Croatian Science Foundation project IP-2019-04-1140

Multiscale problems in fluid mechanics (MultiFM)

Principal investigator: Igor Pa┼żanin

Host institution: Faculty of Science, University of Zagreb

From: January 2020; Duration: 48 months

Public presentation of the project. ... to be announced ...

  • Problems of interest:

    • Investigating effective behaviour of the non-newtonian fluid flows
    • Proposing new models for fluid flow through domains with porous/poroelastic walls
    • Study of multi-species diffusion systems in porous media
    • Existence, uniqueness and regularity results
  • Physical proceses:

    • Convection, diffusion, reactions, conduction; Newtonian or micropolar fluids, transport of chemical mixtures in porous media
  • Analytical tools:

    • Asymptotic analysis, homogenization techniques, entropy methods, Faedo-Galerkin approach, fixed-point theorems, compactness results
  • Applications:

    • Mechanical engineering, hydrogeology and biomedicine
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The problems in fluid mechanics are usually described by the systems of partial differential equations resulting from various conservation laws and constitutive relations. Such systems are most often too complex to be directly solved numerically, due to its nonlinearity and/or coupled nature. In some situations, simpler empiric laws proposed in the engineering literature can represent good substitutes for the original physical laws. However, to be sure of that, one needs to justify the usage of such simplified models, i.e. to deduce the information about its order of accuracy. This justification can be done either theoretically by establishing to what extent the empirical model deviates from the original conservation law, or numerically by performing numerical simulations and using experimental data. Both means of justifications, theoretical and numerical, are, in many situations, complementary and we will employ them both in this project.

The goal of this project is to derive and analyse higher-order mathematical models describing various multiscale processes in fluid mechanics. In the framework of this particular project we will tackle the problems being demanding from the mathematical point of view and directly motivated by the real-life applications.

More precisely, we will address the fluid flow through thin domains whose walls are rigid, but also could be porous or even poroelastic. We plan to explore the effects of boundary irregularities on the lubrication problems, and to study the low permeability domains such as porous media. The fluids considered will be classical Newton fluids, but most attention will be devoted to non-newtonain fluids (power-law fluids, micropolar fluids). They can be in liquid or gas phase but we will also investigate multiphase fluids where the two phases exist together. Inspired by the applications, non-standard but physically relevant boundary conditions will be imposed and different physical processes occurring in the fluids will be considered. In view of that and taking into account the track record of PI and team members, the project should result with substantial number of papers published in high-ranked journals of applied mathematics.

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