserat rod models consisting of a system of partial and ordinary differential equations. Depending on the formulation of the equations, in particular the compatibility conditions, the semi-discretization in space yields systems of differential-algebraic equations (DAE) in time of different indices. We present a DAE-index monitoring and discuss the numerical results for the application in a rotational 2d fiber spinning scenario. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)