Time-varying MHD flows with free surfaces

Flows over time in time-varying networks

There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques that are the cornerstones of static network flows. The aim of this paper is to advance the state of the art for dynamic network flows by developing the cont...

Two-dimensional Stokes and Hele-Shaw flows with free surfaces

We discuss the application of complex variable methods to Hele-Shaw flows and twodimensional Stokes flows, both with free boundaries. We outline the theory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explore the parallels between t...

A Numerical Method for Fluid Flows with Complex Free Surfaces

1 Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States of America [email protected] 2 Department of Mathematics, University of Houston, 77204-3008, Houston, TX, United States of America [email protected] 3 Institute of Analysis and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland {marco.picasso;jacques...

Numerical simulation of 3D viscoelastic flows with free surfaces

Numerical simulations of viscoelastic flows with free surfaces

We present a new methodology to simulate viscoelastic flows with free-surfaces. These simulations are motivated by the modelling of polymers manufacturing techniques, such as extrusion and injection moulding. One of the consequences of viscoelasticity is that polymeric materials have a “memory” of their past deformations. This generates some numerical difficulties which are addressed with the l...