Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations

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 develo...

• Type: Journal
• Year: 2011
• Where: JCPHY
• Authors: Paul J. Atzberger
• Keywords: JCPHY 2011, Lagrangian Methods, Mathematical Formalism, Periodic Boundary Conditions