- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
4
A nonsmooth model for discontinuous shear thickening fluids: Analysis and numerical solution
Juan Carlos
De los Reyes
Escuela Politécnica Nacional, QUITO, ECUADOR
Georg
Stadler
New York University, NEW YORK, UNITED STATES
Shear thickening, non-Newtonian fluid mechanics, variational inequality, additional regularity, mixed discretization, semismooth Newton method, fictitious domain method
We propose a nonsmooth continuum mechanical model for discontinuous shear thickening flow. The model obeys a formulation as energy minimization problem and its solution satisfies a Stokes type system with a nonsmooth constitute relation. Solutions have a free boundary at which the behavior of the fluid changes. We present Sobolev as well as H¨older regularity results and study the limit of the model as the viscosity in the shear thickened volume tends to infinity. A mixed problem formulation is discretized using finite elements and a semismooth Newton method is proposed for the solution of the resulting discrete system. Numerical problems for steady and unsteady shear thickening flows are presented and used to study the solution algorithm, properties of the flow and the free boundary. These numerical problems are motivated by recently reported experimental studies of dispersions with high particle-to-fluid volume fractions, which often show a sudden increase of viscosity at certain strain rates.
Fluid mechanics
Partial differential equations
Calculus of variations and optimal control; optimization
575
602
10.4171/IFB/330
http://www.ems-ph.org/doi/10.4171/IFB/330