Active Flux & High Order Methods in CFD

From Godunov to Active Flux

Modern computational fluid dynamics emerged from mid-twentieth-century efforts to use digital computation to solve the equations governing fluid flow. In the 1940s, John von Neumann pioneered finite-difference approaches for simulating compressible flow, using artificial viscosity to stabilize shock waves. More than a decade later, in 1959, Sergei Godunov introduced a different approach: a finite-volume method for conservation laws that used local wave solutions to determine how information passes between neighboring cells. Beginning in the late 1970s, work by Phil Roe and others made these methods practical and accurate via approximate Riemann solvers. Eitan Tadmor’s work around 1990 provided a way to view Godunov-type methods as a central numerical flux combined with carefully designed diffusion. These advances made it possible to achieve stable, high-resolution calculations, but several gaps still remained. One example is that multidimensional flow was still commonly treated through a sequence of essentially one-dimensional interface problems.

In 2011, Phil Roe developed Active Flux as a new response to that remaining challenge. A key conceptual precursor was Bram van Leer’s 1977 Scheme V, which introduced a continuous piecewise-quadratic reconstruction for one-dimensional advection. Active Flux uses adaptive multidimensional diffusion to stabilize wave propagation directly in multiple dimensions rather than relying solely on one-dimensional approximations at cell interfaces. By combining cell averages with point values along cell boundaries, Active Flux offers a promising high order framework for resolving multidimensional wave behavior, preserving important mathematical and physical structures, accommodating unstructured meshes, and achieving strong accuracy on relatively coarse grids.

This symposium will celebrate that legacy while bringing together leading researchers to examine the foundations, current advances, open challenges, and future possibilities of Active Flux and other high-order approaches for conservation laws. It will also mark the 30th anniversary of the Godunov Symposium, organized by Bram van Leer at the University of Michigan.

Confirmed Speakers

• • Christian Klingenberg, Professor of Mathematics, University of Würzburg, Germany
  • Rémi Abgrall, Professor of Mathematics, University of Zurich, Switzerland
  • Christiane Helzel, Professor of Applied Mathematics, Heinrich Heine University Düsseldorf, Germany
  • Chi-Wang Shu, Theodore B. Stowell University Professor of Applied Mathematics, Brown University
  • Hiroaki Nishikawa, Research Fellow, National Institute of Aerospace, NASA Langley Research Center
  • Mario Ricchiuto, Senior Research Scientist and Team Leader, CARDAMOM, Inria Centre at the University of Bordeaux, France
  • David Zingg, Distinguished Professor of Computational Aerodynamics and Sustainable Aviation, University of Toronto Institute for Aerospace Studies, Canada
  • Timothy Eymann, Technical Advisor, High Speed Systems Vehicle Technology Branch, United States Air Force
  • ZJ Wang, Spahr Professor of Aerospace Engineering, University of Kansas
  • Iman Samani, Senior Software Engineer, NVIDIA
  • Chad D. Meyer, Scientist, Michigan SPARC and XCP-4 (Continuum Models and Numerical Methods) Group, Los Alamos National Laboratory
  • Karthik Duraisamy, Arthur B. Modine Professor; Samir and Puja Kaul Director of MICDE, University of Michigan
  • Krzysztof J. Fidkowski, Professor of Aerospace Engineering, University of Michigan

More to be confirmed.

Program

Coming soon!