Implementation of a branch tracing algorithm for reacting flow systems

Kurzbeschreibung

Beschreibung Thermoacoustic instabilities are a highly unwanted phenomenon, reducing performance and safe operation of combustion systems. To gain insight into the instability mechanisms of a combustion systems, one can linearize the governing reacting flow equitations about their steady fixed point to analyse the system modes. Very often, we are interested in the influence of a system parameter on stability. In this case, it becomes crucial to follow the branch of steady solutions in a computationally efficient manner as the relevant system parameter changes. To this end, the goal of the proposed project is to implement a branch tracing algorithm [1] in an in-house flow solver. If you are interested in computational fluid dynamics and numerical methods, we are looking forward to you joining our team for a project. Details of the project can be adapted and discussed according to personal preferences and interests. [1] Christopher M. Douglas and Pierre Jolivet. ff-bifbox: A scalable, open-source toolbox for bifurcation analysis of nonlinear PDEs, September 2025. arXiv:2509.18429 [math]. [2] Christopher M. Douglas, Wolfgang Polifke, and Lutz Lesshafft. Flash-back, blow-off, and symmetry breaking of premixed conical flames. Combust. Flame, 258, 2023. Voraussetzungen • Computational fluid dynamics • Interest in non-linear dynamics • Programming in python or similar • Working in linux