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Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials

Project goals

This project proposal focuses on theoretical and computer analysis, and their mutual interplay, related to several classes of evolutionary models that have been recently designed to capture complex behavior of various fluid-like materials within the framework of nonlinear continuum mechanics. The characteristic keywords of these particular classes are implicit constitutive relations, nonlinear rate type fluids, nonlinear integral type fluid-like materials, inhomogeneous incompressible fluids, compressible non-Newtonian fluids, and chemically reacting fluids. Regarding specific applications, we intent to concentrate on unsteady flows of biological liquids and time-dependent processes in geophysical materials. The goal is to develop new methods and toolsto solve initial boundary-value problems for large data, both theoretically and numerically.

Keywords

viscoelasticfluid-likematerialratetypefluidintegraltypefluidimplicitconstitutiverelationshipweaksolutionexistencefiniteelementmethodfinitevolumemethodcomputersimulation

Public support

  • Provider

    Czech Science Foundation

  • Programme

    Standard projects

  • Call for proposals

    Standardní projekty 12 (SGA02009GA-ST)

  • Main participants

  • Contest type

    VS - Public tender

  • Contract ID

    201-09-0917

Alternative language

  • Project name in Czech

    Matematická a počítačová analýza evolučních procesů v nelineárních viskoelastických tekutinách

  • Annotation in Czech

    Navrhovaný projekt je zaměřen na teoretickou a počítačovou analýzu několika tříd evolučních modelů, které jsou schopny zachytit složité chování rozličných tekutin v rámci nelineární mechaniky kontinua. Charakteristickými rysy jednotlivých tříd, které jsou předmětem navrhovaného výzkumu, jsou implicitní konstitutivní vztahy, nelineární modely rychlostního typu, nelineární modely integrálního typu, nehomogenní nestlačitelné tekutiny, stlačitelné nenewtonovy tekutiny, a chemicky reagující tekutiny. Výzkumje motivován zejména aplikacemi v mechanice biologických tekutin a v geofyzice. Cílem projektu je vyvinout nové teoretické, numerické a počítačové metody, nástroje a postupy, které by umožnily řešit počáteční a okrajové úlohy těchto modelů pro velká data.

Scientific branches

  • R&D category

    ZV - Basic research

  • CEP classification - main branch

    BA - General mathematics

  • CEP - secondary branch

    BK - Liquid mechanics

  • CEP - another secondary branch

  • 10101 - Pure mathematics
    10305 - Fluids and plasma physics (including surface physics)

Completed project evaluation

  • Provider evaluation

    V - Vynikající výsledky projektu (s mezinárodním významem atd.)

  • Project results evaluation

    This very successful project was devoted to mathematical analysis and computer simulations of initial and boundary value problems in nonlinear models of fluid and solid mechanics. Significant attention was paid to models in applications of asphalt deformation or coagulation in blood. Results were published in total 103 publications including 2 books, 4 chapters in monographs and 9 dissertations.

Solution timeline

  • Realization period - beginning

    Jan 1, 2009

  • Realization period - end

    Dec 31, 2013

  • Project status

    U - Finished project

  • Latest support payment

    Jun 12, 2013

Data delivery to CEP

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

  • Data delivery code

    CEP14-GA0-GA-U/01:1

  • Data delivery date

    Jul 1, 2014

Finance

  • Total approved costs

    10,651 thou. CZK

  • Public financial support

    10,651 thou. CZK

  • Other public sources

    0 thou. CZK

  • Non public and foreign sources

    0 thou. CZK

Recognised costs

10 651 CZK thou.

Public support

10 651 CZK thou.

0%


Provider

Czech Science Foundation

CEP

BA - General mathematics

Solution period

01. 01. 2009 - 31. 12. 2013