Transition from Kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms

References

• Kaniel , S. 1988 . A Kinetic Model for Compressible Flow Equations . Indiana University Mathematics Journal , 37 : 537 – 563 .
   Web of Science ®Google Scholar
• Tiwari , S. and Rjasanow , S. 1997 . Sobolev Norm as a Criterion of Local Thermal Equilibrium . Eur. J. Mech. B , 16 : 863 – 876 .
   Web of Science ®Google Scholar
• Tiwari , S. 1998 . Domain Decomposition in Particle Methods for the Boltzmann and Euler Equations , University of Kaiserslautern, Shaker Verlag . PhD-thesis
   Google Scholar
• Tiwari , S. and Klar , A. 1998 . An Adaptive Domain Decomposition Procedure for Boltzmann and Euler Equations . J. Comp. Appl. Math. , 90 : 223 – 237 .
   Web of Science ®Google Scholar
• Boyd , I. D. , Chen , G. and Candler , G. V. 1994 . Predicting Failure of the Continuum Fluid Equations in Transitional Hypersonic Flows . AIAA , : 94 – 2352 .
   Google Scholar
• Kreuzer , H. J. 1981 . Nonequilibrium Thermodynamics and its Statistical Foundation , Oxford : Clarendon Press .
   Google Scholar
• Liepmann , H. W. , Narasimha , R. and Chahine , M. T. 1962 . Structure of a Plane Shock Layer . Phys. Fluids , 5 : 1313
   Web of Science ®Google Scholar
• Meixner , J. 1941 . Zur Thermodynamik der Irreversiblen Prozesse . Z. Phys. Chem. B , 53 : 253
   Google Scholar
• Arnold , A. and Giering , U. 1997 . An Analysis of the Marshak Conditions for Matching Boltzmann and Euler Equations . Math. Models Methods Appl. Sci. , 7 : 557 – 577 .
   Web of Science ®Google Scholar
• Klar , A. 1996 . Domain Decomposition for Kinetic Problems with Nonequilibrium States . Eur. J. Mech./B Fluids , 15 : 203 – 216 .
   Web of Science ®Google Scholar
• Giering , U. 1995 . Matching of Kinetic and Aerodynamics Equations , University of Kaiserslautern, Shaker Verlag . PhD thesis
   Google Scholar
• Junk , M. 1997 . Kinetic Schemes — A new Approach and Applications , University of Kaiserslautern, Shaker Verlag . PhD thesis
   Google Scholar
• Neunzert , N. and Struckmeier , J. 1995 . “ Particle Methods for the Boltzmann Equation ” . In ACTA NUMERICA 1995 Cambridge
   Google Scholar
• He , Xiaoyi and Luo , Li-Shi . 1997 . Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation . J. Stat. Physics , 88 : 927 – 944 .
   Web of Science ®Google Scholar