In March 2022, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa)” (SPP 2410)(externer Link). The programme is designed to run for six years. The present call invites proposals for the second three-year funding period.

Nonlinear hyperbolic balance laws are ubiquitous in the modelling of fluid mechanical processes. They enable the development of powerful numerical simulation methods that support decision-making for critical applications such as in-silico aircraft design or climate change research. However, fundamental questions about distinctive hyperbolic features remain open for compressible flow regimes including the multiscale interference of shock and shear waves or the interplay of hyperbolic transport and random environments. The largely unsolved well-posedness problem for multidimensional inviscid flow equations is deeply connected to the laws of turbulent fluid motion in the high Reynolds number limit. Further progress requires a concerted effort of both fluid mechanics and the mathematical fields of analysis, numerics and stochastics.

The Priority Programme is devoted to the development of new mathematical models and methods to understand the dynamic creation of small scales and mechanisms which are either enhanced or depleted by the hyperbolic nonlinearity. It aims at a novel numerical paradigm for hyperbolic transport that can provide firm grounds for the upcoming theory of small-scale turbulence in the large Reynolds number limit.

The Priority Programme will evolve around three major research directions:

1. Novel solution concepts: this includes the analysis for hyperbolic systems arising in fluid mechanics (via e.g. generalised entropy methods, dissipative limits or probabilistic and moment-based solutions), the design of high-resolution numerics for these solution concepts, and exploring the connections to modern statistical turbulence modelling and perturbation/filtering techniques.
2. Multiscale models and asymptotic regimes: research here includes the development and analysis of model hierarchies (e.g. Boltzmann-Euler or statistical turbulence) and their closures that account for asymptotic flow regimes (e.g. Mach number limits). Entropy- and structure-preserving numerical methods need to be designed that allow well-balancing and preservation of asymptotic states while traversing through hierarchies and regimes by accuracy-controlled model selection.
3. Probabilistic models: this area comprises the analysis, numerics and uncertainty quantification for stochastic models of hyperbolic systems arising in fluid mechanics. It includes probabilistic modelling concepts to explore statistical turbulence using, for example, stochastic variational principles and the exploration of stochastic/data-driven tools for hybrid perturbation/filtering techniques. Methods of uncertainty quantification should account for preservation of hyperbolic features.

It is expected that participants will establish cross-connections between these directions addressing a mathematical and/or fluid mechanical problem. Successful proposals with an emphasis on mathematics address hyperbolic modelling in a context relevant for fluid mechanics. Successful proposals with an emphasis on fluid mechanics must not focus on pure applications or large-scale numerical simulation but contribute to the development of models and methods. Research on numerical methods for purely incompressible regimes should emphasise hyperbolic aspects, and proposals addressing viscous flow must focus on convection-dominated regimes.

Tandem projects that typically combine two groups from different research areas are encouraged. These projects can either provide a bridge between different mathematical research directions or connect a group from mathematics to one from engineering sciences or physics. 

Formal Requirements and Proposal Submission

Proposals must be written in English and submitted to the DFG by 30 January 2026. Proposals are to be submitted solely via the elan portal in order to ensure proposal-related data is recorded and documents are securely transmitted. To enter a new proposal within the existing Priority Programme, go to Proposal Submission – New Project/Draft Proposal – Priority Programmes and select “SPP 2410” from the current list of calls. Previous applicants should submit a proposal for the renewal of an existing project under Proposal Submission – Proposal Overview/Renewal Proposal. 

If this is the first time you are submitting a proposal to the DFG, please note that you must register in the elan portal before you can submit your proposal. You must do so by 20 January 2026. You will normally receive confirmation of your registration by the next working day. If your contact data in “elan” is outdated, please also update it before that date.

When preparing your proposal, please refer to the programme guidelines (DFG form 50.05(interner Link), section B) and follow the proposal preparation instructions (DFG form 54.01(interner Link)). The specific proposal has to be structured according to DFG form 53.01(interner Link). However, it is admissible to prepare the proposal as a pdf-file, e.g., using LaTeX instead of using the rtf-file which is available online. 

The work programme within the proposal should include detailed information on the role and tasks of the different groups and their synergies for the success of the envisaged project proposal and the specific role of the doctoral and/or postdoctoral researchers, respectively. From the work programme within the proposal it should become clear which parts are assigned to which scientific co-worker, especially which tasks should be fulfilled by (post)doctoral researchers. In case of joint proposals, the assignment of requested funds to the individual principal investigators should be made clear. The proposals should also indicate how they fit into the programme as a whole.

Note that the descriptions of the projects and all CVs (DFG form 53.200(interner Link)) need to be prepared in English. Furthermore, the DFG’s Guidelines for Preparing Publication Lists (DFG form 1.91(interner Link)) need to be respected: within the project- and subject related list of publications, a maximum of ten publications by the applicant(s) (and/or members of their group) that relate directly to the project should be highlighted in bold.  

With the submission of a proposal within this programme, the applicants agree that the DFG shares all necessary information with the coordinator of the Priority Programme after the call deadline.

A review colloquium with reviewers and applicants will be held at the University of Mainz on 28 April 2026. Please check the Priority Programme’s website for possible additional information which may be communicated there.

Equity and Diversity

The DFG strongly welcomes proposals from researchers of all genders and sexual identities, from different ethnic, cultural, religious, ideological or social backgrounds, from different career stages, types of universities and research institutions, and with disabilities or chronic illness. With regard to the subject-specific focus of this call, the DFG encourages female researchers in particular to submit proposals.

Good Research Practice

According to a resolution of the DFG General Assembly, DFG funding may only be awarded to research institutions that have implemented the guidelines laid down in the Code of Conduct for Safeguarding Good Research Practice(externer Link) in their own regulations. The management of your institution is responsible for implementing the guidelines in a legally binding manner. In order to avoid delays in the disbursement of funding, please verify implementation within your institution in good time. For information regarding the implementation, please refer to the Research Integrity Portal(externer Link). If you have any questions on this subject, please contact the Research Integrity team(externer Link) at the DFG Head Office.

Further Information 

More information on the Priority Programme is available here(externer Link).

The elan system can be accessed here(externer Link).

Please also refer to the DFG forms 50.05(interner Link) and 54.01(interner Link).

For scientific enquiries please contact the Priority Programme coordinator:

Professor Dr. Christian Rohde, Universität Stuttgart, Fachbereich Mathematik, Institut für Angewandte Analysis und Numerische Simulation, Pfaffenwaldring 57, 70569 Stuttgart, phone +49 711 685-65524, crohde@mathematik.uni-stuttgart.de(externer Link)

Contact Persons at the DFG Head Office:

Programme contact: Dr. Frank Kiefer, phone +49 228 885-2567, frank.kiefer@dfg.de(externer Link)

Administrative contact: Luka Madunic, phone +49 228 885-2883, luka.madunic@dfg.de(externer Link)

Privacy Policy

We, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), take the protection of your personal data and its confidential treatment extremely seriously. Therefore, please refer to the DFG’s Privacy Policy(interner Link). If you intend to transmit personal data of third parties, please make sure to do so only if the necessary legitimation under data protection law exist. Before transmitting data of third parties to the DFG, please forward the DFG’s Data Protection Notice to the individuals affected (data subjects). If there is a legitimate interest not to inform individuals beforehand (e.g. for reasons of secrecy or in case of a nomination or candidate proposal), these individuals should be informed no later than at the time of publication.