Numerical study of the equation on the graph for the steady state non-Newtonian flow in thin tube structure

The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions in the vertices. Non-Newtonian rheology of the flow generates nonlinear equations on the graph. A new numerical method for second...

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Published inMathematical modelling and analysis Vol. 28; no. 4; pp. 581 - 595
Main Authors Kozulinas, Nikolajus, Panasenko, Grigory, Pileckas, Konstantinas, Šumskas, Vytenis
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 20.10.2023
Subjects
Apexes
asymptotic dimension reduction
Boundary value problems
Differential equations
equation on the graph
Equilibrium flow
Graph theory
Mathematical analysis
Non Newtonian flow
Nonlinear differential equations
Nonlinear equations
Numerical analysis
Numerical methods
Ordinary differential equations
quasi-Poiseuille flows
Rheological properties
Rheology
strain rate dependent viscosity
Viscosity
Viscous flow
equation on the graph
strain rate dependent viscosity
asymptotic dimension reduction
non-Newtonian flow
quasi-Poiseuille flows
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Summary:The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions in the vertices. Non-Newtonian rheology of the flow generates nonlinear equations on the graph. A new numerical method for second order nonlinear differential equations on the graph is introduced and numerically tested.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2023.18311