Recent explorations of higher-order adaptive methods in fluid dynamics
Massachusetts Institute of Technology
Abstract
In this talk, we will discuss some recent work in the application of higher-order and adaptive methods to fluid dynamics. First, we will consider the use of higher-order, adaptive finite element methods to sonic boom propagation. The computational cost to analyze and design the next generation of low boom aircraft is significant as a direct result of the increasingly tighter control required on sonic boom noise generation. We will provide a general overview of the sonic boom modeling process and then focus on the development of an adaptive finite element method to solve the boom propagation problem. Results demonstrate that the new adaptive method can efficiently and reliably produce high accuracy solutions to the boom propagation problem.
Second, we will consider the impact of higher-order methods in the simulation of chaotic problems, such as Large Eddy and Direct Numerical Simulations. We develop a simple model for discretization and statistical errors, including effects of start-up errors as well as parallel ensemble averaging. Then, we analyze the model to show how the potential benefits of higher-order discretization are significantly constrained by statistical errors.
About the speaker
Dr. David Darmofal is the Jerome C. Hunsaker Professor of Aeronautics and Astronautics at MIT and a member of the MIT Aerospace Computational Design Laboratory (ACDL) and the MIT Center for Computational Science & Engineering (CCSE). His principal areas of interest are computational methods for partial differential equations, especially fluid dynamics; and engineering education innovation. Darmofal earned his BS in Aerospace Engineering from the University of Michigan (1989), and SM (1991) and PhD (1993) in Aeronautics and Astronautics from MIT. From 1995–1998, he was an assistant professor in the Department of Aerospace Engineering at Texas A&M University. He joined MIT in 1998, became a full professor there in 2010, and has served as the Department of Aeronautics and Astronautics associate and interim chair.
