Numerical simulation of an astrophysical Jet with a Mach number of about 2000. We solve the compressible Euler equations of gas dynamics with a FCT-type subcell limiting approach combining a (forth-order accurate) discontinuous Galerkin (DG) method with a first-order accurate finite volume (FV) method at the node level to impose positivity of density and pressure. Additionally, a new mortar approach also ensures positivity of density and pressure.

At end time T=0.0015, we have 79,708 elements which result in 1,275,328 degrees of freedom. We use the entropy-conserving and kinetic energy preserving flux of Chandrashekar for the volume fluxes and the local Lax-Friedrichs flux for the surface fluxes of the DG and FV methods.

The results were obtained using Trixi.jl.

Reference:
[1] A. M. Rueda-Ramírez, B. Bolm, D. Kuzmin, G. J. Gassner: Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral Element Methods, https://link.springer.com/article/10.1007/s42967-023-00321-6

With the increasing complexity of deep neural networks and continual architectural improvements, AI models have achieved remarkable success in image classification, surpassing 90% TOP-1 accuracy on ImageNet. Such high performance highlights their effectiveness across diverse domains and supports reliable transfer learning for smaller, specialized datasets. Artifact classification is one example where knowledge transfer from large-scale datasets proves highly beneficial. In (a), a pretrained CNN from ImageNet provides powerful feature extraction for archaeological image classification. In (b), this transferred knowledge is further extended to multi-image classification tasks through optimized feature fusion, enhancing overall model performance.

The videos show a result of simulations with DGSEM and a polynomial degree of 3. At the end of the simulation, the solution has about 150000 degrees of freedom. Subcell IDP/FCT-type Limiting provides for stability. Moreover, the simulation uses adaptive mesh refinement, combined with a new IDP mortar type that ensures positivity of density and pressure.
On the left side, local (shock-capturing) limiters are used in the volume integral, while on the right side only limiters that ensure physics admissibility (positivity of density and pressure) are enabled.

Simulation of a freediving bifin, modelling the fluid with δ+-SPH and periodic boundaries and the fin with Total Lagrangian SPH.

The software TrixiParticles.jl was used for this simulation.

Our research group is currently utilizing TrixiAtmo.jl to explore the Held-Suarez test case, a widely recognized benchmark for atmospheric general circulation and climate models. First proposed by Held and Suarez in their 1994 paper, this idealized setup is designed to capture fundamental large-scale flow features of Earth’s atmosphere.

The model incorporates a simplified atmospheric forcing that establishes a decreasing temperature gradient from the equator to the poles and maintains a vertically balanced state. It also accounts for idealized boundary layer friction affecting the wind field. This configuration drives a characteristic atmospheric circulation: warm air rises at the equator, while colder air flows towards it at lower levels. The Coriolis force deflects this moving air, leading to the development of prominent jet streams in both the Northern and Southern Hemispheres.

For our simulations, TrixiAtmo.jl employs a Discontinuous Galerkin Spectral Element Method (DGSEM) with flux differencing. We discretize the Earth’s atmosphere using a cubed sphere grid with 6 patches, each consisting of 10 x 10 x 8 cells. Starting from a state with constant temperature and without any motion, the video visualizes the simulated near-surface air temperature and the developing flow patterns.

The video shows the evolution of a barotropic instability in Earth’s polar jet stream. Initially uniform, the jet stream undergoes perturbations, leading to vortex formation driven by the Coriolis force due to Earth’s rotation. To simulate this phenomenon, we discretize the Shallow Water Equations on the sphere using a discontinuous Galerkin method. We compare two scenarios: an ocean-covered Earth (without orography) and a more realistic representation that includes Earth’s orography. Orography is incorporated into the equations as a non-conservative term, with values sourced from the ETOPO dataset provided by the National Oceanic and Atmospheric Administration (NOAA). The simulations are performed using TrixiAtmo.jl.

This research has been carried out by Simone Chiocchetti, funded by the European Union’s Horizon Europe Research and Innovation Programme under the Marie Skłodowska-Curie Postdoctoral Fellowship MoMeNTUM (grant agreement No. 101109532).

x-z central cross section of 3d Lid-Driven Cavity flow, solving the unified model of Godunov, Peshkov, and Romenski for hyperbolic viscous flow. The upper row shows the macroscopic flow state, while the bottom row shows the distortion field, tracking fluid flow deformations as if it were a solid. The numerical solver is a simple explicit second order Finite Volume method (MUSCL-Hancock) using an HLL-type Riemann solver based on Toro-Vazquez flux splitting. The Reynolds number is 1000 and the mesh resolution is 384^3.

Boqiang Huang received his Ph.D. in Biomedical Engineering from the Department of Electronic Engineering at Fudan University, Shanghai, China, in 2010. Following his doctoral studies, he was awarded the Alexander von Humboldt Postdoctoral Fellowship and worked under the mentorship of Prof. Angela Kunoth. During this time, he contributed as a research scientist in Prof. Kunoth’s group (AG-Kunoth) at the Institute of Mathematics, University of Paderborn, and later at the University of Cologne. In 2021, Dr. Huang joined the group of Prof. Dorit Merhof (AG-Merhof) at the Institute of Imaging and Computer Vision at RWTH Aachen University, and subsequently at the University of Regensburg. His research expertise spans multiple disciplines in the field of data science, including biomedical engineering, electronic engineering, applied mathematics and applied physics.

In July 2024, Dr. Huang became a research scientist in the group of Prof. Gregor Gassner (AG-Gassner). He is also supported by the HESCOR research project (“Human & Earth System Coupled Research” https://hescor.uni-koeln.de/). His current research focuses on the “Machine learning & Culture Clusters” over large timescales, ranging from the Paleolithic era (1.4 million to 24,000 years ago) to the present. He collaborates with researchers from archaeology, geophysics, and the humanities on this interdisciplinary project.

Tristan Montoya completed his PhD at the University of Toronto Institute for Aerospace Studies under the supervision of Prof. David W. Zingg. His doctoral work focused on the development and analysis of provably stable discontinuous spectral-element methods (DSEMs) with the summation-by-parts property for systems of conservation laws, particularly on triangular and tetrahedral meshes.

Tristan joined the Numerical Simulation research group at the University of Cologne in January 2024, and is part of the Trixi.jl development team. His current research involves the development of split-form and entropy-stable DSEMs for atmospheric models and their application to global weather and climate prediction. You can keep up-to-date with Tristan’s research and software contributions on his Google Scholar and GitHub pages, as well as on his personal website.

2D single-phase simulation of the liquefaction of the Julia logo with TrixiParticles.jl. The letters are simulated as a fluid with the Weakly Compressible SPH (WCSPH) method and the dots are simulated as an elastic solid with the Total Lagrangian SPH (TLSPH) method for structure mechanics.

This Snapshot was created by Niklas Neher (https://www.hlrs.de/de/team/niklas-neher).