Project description
Computer-assisted enhancements to the mathematical descriptions of fluid mechanics
Fluid interface problems are widespread in engineering and design. Incompressible fluids with moving interfaces are a special case of this category of problems that includes inkjet and bubble dynamics and a fish or submarine in motion. While there are no completely incompressible fluids, most fluids, including water, are treated as incompressible for practical purposes. This makes developing numerical methods to describe applications particularly relevant – and it is also particularly challenging. With the support of the Marie Skłodowska-Curie Actions programme, the CAMINFLOW project will develop computer-assisted mathematical proofs and arithmetic libraries to complement existing methods for the mathematical analysis of fluid interface problems.
Objective
The CAMINFLOW project aims to further explore the question of global regularity versus finite-time singularity formation in mathematical fluid mechanics. It proposes three horizons: 1) Modulated self-similar finite-time singularities in degenerate parabolic equations, 2) Fluid-interface finite-time singularities, 3) Rigorous analysis of fluid-structure moving interfaces.
Module 1 is organized in two Work Packages: 1.1) Finite-time self-similar pinchoff for the axisymmetric surface diffusion equation (local, 1d), 1.2) Self-similar finite-time singularity in incompressible porous medium (nonlocal, 2d).
Module 2 focuses on the blowup of the curvature of the Muskat problem (also known as Hele-Shaw).
Module 3 contains two Work Packages: 3.1) Local and global well-posedness theory for the inextensible membrane problem. 3.2) Rigorous proof of the tumbling/tank-treading transition for inextensible membranes in a shear flow.
A central and unifying method in this action is Computer-Assisted Proofs (CAP). Due to the highly demanding technical level of the analysis involved, new interval arithmetic libraries for singular integrals will be developed in Arb. Moreover, new modules in the framework Dedalus will be developed as well to perform accurate numerical simulations (that will help deciding whether a singularity is forming or not). These techniques will be applied complementing the methods from contour dynamics, harmonic analysis, and energy methods, needed to obtain results in the mathematical analysis of fluid interface problems.
The CAMINFLOW project will be carried out by the experienced researcher, who worked during his PhD thesis on the global regularity question for incompressible fluid interfaces coming from nonlinear, nonlocal parabolic partial differential equations, and then as a postdoc moved on to fluid-structure elastic interfaces. The ER will collaborate with a Supervisor who is a prominent expert in CAP and their application to the fluid mechanics.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesphysical sciencesclassical mechanicsfluid mechanicsfluid dynamicscomputational fluid dynamics
- natural sciencesmathematicsapplied mathematicsmathematical model
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Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
08007 Barcelona
Spain