Issues in Solving the Boltzmann Equation for Aerospace Applications (June 3-7, 2013)

Organizing Committee
  • Alex Alekseenko
    (California State University, Northridge/AFRL at Wright-Patterson AFB)
  • Jose Camberos
    (AFRL Wright-Patterson AFB)
  • Irene Gamba
    (University of Texas at Austin)
  • Sergey Gimelshein
    (University of Southern California)
  • Prakash Vedula
    (University of Oklahoma, Norman)
  • Ingrid Wysong
[Image courtesy of Vladimir Kolobov]
Simulations of supersonic flows around a cylinder for
different Knudsen numbers Kn using a Unified Flow Solver
(J. Comput. Phys. 223 (2007) 589): Gas density (left),
computational mesh and domain decomposition
into Boltzmann (red) and continuum (blue) regions (right).

Being central to gas dynamics, the Boltzmann equation describes gas flows at the microscopic level in regimes from free molecular to continuum. Its descriptive power makes it indispensable for predicting non-continuum phenomena in gases when experimental data is limited or not available. The Boltzmann equation is used in a wide range of applications, from external aerodynamics and thruster plume flows to vacuum facilities and microscale devices. Accurate solution of the Boltzmann equation for modeling gas flows arising in aerospace applications continues to be a challenge. Existing numerical capabilities fall short of capturing the complexities of engineering design. Reasons for this range from the absence of mathematical models that capture the physics properly to higher dimensionality of kinetic models and the resulting high cost of computations to the failure of mathematical theories to handle complex geometries of real life applications.

The goal of this workshop is to facilitate the development of high-fidelity computational capabilities for the solution of the Boltzmann equation in application to simulation of non-continuum flows. This will be accomplished by addressing the gaps in communication between mathematicians, engineers and researchers in various fields of research.

Topics of the workshop include but are not be limited to: different forms of the Boltzmann equation; reduced order models for the Boltzmann equation; mesh adaptation in velocity space; fast evaluation of the Boltzmann collision integral; simulations that account for real gas effects and chemical and electromagnetic interaction of particles; complex geometry simulations; coupling of continuum and non-continuum models; and quantification of numerical error and uncertainty of simulations.

To address the goal of the workshop, the presenters were asked to incorporate in their lectures at least one of the following three common topics:

  • Communication of issues related to high computational costs of simulations;
  • Communication of issues related to accuracy of models that is the accuracy in approximating the solutions to the Boltzmann equation and the accuracy in approximating physics of gas flows;
  • Communication of progress in the analysis of numerical errors.

  • Alexander Alekseenko
    (California State University Northridge)
  • Kazuo Aoki *
    (Kyoto University)
  • Florian Bernard
    (Politecnico di Torino)
  • Iain Boyd*
    (University of Michigan)
  • Jose Camberos
    (Air Force Institute of Technology)
  • Matthew Causley
    (Michigan State University)
  • Yingda Cheng *
    (Michigan State University)
  • Irene Gamba *
    (University of Texas at Austin)
  • Sergey Gimelshein
    (University of Southern California)
  • Yaman Guclu*
    (Michigan State University)
  • Ernesto Gutierrez-Miravete
    (Rensselaer at Hartford)
  • Jeffrey Haack *
    (University of Texas at Austin)
  • Nicolas Hadjiconstantinou*
    (Massachusetts Institute of Technology)
  • Jack Hoffman
    (Orange Coast College)
  • Mikhail Ivanov*
    (Siberian Branch Russian Academy of Sciences)
  • Eswar Josyula*
    (US Air Force Research Laboratory)
  • Elizabeth Kallman
    (Harvard University)
  • Vladimir Kolobov*
    (CFD Research Corporation)
  • Elena Kustova*
    (St. Petersburg State University)
  • Hai Le
    (University of California, Los Angeles)
  • David Levermore *
    (University of Maryland)
  • Deborah Levin *
    (Pennsylvania State University)
  • Fengyan Li*
    (Rensselaer Polytechnic Institute)
  • Chunting Lu
    (University of Maryland)
  • Thierry Magin*
    (Von Karman Institute for Fluid Dynamics)
  • Luc Mieussens*
    (Université de Bordeaux I)
  • Alessandro Munafo
    (Von Karman Institute for Fluid Dynamics)
  • Taku Ohwada*
    (Kyoto University)
  • Lorenzo Pareschi *
    (Università di Ferrara)
  • Leonid Pekker*
    (Victor Technologies)
  • Gabriella Puppo*
    (Università dell'Insubria)
  • David Seal *
    (Michigan State University)
  • Jie Shen *
    (Purdue University)
  • Henning Struchtrup *
    (University of Victoria)
  • Philip Varghese *
    (University of Texas at Austin)
  • Prakash Vedula*
    (University of Oklahoma)
  • Aihua Wood*
    (Air Force Institute of Technology)
  • Ingrid Wysong
    (US Air Force Research Laboratory)
  • He Yang
    (Rensselaer Polytechnic Institute)
  • Yubei Yue