Department of Mechanical Engineering
Pennsylvania State University
"Entropy Stability and Finite Element Methods: Simulating Fluid Flows without Blow-Up."
There are many unique challenges in designing robust and high-fidelity methods for solving the compressible Navier-Stokes equations. These challenges can be (at least partially) remedied by embracing methods that are constructed within a rigorous mathematical framework. This is one of the reasons why finite element methods with their strong mathematical foundation are attractive. However, there remain several open questions regarding their suitability for solving the compressible Navier-Stokes equations. In particular, there are questions about the possibility of constructing robust, and versatile stabilization for finite element methods at high Reynolds and Mach numbers. In this talk, the speaker (David M. Williams) will attempt to discuss the non-linear stability of finite element methods, and in particular 'entropy stability' and 'L2 stability'. In addition, he will discuss the limitations/opportunities for improvement of the current mathematical results in this area.