Project description
Pioneering numerical methods preserve model structure on continuum mechanics
Simulating complex dynamical fluid and solid mechanics, such as those of the cardiovascular system, involves solving challenging non-linear hyperbolic partial differential equations. Leveraging unstructured grids to partition the physical domain of such problems allows flexibility, making them ideal for complex shapes and fluid dynamics simulations. The ERC-funded SUPREMUM project aims to develop pioneering structure-preserving methods on unstructured grids for such problems. It will devise efficient high-order numerical methods, design an efficient and accurate fluid-structure interaction solver able to represent both solids and fluids, as well as bridge structure-preserving and reduced-order methods. Ultimately, the approach will produce the first numerical methods simultaneously verifying all structural properties of the continuous models at the discrete level.
Objective
SUPREMUM aims to develop and theoretically study innovative structure-preserving (SP) numerical methods to solve challenging non-linear hyperbolic partial differential equations (PDE) modelling continuum mechanics. The ultimate groundbreaking goal consists on devising the first existing numerical methods simultaneously verifying at the discrete level all structural properties of the continuous models: provable thermodynamical compatibility, so that the systems satisfy an extra conservation law for the total energy in order to rigorously prove non-linear stability; conservation of equilibrium solutions, needed to perform very long-time stable simulations; verification of natural involution constraints, of the divergence and curl type; and preservation of the asymptotic limits, arising for some characteristic scales tending to zero. We will devise efficient high order numerical schemes combining different families of numerical methods on unstructured staggered grids configurations, leading to the advance of fundamental mathematical knowledge on numerical analysis. The use of an arbitrary Eulerian-Lagrangian approach will allow the design of an efficient and accurate fluid structure interaction (FSI) solver based on the unified hyperbolic Godunov-Peshkov-Romenski (GPR) model of continuum mechanics able to represent both solids and fluids. Fundamental progress in practical applications of the developed methodologies will initially target the design of a monolithic approach for the simulation of entire cardiovascular systems, coupling 1D blood flow models to the 3D FSI approach. Finally, we will build the bridge between SP methods for hyperbolic PDEs and reduced order modelling (ROM) breaking the frontiers of present research to obtain a novel SP-ROM approach for conservation laws founded on a solid mathematical background. The investigations pursued will impact digital transformation opening new research avenues in numerical analysis, engineering and biomedicine.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
This project's classification has been human-validated.
- natural sciences mathematics applied mathematics dynamical systems
- natural sciences physical sciences classical mechanics fluid mechanics fluid dynamics computational fluid dynamics
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
- natural sciences mathematics applied mathematics numerical analysis
- natural sciences mathematics applied mathematics mathematical model
Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2025-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
15782 Santiago De Compostela
Spain
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