242 Works

On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn

David Janke, Alfonso Caiazzo, Naveed Ahmed, Najib Alia, Oswald Knoth, Baptiste Moreau, Ulrich Wilbrandt, Dilya Willink, Thomas Amon & Volker John
Two transient open source solvers, OpenFOAM and ParMooN, are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a <i>1:100</i> scaled wind tunnel model. Both solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for time-averaged stream-wise and vertical-wise velocities. In particular, the air exchange was predicted with...

Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations

Etienne Emmrich & Robert Lasarzik
A nonlinear model due to Soddemann et al. [37] and Stewart [38] describing incompressible smectic-A liquid crystals under flow is studied. In comparison to previously considered models, this particular model takes into account possible undulations of the layers away from equilibrium, which has been observed in experiments. The emerging decoupling of the director and the layer normal is incorporated by an additional evolution equation for the director. Global existence of weak solutions to this model...

Stochastic Eulerian model for the flow simulation in porous media

Dmitry R. Kolyukhin & Karl K. Sabelfeld
This work deals with the stochastic flow simulation in statistically isotropic and anisotropic saturated porous media in 3D case. The hydraulic conductivity is assumed to be a random field with lognormal distribution. Under the assumption of smallness of fluctuations in the hydraulic conductivity we construct a stochastic Eulerian model for the incompressible flow as a divergenceless Gaussian random field with a spectral tensor of a special structure derived from Darcy's law. A randomized spectral representation...

Balanced-Viscosity solutions for multi-rate systems

Alexander Mielke, Riccarda Rossi & Giuseppe Savaré
Several mechanical systems are modeled by the static momentum balance for the displacement u coupled with a rate-independent flow rule for some internal variable z. We consider a class of abstract systems of ODEs which have the same structure, albeit in a finite-dimensional setting, and regularize both the static equation and the rate-independent flow rule by adding viscous dissipation terms with coefficients εα and ε, where 00 is a fixed parameter. Therefore for α different...

Element method for epitaxial growth with attachment-detachment kinetics

Eberhard Bänsch, Frank Haußer, Omar Lakkis, Bo Li & Axel Voigt
An adaptive finite element method is developed for a class of free or moving boundary problems modeling island dynamics in epitaxial growth. Such problems consist of an adatom (adsorbed atom) diffusion equation on terraces of different height, boundary conditions on terrace boundaries including the kinetic asymmetry in the adatom attachment and detachment, and the normal velocity law for the motion of such boundaries determined by a two-sided flux, together with the one-dimensional "surface" diffusion. The...

Dynamo action in cellular convection

Norbert Seehafer & Ayhan Demircan
The dynamo properties of square patterns in Boussinesq Rayleigh-Benard convection in a plane horizontal layer are studied numerically. Cases without rotation and with weak rotation about a vertical axis are considered, particular attention being paid to the relation between dynamo action and the kinetic helicity of the flow. While the fluid layer is symmetric with respect to up-down reflections, the square-pattern solutions may or may not possess this vertical symmetry. Vertically symmetric solutions, appearing in...

Coarse-graining via EDP-convergence for linear fast-slow reaction systems

Alexander Mielke & Artur Stephan
We consider linear reaction systems with slow and fast reactions, which can be interpreted as master equations or Kolmogorov forward equations for Markov processes on a finite state space. We investigate their limit behavior if the fast reaction rates tend to infinity, which leads to a coarse-grained model where the fast reactions create microscopically equilibrated clusters, while the exchange mass between the clusters occurs on the slow time scale. Assuming detailed balance the reaction system...

Error estimates for nonlinear reaction-diffusion systems involving different diffusion length scales

Sina Reichelt
We derive quantitative error estimates for coupled reaction-diffusion systems, whose coefficient functions are quasi-periodically oscillating modeling microstructure of the underlying macroscopic domain. The coupling arises via nonlinear reaction terms, and we allow for different diffusion length scales, i.e. whereas some species have characteristic diffusion length of order 1, other species may diffuse much slower, namely, with order of the characteristic microstructure-length scale. We consider an effective system, which is rigorously obtained via two-scale convergence, and...

Stochastic Lagrangian footprint calculations over a surface with an abrupt change of roughness height

Orazgeldi Kurbanmuradov, Ullar Rannik, Alexander I. Levykin, Karl Sabelfeld & Timo Vesala
Forward and backward stochastic Lagrangian trajectory simulation methods are developed to calculate the footprint and cumulative footprint functions of concentration and fluxes in the case when the ground surface has an abrupt change of the roughness height. The statistical characteristics to the stochastic model are extracted numerically from a closure model we developed for the atmospheric boundary layer. The flux footprint function is perturbed in comparison with the footprint function for surface without change in...

On the velocity of the Biot slow wave in a porous medium: Uniform asymptotic expansion

Inna Edelman
Asymptotic behavior of the Biot slow wave is investigated. Formulae for short- and long-wave approximations of phase velocity of the P2 wave are presented. These asymptotic expansions are compared with exact solution, constructed numerically. It is shown that both expansions fit very well the real velocity of the P2 mode. Procedure for matching of short- and long-wave asymptotic expansions is suggested.

Classical solutions of quasilinear parabolic systems on two-dimensional domains

Hans-Christoph Kaiser, Hagen Neidhardt & Joachim Rehberg
Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of 푝-integrable functions, for some 푝 > 1, over a bounded two dimensional space domain. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck's...

Wavelet approximation of correlated wavefunctions. II. Hyperbolic wavelets and adaptive approximation schemes

Hongjun Luo, Dietmar Kolb, Heinz-Jürgen Flad, Wolfgang Hackbusch & Thomas Koprucki
We have studied various aspects concerning the use of hyperbolic wavelets and adaptive approximation schemes for wavelet expansions of correlated wavefunctions. In order to analyze the consequences of reduced regularity of the wavefunction at the electron-electron cusp, we first considered a realistic exactly solvable many-particle model in one dimension. Convergence rates of wavelet expansions, with respect to L2 and H1 norms and the energy, were established for this model. We compare the performance of hyperbolic...

A mathematical model for induction hardening including mechanical effects

Dietmar Hömberg
In most structural components in mechanical engineering, there are surface parts, which are particularly stressed. The aim of surface hardening is to increase the hardness of the corresponding boundary layers by rapid heating and subsequent quenching. This heat treatment leads to a change in the microstructure, which produces the desired hardening effect. The mathematical model accounts for electromagnetic effects that lead to the heating of the workpiece as well as thermomechanical effects that cause the...

Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities

Carmen Gräßle, Michael Hintermüller, Michael Hinze & Tobias Keil
We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn--Hilliard Navier--Stokes system involving a nonsmooth energy potential.We establish the existence of optimal solutions and present two distinct approaches to derive suitable stationarity conditions for the bilevel problem, namely C- and strong stationarity. Moreover, we demonstrate the numerical realization of these concepts at the hands of two adaptive solution algorithms relying on a specifically developed goal-oriented error...

A large-deviations approach to gelation

Luisa Andreis, Wolfgang König & Robert I. A. Patterson
A large-deviations principle (LDP) is derived for the state, at fixed time, of the multiplicative coalescent in the large particle number limit. The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic. In particular, it clearly captures the well known gelation phase transition given by the formation of a particle containing a positive fraction of the system mass at time t=1. Via a standard map of...

Transient conductive-radiative heat transfer: Discrete existence and uniqueness for a finite volume scheme*

Olaf Klein & Peter Philip
This article presents a finite volume scheme for transient nonlinear heat transport equations coupled by nonlocal interface conditions modeling diffuse-gray radiation between the surfaces of (both open and closed) cavities. The model is considered in three space dimensions, modifications for the axisymmetric case are indicated. Proving a maximum principle as well as existence and uniqueness for roots to a class of discrete nonlinear operators that can be decomposed into a scalar-dependent sufficiently increasing part and...

A mathematical model for Alzheimer's disease: An approach via stochastic homogenization of the Smoluchowski equation

Bruno Franchi, Martin Heida & Silvia Lorenzani
In this note, we apply the theory of stochastic homogenization to find the asymptotic behavior of the solution of a set of Smoluchowski's coagulation-diffusion equations with non-homogeneous Neumann boundary conditions. This system is meant to model the aggregation and diffusion of β-amyloid peptide (Aβ) in the cerebral tissue, a process associated with the development of Alzheimer's disease. In contrast to the approach used in our previous works, in the present paper we account for the...

A quantum transmitting Schrödinger-Poisson system

Michael Baro, Hans-Christoph Kaiser, Hagen Neidhardt & Joachim Rehberg
We consider a stationary Schrödinger-Poisson system on a bounded interval of the real axis. The Schroedinger operator is defined on the bounded domain with transparent boundary conditions. This allows to model a non-zero current flow trough the boundary of the interval. We prove that the system always admits a solution and give explicit a priori estimates for the solutions.

Global behavior and asymptotic reduction of a chemical kinetics system with continua of equilibria

Klaus R. Schneider & Leonid V. Kalachev
We consider a model chemical kinetics system describing the dynamics of species concentrations taking part in a consecutive-competitive reaction in a continuously stirred tank reactor. Corresponding dynamical system has a continua of equilibria. The solution of the system tends to a particular equilibrium depending on the initial conditions. Global behavior of the system and its reductions via invariant manifold theory and the boundary function methods are studied.

Stochastic models and Monte Carlo algorithms for Boltzmann type equations

Wolfgang Wagner
In this paper we are concerned with three typical aspects of the Monte Carlo approach. First there is a certain field of application, namely physical systems described by the Boltzmann equation. Then some class of stochastic models is introduced and its relation to the equation is studied using probability theory. Finally Monte Carlo algorithms based on those models are constructed. Here numerical issues like efficiency and error estimates are taken into account. In Section 1...

Existence of the Stoneley surface wave at vacuum/porous medium interface: Low-frequency range

Inna Edelman
Existence and asymptotic behavior of the Stoneley surface wave at vacuum/porous medium interface are investigated in the low frequency range. It is shown that the Stoneley wave possesses a bifurcation in the vicinity of critical wave number 푘cr. It is proven also that within the 푘-domain of existence, the Stoneley wave cannot appear for certain values of elastic moduli of the solid phase. Asymptotic formulae for the phase velocity of the Stoneley wave are presented.

Phase transitions for chase-escape models on Gilbert graphs

Alexander Hinsen, Benedikt Jahnel, Eli Cali & Jean-Philippe Wary
We present results on phase transitions of local and global survival in a two-species model on Gilbert graphs. At initial time there is an infection at the origin that propagates on the Gilbert graph according to a continuous-time nearest-neighbor interacting particle system. The Gilbert graph consists of susceptible nodes and nodes of a second type, which we call white knights. The infection can spread on susceptible nodes without restriction. If the infection reaches a white...

A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem

Mine Akbas, Thierry Gallouët, Almut Gaßmann, Alexander Linke & Christian Merdon
A novel notion for constructing a well-balanced scheme --- a gradient-robust scheme --- is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient --- if there is enough mass in the system to compensate the force. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent...

Macroscopic modeling of porous and granular materials --- microstructure, thermodynamics and some boundary-initial value problems

Krzysztof Wilmanski
This work contains the material presented in the key lecture during the Congress Cancam 2003 (Calgary, Canada). It contains a review of the recent development of thermodynamic modeling of porous and granular materials. We present briefly main features of the thermodynamic construction of a nonlinear poroelastic model but the emphasis is put on the analysis of a linear two-component model. In particular we indicate similarities and differences of the thermodynamic model with the classical Biot's...

Analogues of non-Gibbsianness in joint measures of disordered mean-field models

Christof Külske
It is known that the joint measures on the product of spin-space and disorder space are very often non-Gibbsian measures, for lattice systems with quenched disorder, at low temperature. Are there reflections of this non-Gibbsianness in the corresponding mean-field models? We study the continuity properties of the conditional expectations in finite volume of the following mean field models: a) joint measures of random field Ising, b) joint measures of dilute Ising, c) decimation of ferromagnetic...

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