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- ItemLow Mach asymptotic preserving scheme for the Euler-Korteweg model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Giesselmann, JanWe present an all speed scheme for the Euler-Korteweg model.We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach number. Based on this we present a fully discrete finite difference scheme. In particular, the scheme is asymptotic preserving, i.e., it converges to a stable discretisation of the incompressible limit of the Euler-Korteweg model when the Mach number tends to zero.
- ItemHomogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Bovier, Anton; Hollander, Frank den; Spitoni, CristianIn this paper we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let $b$ denote the inverse temperature and let $L_b subset Z^2$ be a square box with periodic boundary conditions such that $lim_btoinfty L_b =infty$. We run the dynamics on $L_b$ starting from a random initial configuration where all the droplets (= clusters of plus-spins, respectively, clusters of particles) are small. For large $b$, and for interaction parameters that correspond to the metastable regime, we investigate how the transition from the metastable state (with only small droplets) to the stable state (with one or more large droplets) takes place under the dynamics. This transition is triggered by the appearance of a single emphcritical droplet somewhere in $L_b$. Using potential-theoretic methods, we compute the emphaverage nucleation time (= the first time a critical droplet appears and starts growing) up to a multiplicative factor that tends to one as $btoinfty$. It turns out that this time grows as $Ke^Gammab/ L_b $ for Glauber dynamics and $Kb e^Gammab/ L_b $ for Kawasaki dynamics, where $Gamma$ is the local canonical, respectively, grand-canonical energy to create a critical droplet and $K$ is a constant reflecting the geometry of the critical droplet, provided these times tend to infinity (which puts a growth restriction on $ L_b $). The fact that the average nucleation time is inversely proportional to $ L_b $ is referred to as emphhomogeneous nucleation, because it says that the critical droplet for the transition appears essentially independently in small boxes that partition $L_b$.
- ItemAdvanced numerical investigation of the heat flux in an array of microbolometers([London] : Macmillan Publishers Limited, part of Springer Nature, 2019) Stocchi, Matteo; Mencarelli, Davide; Pierantoni, Luca; Göritz, Alexander; Kaynak, Canan Baristiran; Wietstruck, Matthias; Kaynak, MehmetThe investigation of the thermal properties of an array of microbolometers has been carried out by mean of two independent numerical analysis, respectively the Direct-Simulation Monte Carlo (DSMC) and the classic diffusive approach of the Fourier's equation. In particular, the thermal dissipation of a hot membrane placed in a low-pressure cavity has been studied for different values of the temperature of the hot body and for different values of the pressure of the environment. The results for the heat flux derived from the two approaches have then been compared and discussed.
- ItemGrounding-line flux formula applied as a flux condition in numerical simulations fails for buttressed Antarctic ice streams(Katlenburg-Lindau : Copernicus, 2018) Reese, Ronja; Winkelmann, Ricarda; Gudmundsson, G. HilmarCurrently, several large-scale ice-flow models impose a condition on ice flux across grounding lines using an analytically motivated parameterisation of grounding-line flux. It has been suggested that employing this analytical expression alleviates the need for highly resolved computational domains around grounding lines of marine ice sheets. While the analytical flux formula is expected to be accurate in an unbuttressed flow-line setting, its validity has hitherto not been assessed for complex and realistic geometries such as those of the Antarctic Ice Sheet. Here the accuracy of this analytical flux formula is tested against an optimised ice flow model that uses a highly resolved computational mesh around the Antarctic grounding lines. We find that when applied to the Antarctic Ice Sheet the analytical expression provides inaccurate estimates of ice fluxes for almost all grounding lines. Furthermore, in many instances direct application of the analytical formula gives rise to unphysical complex-valued ice fluxes. We conclude that grounding lines of the Antarctic Ice Sheet are, in general, too highly buttressed for the analytical parameterisation to be of practical value for the calculation of grounding-line fluxes.
- ItemResults of the third Marine Ice Sheet Model Intercomparison Project (MISMIP+)(Katlenburg-Lindau : Copernicus, 2020) Cornford, Stephen L.; Seroussi, Helene; Asay-Davis, Xylar S.; Gudmundsson, G. Hilmar; Arthern, Rob; Borstad, Chris; Christmann, Julia; dos Santos, Thiago Dias; Feldmann, Johannes; Goldberg, Daniel; Hoffman, Matthew J.; Humbert, Angelika; Kleiner, Thomas; Leguy, Gunter; Lipscomb, William H.; Merino, Nacho; Durand, Gaël; Morlighem, Mathieu; Pollard, David; Rückamp, Martin; Williams, C. Rosie; Yu, HongjuWe present the result of the third Marine Ice Sheet Model Intercomparison Project, MISMIP+. MISMIP+ is intended to be a benchmark for ice-flow models which include fast sliding marine ice streams and floating ice shelves and in particular a treatment of viscous stress that is sufficient to model buttressing, where upstream ice flow is restrained by a downstream ice shelf. A set of idealized experiments first tests that models are able to maintain a steady state with the grounding line located on a retrograde slope due to buttressing and then explore scenarios where a reduction in that buttressing causes ice stream acceleration, thinning, and grounding line retreat. The majority of participating models passed the first test and then produced similar responses to the loss of buttressing. We find that the most important distinction between models in this particular type of simulation is in the treatment of sliding at the bed, with other distinctions - notably the difference between the simpler and more complete treatments of englacial stress but also the differences between numerical methods - taking a secondary role. © 2020 Wolters Kluwer Medknow Publications. All rights reserved.