bluuebunny/crossref_metadata_2025 huggingface dataset:
Calibrating microfluidic pressure correction functions in Laval nozzle flow by eliminating production accuracy influences
Authors: Groll Rodion , Gomez Juan
Published: October 2016

The investigated case is a micronozzle flow with Knudsen numbers in the slip‐flow regime near the nozzle throat in vacuum environment. Compared gases are neon, argon, krypton and xenon. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Nonlinear instability of a viscous liquid jet
Authors: Renoult Marie‐Charlotte , Brenn Günter , Mutabazi Innocent
Published: October 2016

We investigate the weakly nonlinear temporal instability of an axisymmetric Newtonian liquid jet. Early nonlinear studies on the capillary instability of inviscid liquid jets were carried up to the third order contributions to the jet deformation and showed the nonlinear interaction between different modes. A recent study on the weakly nonlinear instability of planar Newtonian liquid sheets revealed the role of the liquid viscosity in the sheet stability behavior and showed a complicated influence [1]. Here, the instability of a liquid jet is examined as the axisymmetric counterpart of the sheet, in search for corresponding insight into the role of the liquid viscosity in the jet instability mechanism. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Jungebad apparatus for the production of oil‐dispersion baths
Authors: Höffmann Ann Kathrin , Lakshmanan Peter , Ehrhard Peter , Ostermann Thomas
Published: October 2016

The Jungebad apparatus is used to generate oil‐dispersion baths in medical applications. The oil‐water dispersion is produced by dispersing medically‐effective oil while filling the bathtub. The aim is to produce smaller droplets in comparison to conventionally produced oil‐dispersion baths to generate a high surface‐to‐volume ratio of the oil. Additionally, the oil should be dispersed homogenously in the bath. Due to the greater surface of the oil, a better admission through the skin of the patient is achieved.

Experimental investigations with regard to the functionality of the Jungebad apparatus are presented. The analysis of the functionality and the oil‐water dispersion generation is accomplished by observations with a high‐speed camera. Results are discussed with respect to the required characteristics of the dispersion. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Transport of Mass, Momentum and Energy through Periodic Open Cell Metal Foams Applied in Catalysis
Authors: Horneber Tobias , Rauh Cornelia , Delgado Antonio
Published: October 2016

An ODE model to predict the temperature field of periodic open cell metal foams applied in catalysis as carrier structures is presented. The catalytic and highly endothermic reaction takes place in a porous layer which surround the struts of the foam and releases gas from a fluid. The one‐dimensional model includes dependencies of the foam structure (strut radius, shape of strut), process conditions (surrounding velocity, surrounding fluid: liquid and/or gas), chemical conditions (reaction enthalpy, activation energy) and material parameters (thermal conductivity, density, viscosity). This makes it possible to estimate optimal parameters, that are able to provide sufficient heat to the reaction. The advantage of this model is the substantial time saving in contrary to three dimensional finite volume simulations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical investigation into a liquid displacing a gas in thin porous layers
Authors: Neumann Tim , Boettcher Konrad , Ehrhard Peter
Published: October 2016

To examine the filling process in a lithium‐ion battery, a numerical model to characterize the displacing flow of a liquid in air‐filled pores of thin heterogeneous porous materials is elaborated. The investigation is based on the volume‐averaged Navier‐Stokes equations for small Reynolds numbers, using a volume‐of‐fluid method to cover the multiphase flow. The flow is investigated with respect to the wall effect and to capillary action within the porous matrix. On the one hand, model experiments with similar particle‐size distributions as in the battery layers are conducted to extract the porosity as function of the wall distance. On the other hand, experiments with the three different porous layers of the battery are performed to receive mean values for the most important properties related to the two‐phase flow. Results for the displacement flow in parts of the battery are presented and discussed, showing a considerable influence of the modeled effects onto the flow characteristics. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulations of Particle‐laden Flows with the Lattice Boltzmann Method
Authors: Rettinger Christoph , Rüde Ulrich
Published: October 2016

A lattice Boltzmann method is presented which enables the direct numerical simulation of particle‐laden flows. It applies a fluid‐solid coupling technique based on the momentum exchange method to represent geometrically fully resolved particles of arbitrary shape. The test case of a single moving sphere allows an in‐depth evaluation of the algorithm. The method is fully parallelizable and yields results with an accuracy comparable to classical CFD simulations. This forms the basis for simulations of complex systems involving several thousand particles like the sediment transport in river beds. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the predictive capabilities of a multiphase SPH model for hydrodynamic spreading dynamics
Authors: Sivanesapillai Rakulan , Steeb Holger
Published: October 2016

We assess the predictive capabilities of a multiphase Smoothed‐Particle Hydrodynamics (SPH) model to simulate two‐phase flow processes that are decisively governed by the dynamics of hydrodynamically moving contact lines. The spreading of a liquid droplet on a completely wettable, smooth and flat substrate serves as prototype validation problem. Our simulation results reproduce the main features of hydrodynamic spreading in the quasi‐static limit, i. e. when the balance of viscous and capillary forces near the contact line governs the dynamics. The exponential spreading rate is consistent with Tanner's law. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The excitation mechanism of a shear stress induced rotary wave
Authors: Steinrück Herbert , Gusner Lorenz
Published: October 2016

The free surface flow in a vertical, cylindrical, rotating container will be considered when axis‐symmetric angular and radial shear stress distributions are applied on the free surface. It is well known that in the inviscid case a rotary wave which can be described by a flow potential exists. We want to determine the stability limit of the axis‐symmetric base state with respect to the rotary wave for small Ekman and Froude numbers. Under the above assumption, the critical flow conditions can be determined analytically. The results can be verified experimentally using a vertical, cylindrical container partially filled with water where the top lid rotates with a given angular velocity. Thus, the induced air flow will exert shear stresses in the angular and radial direction onto the water surface. Above a certain threshold, rotary waves can be observed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Computational magneto‐hydrodynamic modeling of hypersonic flows with resolved shock wave diffusion
Authors: Chelem Mayigue Charles , Groll Rodion
Published: October 2016

The present model describes magneto‐hydrodynamic (MHD) effects on diffusing shock waves in compressible flows. The accurateness and the robustness of these new density‐based numerical algorithm in his ideal form was tested on a series of benchmark numerical experiments like the present MHD shock tube [1]. Interpolation schemes are used for interpolation of density, temperature, velocity and the magnetic field. For the discretization of laplacian terms with diffusion coefficient for polyhedral meshes, we make use of the Gauss linear uncorrected schemes to deal with the case that the consecutive cell faces are non‐orthogonal. The approach described above and developed in the present project has been coupled with semi‐discrete central schemes (e.g. Greenshields et al. [2]). All computational results are validated with verified data and analytical results. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A strategy to implement volume sources into Galbrun equation
Authors: Retka Stefanie
Published: October 2016

When considering noise propagation in flow in frequency domain computations, the standard Helmholtz equation is not sufficient to describe these effects. Therefore, using the linearized Euler equations (LEE) is common practice to describe sound propagation based on displacement perturbation. Galbrun reformulated the LEE in terms of an arbitrary Eulerian‐Lagrangian description, which resulted in the displacement based Galbrun equation. This equation can also be formulated in terms of pressure and displacements.

We want to include sources (monopoles, dipoles and quadrupoles) in the harmonic analysis of Galbrun equation when a volume flow is present. In a first step we will solve Galbrun equation considering a volume flow. The velocity field is obtained in a CFD computation. Afterwards, the sources will be included in the acoustic computations as well.

Preliminary computational results are discussed and implications for future directions of research are addressed. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Interaction between inner and outer layer in drag‐reduced turbulent flows
Authors: Cormier Marion , Gatti Davide , Frohnapfel Bettina
Published: October 2016

Effects of wall‐based skin‐friction drag reduction strategies on the statistical properties of large‐scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data‐driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall‐based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two‐point statistics, as cross‐correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large‐scale footprinting at the wall, as cross‐correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag‐reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag‐reduced flows. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Transportation of dry fine powders by coordinated friction manipulation
Authors: Dunst Paul , Bornmann Peter , Hemsel Tobias , Littmann Walter , Sextro Walter
Published: October 2016

The transportation of dry fine powders is an emerging technologic task, as in biotechnology, pharmaceutical or coatings industry particle sizes of processed powders are getting smaller and smaller. Fine powders are primarily defined by the fact that adhesive and cohesive forces outweigh the weight forces. This leads to mostly unwanted agglomeration (clumping) and adhesion to surfaces, what makes it more difficult to use conventional conveyor systems (e. g. pneumatic or vibratory conveyors) for transport. A rather new method for transporting these fine powders is based on ultrasonic vibrations, which are used to reduce friction and adhesion between powder and the substrate. One very effective set‐up consists of a pipe, which vibrates harmoniously in axial direction at low frequency combined with a pulsed radial high frequency vibration. The high frequency vibration accelerates the particles perpendicular to the surface of the pipe, which in average leads to lower normal and thereby smaller friction force. With coordinated friction manipulation the powder acceleration can be varied so that the powder may be greatly accelerated and only slightly decelerated in each excitation period of the low frequency axial vibration of the pipe. The amount of powder flow is adjustable by vibration amplitudes, frequencies, and pulse rate, which makes the device versatile for comparable high volume and fine dosing using one setup. Within this contribution an experimental set‐up consisting of a pipe, a solenoid actuator for axial vibration and a piezoelectric actuator for the radial high frequency vibration is described. An analytical model is shown, that simulates the powder velocity. Finally, simulation results are validated by experimental data for different driving parameters such as amplitude of low frequency vibration, pipe material and inclination angle. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Enhancement of adjoint topology optimization by approximated L1‐regularization for promotion of sparse distributed control
Authors: Gerdes Anne , Hinze Michael , Rung Thomas
Published: October 2016

An L1‐penalty term is inserted in the cost functional of an optimal control problem in order to promote a sparse distribution of the control variable. The non‐differentiable L1‐regularization term is approximated by differentiable Huber functions. The approach is validated by generic fluid‐dynamic test cases and applied to a cabin air outlet of an aircraft. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Existence of undercompressive weak solutions to the Euler equations
Authors: Kabil Buğra
Published: October 2016

We prove the local existence of an undercompressive hydrodynamical shock to the isothermal Euler equations with a non‐monotone pressure function. This nonlinear problem will be formulated as an abstract hyperbolic initial boundary value problem. The existence of a weak solution to a linearized version of the problem is shown with the use of Riesz theorem. Using the results of the linear system yields by an iteration scheme (local in time) well‐posedness of the nonlinear problem. The system of equations is obtained by modeling the motion of sharp liquid‐vapor interfaces including configurational forces as well as surface tension. The considered non‐viscous Van der Waals fluid is compressible and allows phase transitions. The propagating phase boundary is controlled by a modified version of the Rankine‐Hugoniot jump condition obtained by the Young‐Laplace law. Entropy dissipation at the interface is precisely described by a kinetic relation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Minimization of asymptotic energy of Müller's functional endowed with local nonlinear lower‐order term
Authors: Raguž Andrija
Published: October 2016

We solve a minimization problem associated to a generalization of the Müller functional studied in the paper G. Alberti, S. Müller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54, 761–825 (2001), whereby the lower order term
∫10a(s)v2(s)ds
(involving a primitive of the mass density function,
v = v(s),
and the weight function
a = a(s))
is replaced by
∫10a(s, v(s), v′(s))v2(s)ds
(where a belongs to a suitable Carathéodory class). We calculate the rescaled asymptotic energy of the functional as small parameter epsilon tends to zero. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Analysis of the Flow of Magnetoelastic Materials
Authors: Benešová Barbora , Forster Johannes , García‐Cervera Carlos , Liu Chun , Schlömerkemper Anja
Published: October 2016

We consider evolutionary models for magnetoelastic materials. The PDEs modeling the flow of the material were derived from variational principles in a continuum mechanical setting.

In this article, we discuss the existence of weak solutions for two models, one with gradient flow type dynamics on the magnetic variable and in the other the dynamics of the magnetization is described by the Landau‐Lifshitz‐Gilbert equation. We highlight the main differences of the proofs in the two cases. © 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The sum of squared logarithms inequality in arbitrary dimensions
Authors: Borisov Lev , Neff Patrizio , Sra Suvrit , Thiel Christian
Published: October 2016

We prove the sum of squared logarithms inequality (SSLI) which states that for nonnegative vectors x, y ∈ ℝn whose elementary symmetric polynomials satisfy
ek(x) ≤ ek(y) (for 1 ≤ k < n)
and
en(x) = en(y)
, the inequality
∑i(log xi)2 ≤ ∑i(log yi)2
holds. Our proof of this inequality follows by a suitable extension to the complex plane. In particular, we show that the function
f : M ⊆ ℂn → ℝ with f(z) = ∑i(log zi)2
has nonnegative partial derivatives with respect to the elementary symmetric polynomials of z. We conclude by providing applications and wider connections of the SSLI. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A linear elastic Fuzzy Finite Element Method with two fuzzy input parameters
Authors: Dridger Alex , Caylak Ismail , Mahnken Rolf
Published: October 2016

This work employs a fuzzy finite element method (FFEM) in order to characterize the non‐statistical properties based on the possibility theory [2]. A linear elastic body with fuzzy input material parameters Young's modulus
$\tilde{E}$
and Poisson's ratio
$\tilde{\nu}$
is studied. To this end, the fuzzy parameters are represented by possibility distributions generated from sparse experimental data. A computational approach involving the α‐level discretization technique [4] is used in order to calculate the possibility of the system response. Finally, our method is applied in a numerical example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
SFEM for rubber‐like materials at large deformations
Authors: Penner Eduard , Caylak Ismail , Nörenberg Nicole , Mahnken Rolf
Published: October 2016

This paper investigates the uncertainty of hyper‐elastic model, by random material parameters as stochastic variables. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data in combination with artificial data for elastomers the distribution of the force‐displacement curves are obtained. In the numerical example the PC‐based Stochastic Finite Element Method (SFEM) and the deterministic parameter identification are used for generation of the distribution of Ogden's material parameters. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Solution of the suicide substrate kinetics with an O'Malley/Hoppensteadt approximation of a higher order
Authors: Feist Bernd
Published: October 2016

Solving singularly perturbed initial‐value problems with an two scale approach, the O’Malley/Hoppensteadt approximation (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Plastic limit analysis and optimum design of structures for uncertain conditions.
Authors: Movahedi Rad Majid
Published: October 2016

At the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the plastic limit analysis provides no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore complementary strain energy of the residual forces could be considered an overall measure of the plastic performance of structures and the plastic deformations should be controlled by introducing a bound for magnitude of this energy. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended plastic limit design problem is formed. In this research, due to the uncertainties the bound for the complementary strain energy of the residual forces is given randomly and a general approach to evaluate the limit load capacity of structures for uncertain conditions is presented. The aim of this study is to evaluate limit load capacity of structures with limited residual strain energy on the probabilistically given conditions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Tuning of mass dampers for preventing brittle fracture by employing teaching learning based optimization
Authors: Nigdeli Sinan Melih , Bekdas Gebrail
Published: October 2016

In design of reinforced concrete structures, a ductile design is needed, because the brittle fracture is sudden. Also, the energy absorbed by the structure is effective for ductile structures during earthquake excitations. In design regulations, especially for vertical supporters such as columns, the shear force and axial force capacity is limited, although the strength of the members is not at the limits. For that reason, the shear forces of structures excited by earthquakes can be reduced by adding a tuned mass damper (TMD), but TMD must be optimized and it must not be heavy. If the mass of the TMD is not optimized, the ductile behaviour constraint about the axial force capacity cannot be provided. The compressive strength of the concrete is a measure for the effective application of a TMD to a reinforced concrete structure. Since the mass is limited by the design constraint, the other design variables of TMD such as period and damping ratio are optimized. Using the formulas for frequency and damping ratio related to a preselected mass may not be sufficient and a precise optimum solution for preventing brittle fracture. Metaheuristic methods can be used by using a specific limit. In this study, Teaching Learning Based Optimization (TLBO) is employed to find optimum TMD parameters. Several earthquake excitations were used in the optimization process. A three storey RC frame structures with different compressive strength of concrete is investigated. Three stopping criteria have been used in the proposed methodology. The first criterion is the reduction of the maxi‐mum shear force value for the most critical excitation to the ductile behaviour limit. The second criterion is the reduction of the ratio of maximum first storey displacements of structure with and without TMD. This value is reduced under a user defined value, but the user defined value can be entered as zero. This value can be iteratively increased for minimization. The last criterion is the reduction of the acceleration transfer function of the structure. The proposed method is feasible on finding optimum TMD ensuring ductility conditions. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FEM Shakedown of uncertain structures by chance constrained programming
Authors: Tran Ngoc Trinh , Tran Thanh Ngoc , Matthies H. G. , Stavroulakis G. E. , Staat M.
Published: October 2016

We present a new primal‐dual numerical algorithm of the shakedown problem under uncertainty in which the material strength is considered as a normally distributed random variable. Using chance constrained programming, we obtain deterministic equivalent formulations based on upper bound and lower bound theorems which are dual to each other. The proposed algorithm is tested in numerical examples which are applied to civil engineering structures. The obtained solutions show good performance. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the Positive Definiteness of Cokriging Covariance Matrices
Authors: Sauerbrei Anna , Zimmermann Ralf
Published: October 2016

Variable‐fidelity modeling (VFM), sometimes also termed multi‐fidelity modeling, refers to the utilization of two or more data layers of different accuracy in order to construct an inexpensive emulator of a given numerical high‐fidelity model. In practical applications, this situation arises when simulators of different accuracy for the same physical process are given and it is assumed that many low‐fidelity sample points are affordable, but the high‐fidelity model is extremely costly to assess. More precisely, the VFM objective is to construct a predictor function, which interpolates the primary sample data but is driven by the trend indicated by the secondary data. In view of the computational effort, the objective is to use as few high‐fidelity sample points as possible to achieve a desired level of accuracy.

A widely used VFM method is Cokriging. The technique yields the best linear unbiased estimator based on the given data, taking spatial correlation into account. One way to model spatial correlation is via positive definite correlation kernels that yield positive definite correlation matrices for distinct input sample points.

In this contribution, we will address the positive definiteness of Cokriging correlation matrices which is necessary for the method but not granted, due to the modeling of the cross‐correlations. We discuss both the cases of distinct and coincident low‐ and high‐fidelity sample points. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
C1‐continuous time integration based on cubic Hermite interpolation
Authors: Mergel Janine C. , Sauer Roger A. , Ober‐Blöbaum Sina
Published: October 2016

We discuss a C1‐continuous time integration method based on piecewise cubic Hermite approximation. This method, denoted as p2‐scheme, belongs to a class of one‐step integration methods derived recently [1]. It exhibits a convergence rate of order four and shows properties similar to variational integrators, such as an excellent long‐term energy preservation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive FEM and a posteriori error control for stationary coupled bulk‐surface PDEs
Authors: Eigel Martin , Müller Rüdiger
Published: October 2016

We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. The numerical error of the finite element solution can be controlled by a residual a posteriori error estimator which takes into account the approximation errors due to the discretisation in space as well as the polyhedral approximation of the surface. The estimators naturally lead to refinement indicators for an adaptive algorithm to control the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On accuracy and efficiency of the CESE‐method of C. S. Chang for one‐dimensional unstaedy flow computation
Authors: Niessner Herbert
Published: October 2016

About twenty years ago a NASA‐group around S. C. Chang began to develop a method using space‐time domains as elements for unstaedy flow computation. There are two kinds of elements. One within which the linearized form of the underlying differential equation is satisfied and one whithin which space‐time flux is conserved. Therefore the method is called conservation‐element solution‐element or shortly CESE. Applied to one‐dimensional flow equations we show conditions under which the method in the version of Jerez et al. [1] is

‐ second order accurate and

‐ more efficient than Lax‐Wendroff type methods.

(© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
High order time discretisation methods for incompressible Navier–Stokes equations
Authors: Rang Joachim
Published: October 2016

In this paper we solve incompressible Navier–Stokes equations with higher order time integration schemes such as Radau‐IIA and Lobatto‐IIIC methods. We compare the results with 4th order DIRK and ROW methods to show the advantages of higher order time integration methods. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A discontinuous method for oil‐water flow in heterogeneous porous media
Authors: Bürger Raimund , Kumar Sarvesh , Kenettinkara Sudarshan Kumar , Ruiz‐Baier Ricardo
Published: October 2016

An oil‐water flow‐transport problem in a heterogeneous porous medium (HPM), given by the Brinkman model coupled with a fractional flow formulation, is solved numerically by a discontinuous finite volume element (DFVE) method coupled with a Runge‐Kutta Discontinuous Galerkin (RKDG) scheme. A new (original) numerical example is presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Relaxing the CFL condition for the wave equation on adaptive meshes
Authors: Peterseim Daniel , Schedensack Mira
Published: October 2016

The Courant‐Friedrichs‐Lewy (CFL) condition guarantees the stability of the popular explicit leapfrog method for the wave equation. However, it limits the choice of the time step size to be bounded by the minimal mesh size in the spatial finite element mesh. This essentially prohibits any sort of adaptive mesh refinement that would be required to reveal optimal convergence rates on domains with re‐entrant corners. A simple subspace projection step inspired by numerical homogenisation can remove the critical time step restriction so that the CFL condition and approximation properties are balanced in an optimal way, even in the presence of spatial singularities. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A semi‐smooth NEWTON method for dynamic multifield plasticity
Authors: Schröder Bettina , Kuhl Detlef
Published: October 2016

In the present paper a multifield approach towards isotropic dynamic small strain elastoplasticity is depicted. Its solution procedure is based on a semi‐smooth NEWTON method coupled to a higher order accurate time integration scheme in the context of the finite element method. The appearing interactions are partly analyzed by means of an axisymmetric example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A discontinuous Galerkin Finite Element Method for linear elasticity using a mixed integration scheme to circumvent shear‐locking
Authors: Steiner Tobias , Wriggers Peter , Loehnert Stefan
Published: October 2016

Shear‐locking is a significant problem when using the Finite Element Method (FEM) with standard lower order Langrangian shape functions. To avoid this effect we introduce the discontinuous Galerkin Finite Element Method (dG‐FEM) for linear elasticity. In addition to a standard integration scheme for the dG‐FEM we develop a mixed integration scheme and compare both with established finite elements using a bending dominated benchmark. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On finite discrete operators and equations
Authors: Vasilyev Alexander , Vasilyev Vladimir
Published: October 2016

For discrete operators generated by Calderon–Zygmund kernels we consider certain finite‐dimensional approximations. We compare an initial discrete operator with its finite‐dimensional analogue and obtain invertibility conditions and approximation rate. The error estimate for approximate finite‐dimensional solution of corresponding equation is given also for a special right‐hand side. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive space‐time boundary element methods for the wave equation
Authors: Zank Marco , Steinbach Olaf
Published: October 2016

For the solution of the wave equation a space‐time energetic boundary integral formulation is used. The resulting single layer boundary integral equation is discretised by a conforming ansatz space on the lateral boundary. To derive an adaptive scheme an a posteriori error estimator based on the representation formula is used. Finally, numerical examples for a one‐dimensional spatial domain are presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal control of time discrete two‐phase flow governed by a diffuse interface model
Authors: Garcke Harald , Hinze Michael , Kahle Christian
Published: October 2016

We present results on optimal control of two‐phase flows. The fluid is modeled by a thermodynamically consistent diffuse interface model and allows to treat fluids of different densities and viscosities. In earlier work we proposed an energy stable time discretization for this model that we now employ to derive existence of optimal controls for a time discrete optimal control problem. The control aim is to obtain a desired distribution of the two phases in the system. For this we investigate three control actions. We use tangential Dirichlet boundary control and distributed control. We further consider the inverse problem of finding an initial distribution such that the evolution over a given time horizon starting from this value is close to a desired distribution. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A sharp regularization error estimate for bang‐bang solutions for an iterative Bregman regularization method for optimal control problems
Authors: Pörner Frank
Published: October 2016

In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and a regularity condition on the active sets convergence results are presented. Furthermore we show by numerical examples that the provided a‐priori estimate is sharp in the bang‐bang case. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Time transformed mixed integer optimal control problems with impacts
Authors: Ringkamp Maik , Ober‐Blöbaum Sina , Leyendecker Sigrid
Published: October 2016

The solutions of mixed integer optimal control problems (MIOCPs) yield optimized trajectories for dynamical systems with instantly changing dynamical behavior. The instant change is caused by a changing value of the integer valued control function. For example, a changing integer value can cause a car to change the gear, or a mechanical system to close a contact. The direct discretization of a MIOCP leads to a mixed integer nonlinear program (MINLP) and can not be solved with gradient based optimization methods at once. We extend the work by Gerdts [1] and reformulate a MIOCP with integer dependent constraints as an ordinary optimal control problem (OCP). The discretized OCP can be solved using gradient based optimization methods. We show how the integer dependent constraints can be used to model systems with impact and present optimized trajectories of computational examples, namely of a lockable double pendulum and an acyclic telescope walker. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Switching time optimization for a PDE constrained optimal control problem of bang‐bang type
Authors: Vossen Georg
Published: October 2016

We consider a well‐known optimal control problem subject to the heat equation where the control variable appears linearly as a boundary control in a Robin type boundary condition. Here, we describe an alternative numerical method to solve the problem by a switching time optimization approach. The method has so far been successfully applied to ODE problems and offers several advantages according to second order sufficient conditions and sensitivity analysis. We discuss theoretical aspects and present numerical results to illustrate the effectiveness of the method. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Disturbance decoupling for descriptor systems by behavioral feedback
Authors: Berger Thomas
Published: October 2016

We study disturbance decoupling for linear descriptor systems. Compared to previous approaches, where state feedback is used, we use the concept of behavioral feedback which allows to study a larger class of systems. We derive geometric characterizations for solvability of the disturbance decoupling problem following the classical approach. Exploiting the freedom in the choice of the behavioral feedback we show that whenever disturbance decoupling can be achieved by behavioral feedback we may additionally achieve autonomous zero dynamics. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Some Remarks concerning Flatness and the Parameterization of the System Variables by a Flat Output
Authors: Kolar Bernd , Schöberl Markus , Schlacher Kurt
Published: October 2016

For flat systems, by definition the state‐ and input variables can be parameterized by the flat output and its time derivatives. In the present contribution, for special classes of flat outputs like e.g. flat outputs that only depend on the state, we derive upper bounds for the number of time derivatives that occur in this parameterization. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Inner‐Outer Factorization via Lur'e Equations
Authors: Reis Timo , Voigt Matthias
Published: October 2016

In this paper we construct inner‐outer factorizations of transfer functions governed by linear time‐invariant differential‐algebraic systems. This construction is based on the solution of certain Lur’e equations. In contrast to previous work we do not assume any condition apart from behavioral stabilizability of the underlying system realization. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Tools for assessing and optimizing the energy requirements of high performance scientific computing software
Authors: Diethelm Kai
Published: October 2016

Score‐P is a measurement infrastructure originally designed for the analysis and optimization of the performance of HPC codes. Recent extensions of Score‐P and its associated tools now also allow the investigation of energy‐related properties and support the user in the implementation of corresponding improvements. Since it would be counterproductive to completely ignore performance issues in this connection, the focus should not be laid exclusively on energy. We therefore aim to optimize software with respect to an objective function that takes into account energy and run time. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical simulation of glottal flow in surgically changed larynx
Authors: Hundertmark‐Zaušková Anna , Lehmann Ragnar , Hess Markus , Müller Frank
Published: October 2016

According to clinical experience the shape of the larynx seems to have a significant impact on the airflow degree and breathing pattern. In this study we perform a set of numerical experiments simulating the glottal flow in surgically changed larynx, where the vocal folds or false vocal are modified. We are aiming to find an optimal geometry of the larynx in terms of easiness for breathing. To this goal we numerically solve the system for weakly compressible Navier–Stokes equations using the finite element method and we compare the airflow resistance and the volumetric flow rate for the set of geometries for inspiration as well as expiration. We discuss the optimal geometry with respect to the quality of breathing. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A hybrid weakly nonconforming discretization for linear elasticity
Authors: Krämer Julian , Wieners Christian , Wohlmuth Barbara , Wunderlich Linus
Published: October 2016

We introduce a hybridizable discretization for problems of linear elasticity, based on a flexible weak coupling of the displacement and the normal stress across the inner element boundaries. The dual variables of the Lagrange multiplier are introduced as hybrid trace variables. A reduction of the equation system to these variables allows for an efficient parallel implementation. The performance of an adaptive choice of the hybrid degrees of freedom is demonstrated by a numerical example with a corner singularity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multirate finite step methods for linear acoustics
Authors: Naumann Andreas , Wensch Jörg
Published: October 2016

Many processes contain phenomena on different time scales, leading to model equations with fast and small parts. There are several approaches to solve these equations, like additive Runge Kutta methods or multirate infinitesimal steps methods (MIS). Both methods make use of the additive splitting of the ODE in fast and small parts. The multiple infinitesimal step method integrates the slow part with a large macro stepsize, whereas the fast terms are solved with several smaller steps of a simpler method. The order conditions of a MIS method are derived under the assumption of the exact integration of the fast parts.

We develop the multirate finite step methods (MFS). These methods are derived from the MIS methods, by taking a simple small scale integrator for the fast terms. This small scale integrator uses the same number of steps in each stage. With these assumptions, we derive the order conditions, such that the order is independent in the number of small steps. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Kinetic energy preserving DG schemes based on summation‐by‐parts operators on interior node distributions
Authors: Ortleb Sigrun
Published: October 2016

In this work, a kinetic energy preserving DG scheme in one space dimension using Gauss‐Legendre nodes is presented. Stability problems will be demonstrated when using interface terms that are derived from the Lobatto nodes within the Gauss‐Legendre skew‐symmetric DG formulation. However, combined with correct interface terms, the skew‐symmetric DG scheme constructed on Gauss‐Legendre nodes is expected to yield higher accuracy compared to its Gauss‐Lobatto counterpart. This advantage is demonstrated in the case of viscous compressible flow computation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Automated Generation of Performance Values for Algorithmic Differentiation
Authors: Sagebaum Max , Albring Tim , Gauger Nicolas R.
Published: October 2016

The transition from simulation software to optimization software is often quite cumbersome and error prone. With Algorithmic Differentiation(AD) a semi automatic transition can be achieved, but most of the times the performance characteristics of the modified software are not clear in advance. Therefore the performance model from Griewank is tested against real world examples and an automated measurement for the performance characteristics of the hardware is proposed. This enables a more accurate calculation of the performance characteristics of the modified software. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coupled Thermo‐Mechanical and Wear Effects on the Analysis of High Speed Railway Brake Systems
Authors: Srisupattarawanit T. , Schiefer F. , Ostermeyer G.‐P.
Published: October 2016

The high speed railway brakes transfer a large amount of kinetic energy into heat. The temperature during a brake operation could reach values higher than 90 °C. The dynamics of the brake system is rather complicated with respect to the multiphysical phenomena. In this paper, the thermo‐mechanical coupling are investigated combined with the loos of brake material due to wear. The coupled model is discretized by conventional finite element method. Different coupled algorithms have been tested. Various scenarios have been simulated and shown reasonable results. The temperature and deformation on pad and disc, especially the thermal deformation of disc the so–called coning effect can also be prescribed with this coupled multiphysics model. Furthermore, the tapered wear on brake pads is also discussed as a requirement of railway brake design in terms of durability. Thereby, the Ehlers's model is normally used to minimize tapered wear by selecting an adequate point of applied braking force. An extended Ehlers's model is also presented here, which concerns wear effect based on Archard's model. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Perturbations of positive strongly continuous semigroups on AM spaces
Authors: Wintermayr Jens
Published: October 2016

We give a definition for positivity on an extrapolation space for positive strongly continuous semigroups. We prove a perturbation result on AM spaces for positive semigroups by positive operators. Finally, we give an example for this kind of perturbations. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Dichotomy properties of Hamiltonians for linear systems in extrapolation spaces
Authors: Wyss Christian
Published: October 2016

For the Hamiltonian operator matrix from systems theory the existence of invariant subspaces corresponding to the spectrum in the right and left half‐plane is shown. The control and observation operators are unbounded in the sense that they map into extrapolation spaces, thereby allowing for PDE systems with control and observation on the boundary. The invariant subspaces are then used to construct solutions of the corresponding Riccati equation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Tree forcings and sharps
Authors: Castiblanco Fabiana , Schlicht Philipp
Published: October 2016

The Levy‐Solovay theorem and its variants show that various large cardinals are preserved under small forcings. We study the preservation of consequences of large cardinals under proper forcings. In particular, we consider the preservation of the statement that every real has a sharp for classical tree forcings. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
No large sets which can be translated away from every Marczewski null set
Authors: Brendle Jörg , Wohofsky Wolfgang
Published: October 2016

There is no set of size continuum which is “s0‐shiftable”, i. e., which can be translated away from every set in the Marczewski ideal s0 (where a set of reals is in s0 if for every perfect set there is a perfect subset disjoint from it). (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Homogenization of Cahn–Hilliard‐type equations with unbounded potentials
Authors: Liero Matthias , Reichelt Sina
Published: October 2016

In this note we recall two approaches to evolutionary Γ‐convergence for classical gradient systems: evolutionary variational inequalities versus energy‐dissipation principles. Following [1] we apply both approaches to homogenize Cahn–Hilliard‐type equations with rapidly oscillating coefficients and quite general potential. Here the focus is on the Γ‐convergence of the energy functional, which we prove without assuming any growth conditions for the convex part of the potential. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Physiological loading of cartilage replacement materials in a bioreactor environment
Authors: Fuhrmann‐Nelles Nadine , Willenberg Wolfgang , Stoffel Marcus , Markert Bernd
Published: October 2016

Trying to replace injured cartilage by implants is a common practice in biomedical engineering. These implants can be non‐seeded or seeded with human cartilage cells. To initiate cell multiplication and oriented cell growth in cell seeded implants, the implants are cultivated and usually stimulated electrically or mechanically in a bioreactor before implanting.

In the present study, a knee testing bench combined with a bioreactor environment is developed. Doing so, it is possible to stimulate such implants controlled in a physiologically consistent, multi‐dimensional way. The implants are placed in a recreated human knee joint and stimulated with several physiological load cycles of reproduced walking. After some days, the implanted material can be removed and mechanically and biologically evaluated in cooperation with the RWTH Aachen University Hospital.

The new experimental set‐up enables us for the first time to study the remodelling effect, the efficiency of the preconditioning as well as the influence of the body‐conformable load on the material. Furthermore, the need of cell colonisation in the implants shall be investigated. To understand the correlation between tissue remodelling and mechanical load history, the experiment is also numerically investigated, based on a geometrically realistic FE model of the recreated human knee and appropriate material models for the involved structures. Doing so, the strains and stresses, as well as the shear forces in the implant can be evaluated. The results will be compared to experimental data. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Conservation properties of higher order time stepping schemes based on variational integrators
Authors: Bartelt Matthias , Groß Michael
Published: October 2016

This paper deals with higher order accurate variational integrators for finite element systems. The variational integrator (VI) is based on higher order LAGRANGE polynomials as shape functions and a higher order GAUSSIAN quadrature rule. The goals of this paper are to implement a discrete gradient to preserve the balance of total energy and fulfill the constraints with the LAGRANGE multiplier method and a NEWTON‐COTÊS quadrature rule. We show the calculation of bearing forces from the LAGRANGE multipliers, which are essential for the balance of total linear momentum and the balance of total angular momentum. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)