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MICDE Faculty seminar: Philip Roe, Emeritus Professor, Aerospace Engineering U-M

December 7, 2023 @ 3:00 pm - 4:00 pm

Venue: 1109 FXB

Portrait of Philip Roe

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Bio:  Philip Roe is an Emeritus Professor of Aerospace Engineering at the University of Michigan. He is recognized for his pioneering work in the field of Computational Fluid Dynamics and Magnetohydrodynamics. Roe made many fundamental contributions to the development of high-resolution schemes for hyperbolic conservation laws. He is best known for his work on the flux difference splitting for compressible flows with shocks, typically referred to as the Roe scheme.

Musings of a Computational Philosopher

Philosophy sets a great story by asking the right questions. Indeed a correct answer to the wrong question is seldom of any value. You can even obtain tenure, I am told, by asking questions that you cannot yet answer. For the past decade, I have been trying to ask the right questions about computing compressible flow, and I hope here to provide a glimpse of the answers.

A “good” algorithm should “obviously” be accurate, cheap, and robust. Of these three desiderata, I will try here to clarify the notion of accuracy. Although clearly a good thing, it is almost always defined asymptotically in terms of the behavior at small mesh size or low frequency. This sets precise goals for analysis, and although accuracy can be achieved in this sense, in practice we often cannot afford the asymptotic regime. Moreover, when we deal with compressible flow, we are forced to deal with high frequencies. We require in fact only rather modest accuracy at low frequency, but must extend this into the high frequency regime, and doing this will require answering different questions. I will discuss a double-pronged approach to finding these questions and their answers.

This approach demands that the information flow in the computer should closely match that in real life. A great advance toward this was made by introducing Godunov-type methods, but these merely distinguish left from right, and their reliance on one-dimensional physics has many drawbacks. However, for many kinds of problem there are integral solutions to the linear initial-value problem in multiple dimensions. My first prong is to show how these can be used to derive algorithms for linear and nonlinear problems for compressible fluid flow and other applications. These algorithms have remarkable properties, including true incompressible limits and automatic boundary conditions. The information flow is different for advective and non-advective modes of the solution.

As a second way to achieve correct information flow, I employ solution derivatives as degrees of freedom. This Hermitian representation is common in computer graphics and signal processing but almost unknown in CFD. Its great benefit consists of keeping the stencil compact. This brings about sharp discontinuities, extends the spectrum and reduces communication overheads. Recently, with my graduate student Iman Samani, I have used both prongs of my approach to produce fifth-order solutions for linear elastodynamics on unstructured grids with automatic handling of material interfaces and remote boundaries. I will present these results, summarize what remains to be done and describe some target applications.


December 7, 2023
3:00 pm - 4:00 pm
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1109 FXB
1320 Beal Ave.
Ann Arbor, MI United States
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