Applied Math Seminar I Katrin Rohlf, Compressible flows with pressure-dependent viscosity and slip through local constrictions

MC 6460

Speaker

Katrin Rohlf  | Department of Mathematics, Ryerson University 

Title

Compressible flows with pressure-dependent viscosity and slip through local constrictions 

 Abstract

Understanding the properties of flows through local constrictions is important for assessing potential vessel rupture in blood flow through constricted/stenosed arteries, and for assessing the flow properties in nanochannels just to name a few examples.  The relatively recent use of particle-based methods for flow applications in both applications, especially for flows through constricted cylinders, has shown that the built-in compressibility  of the particle-based method may be more pronounced in such geometries than expected.  In order to quantify the compressibility, an approximate analytical solution for the velocity is derived theoretically from the compressible Navier-Stokes equation with variable viscosity, as well as centerline pressure/density curves.  The method uses the Karman-Pohlhausen approximation technique, which leads to a nonlinear ODE for the pressure gradient that is solved numerically with Maple/Matlab.  Approximate analytical predictions will be used to demonstrate changes as a result of compressibility, slip and pressure-dependent viscosity parameter, and then compared to the velocity/pressure/density curves from particle-based flow simulations.