Musings of a Computational Philosopher - Exploring Accuracy in Compressible Flow Algorithms

Explore the philosophical and computational insights of Philip Roe, Emeritus Professor of Aerospace Engineering at the University of Michigan, in this thought-provoking lecture. Delve into the importance of asking the right questions in computational fluid dynamics, particularly for compressible flow. Examine the concept of accuracy in algorithms, challenging traditional asymptotic definitions and proposing new approaches for high-frequency regimes. Discover a double-pronged strategy for improving information flow in computer simulations, including the use of Godunov-type methods and integral solutions to linear initial-value problems in multiple dimensions. Learn about the benefits of employing solution derivatives as degrees of freedom in Hermitian representation, a technique rarely used in Computational Fluid Dynamics (CFD). Gain insights into recent developments in fifth-order solutions for linear elastodynamics on unstructured grids, featuring automatic handling of material interfaces and remote boundaries.