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Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa)
Deutsche Forschungsgemeinschaft (DFG)
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). The programme is designed to run for six years. The present call invites proposals for the first 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 back 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 strives 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:
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.
Multiscale models and asymptotic regimes: research includes here the development and analysis of model hierarchies (e.g., Boltzmann-Euler or in 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.
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 the 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 may 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 bridge between different mathematical research directions, or connect a group from mathematics to one from engineering sciences or physics.
Proposals must be written in English and submitted to the DFG by 16 January 2023. Please note that proposals can only be submitted via "elan", the DFG's electronic proposal processing system. To enter a new project 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.
Applicants must be registered in "elan" prior to submitting a proposal to the DFG. If you have never before submitted a proposal to DFG through "elan", you need to register in advance. This can be done online by yourself - however, it takes one to two working days to be confirmed by DFG staff. If you need to register, please complete your registration before 9 January 2023. Note that you will be asked to select the appropriate Priority Programme call during both the registration and the proposal process. If your contact data in "elan" is outdated, please also update it before that date.
General information on proposals in the framework of a Priority Programme (in particular concerning eligibility and admissible funding requests) can be found in guideline 50.05 (part B). See also guideline 54.01 for instructions how to prepare a proposal. The specific proposal has to be structured according to form 53.01. 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 become clear. The proposals should also indicate how they fit into the programme as a whole.
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