Organizing Committee
  • Alexander Alekseenko
    California State University Northridge
  • Jose Camberos
    Air Force Institute of Technology
  • Irene Gamba
    University of Texas at Austin
  • Sergey Gimelshein
    University of Southern California
  • Prakash Vedula
    University of Oklahoma
  • Ingrid Wysong
    US Air Force Research Laboratory
Abstract

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.

[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).

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee

Workshop Schedule

Monday, June 3, 2013
TimeEventLocationMaterials
8:30 - 8:50Registration11th Floor Collaborative Space 
8:50 - 9:00Welcome - ICERM Director 11th Floor Lecture Hall 
9:00 - 9:50Perspectives on the Boltzmann equation analysis in hypersonic flows - Eswar Josyula, Air Force Research Laboratory11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Deterministic solvers for the Boltzmann equation - Irene Gamba, University of Texas at Austin11th Floor Lecture Hall
11:35 - 12:25Non-equilibrium Effects in Viscous Reacting Gas Flows - Elena Kustova, Saint Petersburg State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time  
2:30 - 3:20Multiscale asymptotic solutions to the Boltzmann equation for aerospace applications - Thierry Magin, Von Karman Institute for Fluid Dynamics11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Kinetic Particle Methods – Beyond Number of Time Steps, Cell Size, and Particles per Cell - Deborah Levin, Pennsylvania State University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, June 4, 2013
TimeEventLocationMaterials
9:00 - 9:50Regularized 13 Moment Equations for Maxwell and Hard Sphere molecules - Henning Struchtrup, University of Victoria11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20How to avoid very large discrete velocity grids in deterministic simulation of rarefied gas flows? - Luc Mieussens, Universite de Bordeaux I11th Floor Lecture Hall 
11:35 - 12:25Kinetic Theory, Gaussian Moment Closures, and Fluid Approximations - C. David Levermore, University of Maryland11th Floor Lecture Hall
12:30 - 12:35Group Photo11th Floor Lecture Hall 
12:35 - 2:30Break for Lunch and Free Time  
2:30 - 3:20A hybrid method for hydrodynamic-kinetic flow - Gabriella Puppo, Universita dell'Insubria11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50Boltzmann Solver with Adaptive Mesh in Phase Space - Vladimir Kolobov, CFD Research Corporation11th Floor Lecture Hall
Wednesday, June 5, 2013
TimeEventLocationMaterials
9:00 - 9:50Moving boundary problems for a rarefied gas: Spatially one-dimensional case - Kazuo Aoki, Kyoto University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20High order AP schemes for some discrete-velocity kinetic equations - Fengyan Li, Rensselaer Polytechnic Institute11th Floor Lecture Hall
11:35 - 12:25Energy conserving numerical schemes for Vlasov Ampere and Vlasov Maxwell systems - Yingda Cheng, Michigan State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time  
2:30 - 3:20High order asymptotic preserving methods for the Boltzmann equation - Lorenzo Pareschi, Universita di Ferrara11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:20Poster Session highlights/lightning talks11th Floor Lecture Hall 
7:30 - 9:00Poster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, June 6, 2013
TimeEventLocationMaterials
9:00 - 10:30Morning for Collaborations 11th Floor Lecture Hall 
10:30 - 11:25Approaches for Emulating the Boltzmann Equation When Particle Simulation Becomes Inefficient - Iain D. Boyd, University of Michigan11th Floor Lecture Hall
11:35 - 12:30A Distributional Monte Carlo Method for the Boltzmann Equation - Aihua Wood, Air Force Institute of Technology11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time  
2:30 - 3:25Deviational methods for Efficient Solution of the Boltzmann Equation - Nicolas Hadjiconstantinou, Massachusetts Institute of Technology11th Floor Lecture Hall
3:25 - 3:30Please remember to fill out your survey!  
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:55Lattice based computational approaches for nonequilibrium flows - Prakash Vedula, University of Oklahoma11th Floor Lecture Hall
Friday, June 7, 2013
TimeEventLocationMaterials
9:00 - 9:50An Efficient Discrete Velocity Method for the Boltzmann Equation - Philip Varghese, University of Texas at Austin11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20Does kinetic theory really contribute to shock-capturing schemes for compressible gas-dynamic equations? - Taku Ohwada, Kyoto University11th Floor Lecture Hall 
11:30 - 12:20Fast Spectral-Galerkin Methods for High-Dimensional PDEs in Unbounded Domains - Jie Shen, Purdue University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch and Free Time  
2:30 - 2:50A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit - Jeffrey Haack, University of Texas at Austin11th Floor Lecture Hall
3:00 - 3:20A Closure for Grad's 13 Moment t Equations Using a Hermite Polynomial Representation of Velocity Distribution Function - Leonid Pekker, Victor Technologies11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:20High order semi-Lagrangian schemes and operator splitting for the Boltzmann equation. - Yaman Guclu, Michigan State University11th Floor Lecture Hall
4:30 - 4:50A high-order positivity preserving method for the Vlasov-Poisson System - David C. Seal, Michigan State University11th Floor Lecture Hall

Lecture Videos