SNuBIC is a team of researchers funded by the German Research Foundation (DFG-FOR 5409) that investigates the modeling and simulation of coupled systems described by partial differential equations (PDEs). While accurate numerical methods for individual PDEs are still an active research field, most complex applications — such as magnetised plasmas, complex fluids, and electro-chemical processes — are described by coupled systems of several PDEs, i.e. by heterogeneous models.

The key aspects of our research are bulk- and interface-coupling, structure-preserving numerical methods, and re-usable code development. Rather than a single monolithic simulation code, we develop a flexible, flux-oriented multi-scale and multiphysics coupling software library that is adjustable and available to all researchers.

For full details on the research unit, its people, publications, news, and events, please visit www.snubic.io.

The projects are organised into three focus areas: (A) Modeling of Coupled Systems, (B) Numerical Methods for Coupling, and (C) Coupling Algorithms.

A1 — Consistent Coupling of Electromagnetics to Thermodynamics for Batteries Develops thermodynamically consistent models that couple electromagnetic fields to heat and mass transport in battery systems. The coupling pattern is challenging already at the analytical and modeling level, requiring fundamental modeling research before structure-preserving numerics can be applied. ➡️ Project-A1 repository

A2 — Coupling the two-fluid/Maxwell system to Magnetohydrodynamics/Ohm's law Investigates consistent transitions between the two-fluid/Maxwell description and the magnetohydrodynamics/Ohm's-law regime for plasmas. The project establishes the modeling foundations needed to couple these heterogeneous descriptions across scales. ➡️ Project-A2 repository

A3 — Adaptivity in Computational Cardiac Electrophysiology Addresses adaptive modeling and simulation of electrical activity in cardiac tissue, where multiple coupled physical processes interact. See www.snubic.io for more information on this project.

B1 — A Hybrid Entropy-Stable Spectral Element Method for Magnetized Plasmas Designs hybrid, entropy-stable spectral element discretizations for magnetized plasma models. The method ensures proper momentum and energy exchange while preserving entropy stability across coupled regions. ➡️ Project-B1 repository

B2 — An Active Flux Method for the Vlasov-Maxwell System Develops active flux schemes for the kinetic Vlasov-Maxwell system, combining high-order accuracy with structure preservation. The approach targets faithful coupling of the kinetic and electromagnetic dynamics. ➡️ Project-B2 repository

B3 — Structure-Preserving Multi-Scale Methods for Complex Fluids Builds structure-preserving, multi-scale numerical methods for complex fluids with multiple interacting components. The methods respect the underlying physical structure across the relevant scales. ➡️ Project-B3 repository

B4 — Adaptive Coupling of the Maximum-Entropy Cascade for the Vlasov Equation Implements and studies nonlinear moment-closure techniques based on orthogonal polynomials and the maximum-entropy cascade for the Vlasov equation. The project focuses on adaptive coupling between moment models of different resolution. ➡️ Project-B4 repository

B5 — Dynamical Low-Rank Approximation Methods for Two-Particle Kinetic Equations Explores dynamical low-rank approximation to make high-dimensional two-particle kinetic equations tractable. See www.snubic.io for more information on this project.

C1 — A Multi-Scale and Multi-Physics Time Integration Approach Derives generic time-integration algorithms for the coupling of PDEs across scales and physical models. The project provides reusable building blocks for multi-scale, multi-physics simulations. ➡️ Project-C1 repository

C2 — Parallel Execution of Adaptive Multi-Physics Simulations on Hierarchical Grids Provides the mesh infrastructure and parallel algorithms for adaptive multi-physics simulations on hierarchical grids. It is a cross-sectional project supplying generic coupling machinery to the whole research unit. ➡️ Project-C2 repository