In recent literature concerning multidimensional inviscid fluid flow, one can find numerous instances where the fluid density exhibits significant variation, even becoming infinite at some points. We include a viscosity term in the compressible Euler equations that depends on the density and obtain solutions that are more realistic from the physical point of view. There are two main scenarios of interest which we aim to study: fluid flow in an open space and in interaction with rigid solids. Our plan is to use recent results involving the variable-viscosity Bresch-Desjardins (BD) entropy and its variants, results about interaction of a Navier-Stokes fluid and a solid, different kinds of approximate solutions, finite volume, finite element, Galerkin and other methods, together with the maximum energy dissipation (maximal entropy production) principle and techniques from mathematical analysis. Additionally, for the fluid-solid interaction problem, penalization and decoupling methods will be used as well. The expectation of the project is to provide a new view of highly compressible gases and other compressible fluids, such as plasma, in two directions: making a connection between inviscid models and viscous systems with variable viscosity coefficients, and to analyze the associated fluid-solid interaction problems. The main impact of the project will be a new framework for models for highly compressible fluids and situations when there is high variation in the fluid density.
PI
Marko Nedeljkov has been working on partial differential equations with singularities theory for a long time. He was dealing with conservation and balance laws in continuum physics, other PDEs with singularities, approximate solutions, even unbounded ones, satisfying different kinds of admissibility conditions. In a series of papers, he invented ways how to deal with singularities (shadow wave, split delta measure, for example) in an orderly fashion.
TM1
Srđan Trifunović has been working on mathematical theory of fluids and fluid-structure interaction for the last 5 years. He has shown a high level of comprehension and innovativity throughout his work, and proven that he can carry out high-impact research. He also has valuable experience in joint research, and we believe that he is well-suited to coordinate this work package.
TM2
Danijela Rajter Ćirić has been working on PDE problems including stochastic terms and fractional derivatives. Her intuition from these areas of research and collaborative capacity could help the project.
TM3
Sanja Ružičić obtained her PhD in the area of approximate solutions and Wave Front Tracking numerical scheme.
TM4
Davor Kumozec is PhD student in numerical analysis and PDEs.
EXTERNAL COLLABORATOR
With a help of Endre Süli and his mentoring two young team members, we expect a significant part of the numerical and computational research to be done by them.