CFD by first order PDEs

  • Yoshifumi Suzuki
  • Loc Khieu
  • Bram van Leer
Original Article


This research originally was aimed at modeling all flows (except free-molecular) by systems of hyperbolic-relaxation equations (moments of the Boltzmann equation), and developing efficient numerical methods for these. Such systems have many potential numerical advantages, mainly because there are no second or higher derivatives to be approximated. This avoids accuracy problems on adaptive unstructured grids, and the source terms, though often stiff, are only local; the compact stencils facilitate code parallelization. A single code could simulate flows up to intermediate Knudsen numbers, and be hybridized with DSMC where needed. In this project, one major problem arose that we have not yet solved: the accurate representation of shock structures. This makes the methodology currently unsuited for, e.g., re-entry flows. We have validated it for subsonic and transonic flows and are concentrating on applications to MEMS-related flows. We discuss the challenges of our approach, present numerical algorithms and results based on the 10-moment model, and report progress in our latest research topic: formulating accurate solid-boundary conditions.


First-order PDEs Extended hydrodynamics 10-moment equations Finite-volume method Discontinuous-Galerkin method Slip boundary condition 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringThe University of MichiganAnn ArborUSA
  2. 2.Desktop Aeronautics, Inc.Palo AltoUSA

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