Discontinuous Galerkin Spectral Element Methods for Astrophysical Flows in Multi-physics Applications

In engineering applications, discontinuous Galerkin methods (DG) have been proven to be a powerful and flexible class of high order methods for problems in computational fluid dynamics. However, the potential benefits of DG for applications in astrophysical contexts is still relatively unexplored in its entirety. To this day, a decent number of studies surveying DG for astrophysical flows have been conducted. But the adoption of DG by the astrophysics community is just beginning to gain traction and integration of DG into established, multi-physics simulation frameworks for comprehensive astrophysical modeling is still lacking. It is our firm believe, that the full potential of novel approaches for numerically solving the fluid equations only shows under the pressure of real-world simulations with all aspects of multi-physics, challenging flow configurations, resolution and runtime constraints, and efficiency metrics on high-performance systems involved. Thus, we see the pressing need to propel DG from the well-trodden path of cataloguing test results under "optimal" laboratory conditions towards the harsh and unforgiving environment of large-scale astrophysics simulations. Consequently, the core of this work is the development and deployment of a robust DG scheme solving the ideal magneto-hydrodynamics equations with multiple species on three-dimensional Cartesian grids with adaptive mesh refinement. We chose to implement DG within the venerable simulation framework FLASH, with a specific focus on multi-physics problems in astrophysics. This entails modifications of the vanilla DG scheme to make it fit seamlessly within FLASH in such a way that all other physics modules can be naturally coupled without additional implementation overhead. A key ingredient is that our DG scheme uses mean value data organized into blocks - the central data structure in FLASH. Having the opportunity to work on mean values, allows us to rely on a rock-solid, monotone Finite Volume (FV) scheme as "backup" whenever the high order DG method fails in cases when the flow gets too harsh. Finding ways to combine the two schemes in a fail-safe manner without loosing primary conservation while still maintaining high order accuracy for smooth, well-resolved flows involves a series of careful considerations, which we document in this thesis. The result of our work is a novel shock capturing scheme - a hybrid between FV and DG - with smooth transitions between low and high order fluxes according to solution smoothness estimators. We present extensive validations and test cases, specifically its interaction with multi-physics modules in FLASH such as (self-)gravity and radiative transfer. We also investigate the benefits and pitfalls of integrating end-to-end entropy stability into our numerical scheme, with special focus on highly compressible turbulent flows and shocks. Our implementation of DG in FLASH allows us to conduct preliminary yet comprehensive astrophysics simulations proving that our new solver is ready for assessments and investigations by the astrophysics community

Comparison of different entropy stabilization techniques for discontinuous Galerkin spectral element methods

We review and compare two techniques to get entropy stability for nodal Discontinuous Galerkin Spectral Element Methods (DG) in compressible flows. One technique is based on entropy split-forms, e.g., [8, 15, 5] and one is based on a direct algebraic correction [1]. We have implemented the Flux Differencing methodology for both, Legendre-Gauss-Lobatto (Lobatto) and Legendre-Gauss (Gauss) based spectral element basis functions. While the Lobatto operators belong to the class of diagonal norm summation-by-parts (SBP) operators, the Gauss operators belong to the generalized class of SBP operators, where it is not necessary that the boundary nodes are included. To reach entropy stability, respectively guaranteed entropy dissipation, a key ingredient is an entropy conserving numerical flux function. With this ingredient, only the volume integral term of the DG method has to be modified accordingly. We have also implemented an alternative technique, which is in general applicable for a wide range of discretizations. Abgrall [R. Abgrall, A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes. Journal of Computational Physics, vol 372, 2018] introduced an algebraic correction term that retains conservation of the primary quantities and is furthermore constructed such, that an entropy (in-) equality can be shown. The second technique is at first sight a simpler alternative to the split-form based approach. Hence, questions regarding its advantages and disadvantages naturally come up

Transaldolase in Bacillus methanolicus: Biochemical Characterization and Biological Role in Ribulose Monophosphate Cycle

Pfeifenschneider J, Markert B, Stolzenberger J, Brautaset T, Wendisch VF. Transaldolase in Bacillus methanolicus: Biochemical Characterization and Biological Role in Ribulose Monophosphate Cycle. BMC Microbiology. 2020;20: 63.Background The Gram-positive facultative methylotrophic bacterium Bacillus methanolicus uses the sedoheptulose-1,7-bisphosphatase (SBPase) variant of the ribulose monophosphate (RuMP) cycle for growth on the C1 carbon source methanol. Previous genome sequencing of the physiologically different B. methanolicus wild-type strains MGA3 and PB1 has unraveled all putative RuMP cycle genes and later, several of the RuMP cycle enzymes of MGA3 have been biochemically characterized. In this study, the focus was on the characterization of the transaldolase (Ta) and its possible role in the RuMP cycle in B. methanolicus. Results The Ta genes of B. methanolicus MGA3 and PB1 were recombinantly expressed in Escherichia coli, and the gene products were purified and characterized. The PB1 Ta protein was found to be active as a homodimer with a molecular weight of 54 kDa and displayed KM of 0.74 mM and Vmax of 16.3 U/mg using Fructose-6 phosphate as the substrate. In contrast, the MGA3 Ta gene, which encodes a truncated Ta protein lacking 80 amino acids at the N-terminus, showed no Ta activity. Seven different mutant genes expressing various full-length MGA3 Ta proteins were constructed and all gene products displayed Ta activities. Moreover, MGA3 cells displayed Ta activities similar as PB1 cells in crude extracts. Conclusions While it is well established that B. methanolicus can use the SBPase variant of the RuMP cycle this study indicates that B. methanolicus possesses Ta activity and may also operate the Ta variant of the RuMP

t8code - scalable and modular adaptive mesh refinement

t8code is a versatile open source library for parallel adaptive mesh refinement on hybrid meshes. [1] It is exascale-ready and capable of efficiently managing meshes with up to a trillion elements distributed on a million of cores as already shown in a peer-reviewed research paper. [2] On the top-level, t8code uses forests of trees to represent unstructured meshes with complex geometries. Space-filling curves index individual elements within a forest, which requires only minimal amounts of memory allowing for efficient and scalable algorithms of mesh management. In contrast to existing solutions, t8code has the capability to manage an arbitrary number of tetrahedra, hexahedra, prisms and pyramids within the same mesh. With this poster we want to present the first official release (v1.0) of our software and give a quick overview over its main features. Besides presenting the core algorithms of t8code, we give application scenarios on how our library integrates into major simulation frameworks for weather forecasting, climate modeling and engineering; and how they benefit from our approach to do AMR. [1] https://github.com/DLR-AMR/t8code [2] https://epubs.siam.org/doi/abs/10.1137/20M138303

Azimuthal anisotropy of charged jet production in root s(NN)=2.76 TeV Pb-Pb collisions

We present measurements of the azimuthal dependence of charged jet production in central and semi-central root s(NN) = 2.76 TeV Pb-Pb collisions with respect to the second harmonic event plane, quantified as nu(ch)(2) (jet). Jet finding is performed employing the anti-k(T) algorithm with a resolution parameter R = 0.2 using charged tracks from the ALICE tracking system. The contribution of the azimuthal anisotropy of the underlying event is taken into account event-by-event. The remaining (statistical) region-to-region fluctuations are removed on an ensemble basis by unfolding the jet spectra for different event plane orientations independently. Significant non-zero nu(ch)(2) (jet) is observed in semi-central collisions (30-50% centrality) for 20 <p(T)(ch) (jet) <90 GeV/c. The azimuthal dependence of the charged jet production is similar to the dependence observed for jets comprising both charged and neutral fragments, and compatible with measurements of the nu(2) of single charged particles at high p(T). Good agreement between the data and predictions from JEWEL, an event generator simulating parton shower evolution in the presence of a dense QCD medium, is found in semi-central collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Production of He-4 and (4) in Pb-Pb collisions at root(NN)-N-S=2.76 TeV at the LHC

Results on the production of He-4 and (4) nuclei in Pb-Pb collisions at root(NN)-N-S = 2.76 TeV in the rapidity range vertical bar y vertical bar <1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0-10% central events are found to be dN/dy4(He) = (0.8 +/- 0.4 (stat) +/- 0.3 (syst)) x 10(-6) and dN/dy4 = (1.1 +/- 0.4 (stat) +/- 0.2 (syst)) x 10(-6), respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (T-chem = 156 MeV) as for light hadrons. The measured ratio of (4)/He-4 is 1.4 +/- 0.8 (stat) +/- 0.5 (syst). (C) 2018 Published by Elsevier B.V.Peer reviewe

Forward-central two-particle correlations in p-Pb collisions at root s(NN)=5.02 TeV

Two-particle angular correlations between trigger particles in the forward pseudorapidity range (2.5 2GeV/c. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B. V.Peer reviewe