On Thursday, 15 January 2026, Simone Chiocchetti visited students of the 11. Klasse at Kreuzgasse Gymnasium in Cologne for an interactive meeting on computational physics, engineering, and applied mathematics, with a particular focus on the numerical simulation of fluids.
The discussion covered a wide range of topics: from the mathematical foundations of partial differential equations and their discretization, to real-world applications in civil engineering, astrophysics, and industrial design. Students learned how researchers model phenomena ranging from river floods and debris flows to turbulence in aerodynamics, and why such simulations matter when experiments are expensive, dangerous, or simply impossible. The conversation also touched on the practical challenges of supercomputing, multiphase flows one can observe in a cup of coffee, and the surprising behavior of steel structures under large deformations.
The students participated actively throughout, contributing thoughtful questions on subjects including chaos in planetary orbits and its connection to fluid turbulence, the multiscale nature of turbulent flows, and the computational tricks needed to make large simulations feasible.
Many thanks to the students for their engagement and curiosity, and to Markus Klein, their physics teacher, for contributing to organizing the event.
This activity is funded by the European Union’s Horizon Europe Research and Innovation Programme under the Marie Skłodowska-Curie Postdoctoral Fellowship MoMeNTUM (grant agreement No. 101109532).

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

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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.