Numerical bifurcation analysis of a 3D turing-type reaction–diffusion model

We perform a numerical study of a two-component reaction-diffusion model. By using numerical continuation methods, combined with state-of-the-art sparse linear and eigenvalue solvers, we systematically compute steady state solutions and analyze their stability and relations in both two and three space dimensions. The approach gives a more reliable and complete picture than previous efforts based on time integration schemes and is also typically much more efficient in terms of computing time. We are therefore able to produce a rich bifurcation diagram showing a variety of solution patterns and transitions

A Staggered Grid Multi-Level ILU for steady incompressible flows

We present a parallel fully coupled multi-level incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed in [1]. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the wellknown 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

A staggered‐grid multilevel incomplete LU for steady incompressible flows

Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this article, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner

GMRT observation towards detecting the Post-reionization 21-cm signal

We have analyzed 610 MHz GMRT observations towards detecting the redshifted 21-cm signal from z=1.32. The multi-frequency angular power spectrum C_l(Delta nu) is used to characterize the statistical properties of the background radiation across angular scales ~20" to 10', and a frequency bandwidth of 7.5 MHz with resolution 125 kHz. The measured C_l(Delta nu) which ranges from 7 mK^2 to 18 mK^2 is dominated by foregrounds, the expected HI signal C_l^HI(Delta nu) ~10^{-6}- 10^{-7} mK^2 is several orders of magnitude smaller. The foregrounds, believed to originate from continuum sources, is expected to vary smoothly with Delta nu whereas the HI signal decorrelates within ~0.5 MHz and this holds the promise of separating the two. For each l, we use the interval 0.5 < Delta nu < 7.5 MHz to fit a fourth order polynomial which is subtracted from the measured C_l(Delta nu) to remove any smoothly varying component across the entire bandwidth Delta nu < 7.5 MHz. The residual C_l(Delta nu), we find, has an oscillatory pattern with amplitude and period respectively ~0.1 mK^2 and Delta nu = 3 MHz at the smallest l value of 1476, and the amplitude and period decreasing with increasing l. Applying a suitably chosen high pass filter, we are able to remove the residual oscillatory pattern for l=1476 where the residual C_l(Delta nu) is now consistent with zero at the 3-sigma noise level. We conclude that we have successfully removed the foregrounds at l=1476 and the residuals are consistent with noise. We use this to place an upper limit on the HI signal whose amplitude is determined by x_HI b where x_HI and b are the HI neutral fraction and the HI bias respectively. A value of x_HI b greater than 7.95 would have been detected in our observation, and is therefore ruled out at the 3-sigma level. (abridged)Comment: 29 pages, 13 figures, Accepted to MNRA

Detection and attribution of aerosol-cloud interactions in large-domain large-eddy simulations with the ICOsahedral Non-hydrostatic model

Clouds and aerosols contribute the largest uncertainty to current estimates and interpretations of the Earth’s changing energy budget. Here we use a new-generation large-domain large-eddy model, ICON-LEM (ICOsahedral Non-hydrostatic Large Eddy Model), to simulate the response of clouds to realistic anthropogenic perturbations in aerosols serving as cloud condensation nuclei (CCN). The novelty compared to previous studies is that (i) the LEM is run in weather prediction mode and with fully interactive land surface over a large domain and (ii) a large range of data from various sources are used for the detection and attribution. The aerosol perturbation was chosen as peak-aerosol conditions over Europe in 1985, with more than fivefold more sulfate than in 2013. Observational data from various satellite and ground-based remote sensing instruments are used, aiming at the detection and attribution of this response. The simulation was run for a selected day (2 May 2013) in which a large variety of cloud regimes was present over the selected domain of central Europe. It is first demonstrated that the aerosol fields used in the model are consistent with corresponding satellite aerosol optical depth retrievals for both 1985 (perturbed) and 2013 (reference) conditions. In comparison to retrievals from ground-based lidar for 2013, CCN profiles for the reference conditions were consistent with the observations, while the ones for the 1985 conditions were not. Similarly, the detection and attribution process was successful for droplet number concentrations: the ones simulated for the 2013 conditions were consistent with satellite as well as new ground-based lidar retrievals, while the ones for the 1985 conditions were outside the observational range. For other cloud quantities, including cloud fraction, liquid water path, cloud base altitude and cloud lifetime, the aerosol response was small compared to their natural variability. Also, large uncertainties in satellite and ground-based observations make the detection and attribution difficult for these quantities. An exception to this is the fact that at a large liquid water path value (LWP > 200 g m−2), the control simulation matches the observations, while the perturbed one shows an LWP which is too large. The model simulations allowed for quantifying the radiative forcing due to aerosol–cloud interactions, as well as the adjustments to this forcing. The latter were small compared to the variability and showed overall a small positive radiative effect. The overall effective radiative forcing (ERF) due to aerosol–cloud interactions (ERFaci) in the simulation was dominated thus by the Twomey effect and yielded for this day, region and aerosol perturbation −2.6 W m$^{-2}$. Using general circulation models to scale this to a global-mean present-day vs. pre-industrial ERFaci yields a global ERFaci of −0.8 W m$^{-2}$

HETEAC: The Aerosol Classification Model for EarthCARE

We introduce the Hybrid End-To-End Aerosol Classification (HETEAC) model for the upcoming EarthCARE mission. The model serves as the common baseline for development, evaluation, and implementation of EarthCARE algorithms. It shall ensure the consistency of different aerosol products from the multi-instrument platform as well as facilitate the conform specification of broad-band optical properties necessary for the EarthCARE radiative closure efforts. The hybrid approach ensures the theoretical description of aerosol microphysics consistent with the optical properties of various aerosol types known from observations. The end-to-end model permits the uniform representation of aerosol types in terms of microphysical, optical and radiative properties

Energieversorgung des Emslands mit 100 % erneuerbaren Energien: Szenarien für eine zukünftige Energieversorgung, Empfehlungen für Politik, Verwaltung und Unternehmen

Im Rahmen dieser Untersuchung sollen folgende Fragen beantwortet werden: - Was sind die entscheidenden Aspekte in der zukünftigen Entwicklung der Energieversorgung und des -verbrauchs im Landkreis Emsland? - Welche Annahmen können für den Energieverbrauch im Zieljahr 2040 getroffen werden? - Wie kann ein angemessener Beitrag des Landkreises Emslands zur klimaneutralen Energieversorgung Deutschlands quantifiziert werden? - Welche Energieszenarien sind für den Landkreis Emsland im Jahr 2040 denkbar? - Welche Empfehlungen lassen sich aus diesen Szenarien für Unternehmen, Politik und Verwaltung ableiten

Employing HPC for Analyzing Nonlinear PDE Systems Beyond Simulation

We review techniques of numerical bifurcation and stability analysis with examples from computational fluid dynamics and biology. The methodology allows insight into the complete dynamics of nonlinear PDE systems, where standard simulation tool chains leave the question of existence, proximity and stability of multiple solutions open. The main bottleneck in the method are large and sparse linear systems of equations and eigenvalue problems arising from the discretized steady-state PDE. The use of HPC is therefore attractive to increase the achievable resolution, but remains challenging because nonsymmetric and indefinite systems need to be solved. The `hybrid multi-level solver' HYMLS is a robust multi-level incomplete factorization technique that was designed for this particular class of problems. HYMLS has an intuitive geometric interpretation and good parallelization properties. We present some performance results of a prototypical implementation based on MPI and the Trilinos software. The eigenvalue problems that arise are solved using the Jacobi-Davidson method as implemented in the SPPEXA ESSEX~\cite{essex} project's phist library (https://www.bitbucket.org/essex/phist)

Klimaneutrale Energieversorgung: Strategien für kleine und mittlere Unternehmen

In diesem Weißbuch stellen wir Methoden und Maßnahmen vor, die Unternehmen dabei unterstützen, ihre Energieversorgung auf erneuerbare Energien umzustellen, sich von den Preisschwankungen an den fossilen Weltmärkten unabhängiger zu machen und Entscheidungen für eine Klimastrategie für die nächsten Jahrzehnte zu treffen. Es werden drei mögliche Energiewelten der Zukunft skizziert. Informationen zum Thema Eigenstromerzeugung und zu Effizienzmaßnahmen werden anschaulich dargestellt sowie Links zu Fördermöglichkeiten genannt. Wir zeigen drei verschiedene Szenarien für die Energieversorgung von Unternehmen in der Zukunft auf. Sie geben Unternehmen eine Entscheidungshilfe für die eigene Klimastrategie. Die drei Szenarien haben Unterschiede, aber auch Gemeinsamkeiten. Die EU hat im „Green Deal“ Maßnahmen festgelegt, damit Europa im Jahr 2050 klimaneutral ist. Deutschland hat seine Klimaziele zuletzt noch einmal verschärft und sich als Ziel die Klimaneutralität bis 2045 gesetzt. Um diese Ziele zu erreichen, stehen Industrie und Gewerbe vor der Herausforderung, ihre Energieversorgung auf erneuerbare Energien umzustellen und in Zukunft fossile Brenn- und Kraftstoffe zu ersetzen. Dies gilt für kleine und mittlere Unternehmen (KMU) ebenso wie für die Großindustrie. Es stellt sich also die Frage, wie Unternehmen sich mit Strom, Wärme, Dampf, Kälte und weiteren Energieformen versorgen. Welches ist dabei aus heutiger Sicht die günstigste Technologie? Zentrale Rollen hierbei spielen Energieeffizienzmaßnahmen und die Substitution fossiler durch regenerative Energieträger. Lösungen müssen sowohl technisch als auch ökonomisch realisiert werden können. Im Vorteil ist, wer heute schon eine unternehmensinterne Klimaschutzstrategie verfolgt und die ersten Schritte in Richtung Klimaneutralität unternimmt