Challenges and Opportunities in High-Order Finite Element Simulations of Fluid Mechanics

October 05, 2017

Thursday, October 5, 2017
Dr. Brian Helenbrook
2:00 - 3:00pm
Clarkson University
SEH, B1220



Currently most commercial software for simulating fluid flow is based on second-order accurate finite volume techniques.  These techniques often do not provide sufficient accuracy to make precise design decisions.  Continuous and discontinuous high-order finite element methods (FEM) can provide accurate solutions for complex geometries, but there are still many challenges with making these techniques practical for engineering simulation.  In this talk, several of the challenges of applying high-order finite element techniques are discussed.  These include extending iterative techniques such as a multigrid, which have been successful for finite volume methods, to high-order FEM.  Various multigrid approaches are discussed that could provide significantly improved accuracy at a comparable computational cost to finite volume methods.  Another necessity is combining high-order FEM with mesh adaptation techniques in order to fully realize the benefits of a high-order method.  Techniques for enabling fast, unsteady simulations using continuous finite elements on unstructured adaptive meshes are presented and the advantages of this combination are demonstrated with several practical examples.



Dr. Brian Helenbrook is the Paynter-Krigman Endowed Professor in Engineering Science Simulation in the Mechanical and Aeronautical Engineering Department at Clarkson University.  He received his Ph.D. from Princeton University in 1997 and was part of the Applied Strategic Computing Initiative (ASCI) at Stanford University before joining the faculty at Clarkson University in 2001.  His research interests are mainly in the development and application of new numerical simulation techniques for fluid-flows.  Most of his recent work in numerical methods has been on adaptive, arbitrary-Lagrangian-Eulerian (ALE), hp-finite element methods, which enable efficient high-order of accuracy simulations of single and multi-phase flows. Recent application areas include the optimization of ducted wind turbines, which contributed to the formation of a company (Ducted Turbines International), the modeling of silicon solidification processes for Applied Materials (now spun-off into the startup LECT — Leading Edge Crystal Technologies), and aerodynamic optimization of Luge sleds for the US Olympic Luge Team (current design is used by the top men’s sliders).