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STOCHASTIC EULERIAN-LAGRANGIAN METHODS FOR FLUID-STRUCTURE INTERACTIONS WITH THERMAL
 

Summary: STOCHASTIC EULERIAN-LAGRANGIAN METHODS FOR
FLUID-STRUCTURE INTERACTIONS WITH THERMAL
FLUCTUATIONS AND SHEAR BOUNDARY CONDITIONS
PAUL J. ATZBERGER
Abstract. A computational approach is introduced for the study of the rheological properties of
complex fluids and soft materials. The approach allows for a consistent treatment of microstructure
elastic mechanics, hydrodynamic coupling, thermal fluctuations, and externally driven shear flows.
A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical
system. Microstructure configurations are represented in a Lagrangian reference frame. Conserved
quantities, such as momentum of the fluid and microstructures, are represented in an Eulerian
reference frame. The mathematical formalism couples these different descriptions using general
operators subject to consistency conditions. Thermal fluctuations are taken into account in the
formalism by stochastic driving fields introduced in accordance with the principles of statistical
mechanics. To study the rheological responses of materials subject to shear, generalized periodic
boundary conditions are developed where periodic images are shifted relative to the unit cell to
induce shear. Stochastic numerical methods are developed for the formalism. As a demonstration
of the methods, results are presented for the shear responses of a polymeric fluid, lipid vesicle fluid,
and a gel-like material.
Key words. Statistical Mechanics, Complex Fluids, Soft Materials, Stochastic Eulerian La-
grangian Methods, SELM, Stochastic Immersed Boundary Methods, SIB, Fluctuating Hydrodynam-

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics