Period: January 1, 2010 – September 30, 2017

Status: Completed

Web: gepris.dfg

Materials encountered in industry and medicine often do not conform to the classical models of Newtonian viscous fluids. The aim of the proposed project is to gain a deep understanding of the complex behavior of shear-dependent non-Newtonian fluids in time-dependent moving domains. Thus, our objectives are twofold: theoretical analysis of the corresponding mathematical model and the development of a reliable numerical scheme for experimental simulations. The non-Newtonian fluids we are considering belong to the class of shear-thinning/shear-thickening fluids, for which the viscous stress tensor is a nonlinear function of the shear rate. They are extensively used in industry and biomedicine to simulate the flow of technical oils, composites, polymers, biological fluids, and so on. As an example, we will focus in particular on blood flow in compliant vessels. To ensure that the derived numerical schemes are robust and reliable for such complex models, an in-depth numerical analysis—including convergence and error analysis—will be necessary.

Funding

• DFG-Eigene Stelle, "Mathematical modeling and numerical simulation of shear-dependent non-Newtonian fluids in time-dependent domains," ZA 613/1-1, 2010–2013

• DFG-Own Position, "Mathematical modeling and numerical simulation of fluid-structure interaction for complex viscous fluids," HU 1885/1-2, 09/2015–09/2017,

Funding

DFG

Project Partners

Johannes Gutenberg University Mainz, Department of Physics, Mathematics, and Computer Science