Simulation & Modelling: Selected Projects

We have a long-standing track record in applying simulation to biomedical questions. One of our earliest projects focused on diffusion through human skin. Our simulations predicted diffusion pathways that were not in accordance with the assumptions prevailing at the time. When we presented the model at the annual conference of the Controlled Release Society in Washington D.C., the paper received the Best Paper Award of the conference. Our results were later confirmed experimentally by a group from MIT, a striking example of how computational simulation can lead experimental research. We continue to refine and extend these skin-transport models.

A further topic in this area is the replication dynamics of the Hepatitis C virus. We have developed a 3D simulation model of the viral replication cycle, enabling a spatially resolved analysis of the underlying processes within infected cells.

Computational neuroscience, modelling and simulation for a deeper understanding of neurons and brain function, is one of the most exciting research frontiers today. We have developed a comprehensive pipeline for detailed modelling and simulation of signal processing in neurons.

Our tool NeuRA enables automatic reconstruction of neuron morphologies from microscopy images using specialised image processing. It has been recognised with the 1st prize of the doIT Software Award and has since been extended to run on GPU clusters, enabling real-time reconstruction of high-resolution images. A complementary tool, NeuClass, provides automatic classification of neuron cell types from reconstructed geometries.

Using these reconstructed geometries, we have modelled several key neuronal processes. In collaboration with the Bading lab at IZN Heidelberg, we investigated calcium signalling to the cell nucleus and obtained results on the relationship between calcium dynamics and nuclear shape. We have also modelled electric signal transduction in neurons, deriving a novel process model from the Maxwell equations that describes the electric potential as a function in three-dimensional space. A further project addresses the hydrodynamics of synaptic vesicles.

High-dimensional problems in financial mathematics require methods that go well beyond standard approaches. One prominent example is the fair pricing of basket options, financial derivatives whose value depends on a large number of underlying assets. This problem is governed by the Black-Scholes equations, where the number of space dimensions equals the number of assets.

Standard Monte-Carlo methods for this problem are slow and yield no error bounds. We developed an alternative approach based on sparse grid approximations of the Black-Scholes PDE, combined with a multigrid solver. The method was extended to higher-order approximations, making it possible to compute the important sensitivities known as 'greeks'. Combined with a dimensional reduction technique, the approach yields explicit error bounds. As a result, we can compute options on a basket of 30 assets (such as the DAX index) in a matter of minutes, whereas state-of-the-art Monte-Carlo methods require approximately two days, without any error guarantees.

Groundwater protection, subsurface remediation, waste disposal, and renewable energy are among the most pressing environmental challenges. We address these with high-fidelity simulation tools developed in close cooperation with research partners and industry.

For biological remediation of contaminated aquifers, we developed a simulation model based on a real-world chlorinated solvent spill. The model enabled us to design a concrete remediation strategy for the affected site.

Our software tool d3f computes density-driven flows in porous media in highly general domains, using the full non-linear dispersion model. It is among the most capable tools available for this class of problems. The companion tool r3t simulates the transport, diffusion, sorption, and radioactive decay of contaminants in groundwater, handling up to 160 chemical species in large, complex three-dimensional domains. These tools were developed in cooperation with partners at ETH Zurich, FAU Erlangen, and the Universities of Freiburg and Bonn.

We have also developed simulation models for biogas production, including a tool for simulating the compression process in crop silos and models for the fermentation of biomass. Further work includes two-phase flow simulations in porous media and a novel formulation for flow and transport through fractured porous media using a lower-dimensional approximation for the fractures.

We develop simulation methods for a broad range of flow problems: incompressible and compressible Navier-Stokes equations, turbulence modelling, aeroacoustics, low Mach-number flow, two-phase flow (gas/liquid), and non-Newtonian flows.

For turbulent flows, we developed a Large-Eddy Simulation (LES) model combined with an adaptive multigrid solver. This flexible framework incorporates multiple subscale models and has been successfully applied to industrial-scale geometries, including static mixers.

In aeroacoustics and low Mach-number flow, we developed two complementary approaches: one based on the Multiple Pressure-Variables (MPV) method, which splits the pressure field, and one based on direct multigrid coupling of acoustics with the Navier-Stokes equations.

We further developed methods for multi-phase flows such as rising air bubbles in water, using both the Volume of Fluid (VOF) method and the level-set method. These approaches were applied to gas/liquid two-phase flow and liquid-liquid extraction. Additionally, we developed a simulation model for non-Newtonian Bingham flow, applied to the extrusion of ceramic pastes, and combined it with a design optimisation tool to improve the geometry of a measuring nozzle.

We developed a simulation model for low-frequency electromagnetic phenomena governed by the Maxwell equations (eddy-current case). The model includes a rigorous estimate for the modelling error and has been successfully applied to demanding industrial problems, including transformers and high-performance switching devices.

Beyond standard linear-elastic problems, we developed methods and tools for elasto-plastic problems with non-linear material laws. These tools were used to compute high-quality reference solutions for benchmarking engineering simulation codes. We also coupled the structural mechanics solver with our optimisation framework to perform topology optimisation, enabling the design of structures that are optimal with respect to a given objective.

Detailed modelling of musical instruments requires new mathematical and computational approaches. Building on Erich Schumann's theory of formants, we developed a method and tool to compute the eigenvalues and eigenmodes of instrument components, specifically the top plate of a guitar and harpsichord soundboard. The computed eigenmodes compare well with experimental measurements. This is a first step toward a complete 3D model of the acoustic resonances of a musical instrument.

We develop AI solutions in two closely related areas: the scientifically grounded combination of physics-based models with machine learning, and the application of AI to software development. Our hybrid simulation approach delivers the interpretability and rigour of physical models alongside the pattern-recognition capabilities of modern AI. Our AI-assisted development work helps turn complex requirements into robust, efficient software.