Efforts based on kinetic description of flows Discrete Ordinate Method(DOM)(1 2 Time-splitting scheme for kinetic equations (similar with DSMc dt(time step<(collision time) dx cell size)< (mean-free-path numerical dissipation dt Works well for highly non-equilibrium flows, but encounters difficult fo continuum flows Asymptotic preserving (AP)scheme 3,4) Consistent with the chapman -Enskog representation in the continuum limit (Kn→0) dt (time step) is not restricted by(collision time at least 2nd-order accuracy to reduce numerical dissipation [51 Aims to solve continuum flows, but may encounter difficulties for free molecular flows [1]J. Y. Yang and J. C Huang, J. Comput. Phys. 120, 323(1995 [2]A. N Kudryavtsev and A. A Shershnev, J. Sci. Comput. 57, 42(2013) [3]S Pieraccini and G. Puppo, J. Sci. Comput. 32, 1(2007) [4]M. Bennoune, M. Lemo, and L Mieussens, J Comput. Phys. 227, 3781(2008) [5]K Xu and J -C Huang, J. Comput. Phys. 229, 7747(2010)Efforts based on kinetic description of flows # Discrete Ordinate Method (DOM) [1,2] : • Time-splitting scheme for kinetic equations (similar with DSMC) • dt (time step) < (collision time) • dx (cell size) < (mean-free-path) • numerical dissipation dt # Asymptotic preserving (AP) scheme [3,4] : Works well for highly non-equilibrium flows, but encounters difficult for continuum flows Aimsto solve continuum flows, but may encounter difficultiesfor free molecular flows • Consistent with the Chapman-Enskog representation in the continuum limit (Kn → 0) • dt (time step) is not restricted by (collision time) • at least 2 nd -order accuracy to reduce numerical dissipation [5] [1] J. Y. Yang and J. C. Huang, J. Comput. Phys. 120, 323 (1995) [2] A. N. Kudryavtsev and A. A. Shershnev, J. Sci. Comput. 57, 42 (2013). [3] S. Pieraccini and G. Puppo, J. Sci. Comput. 32, 1 (2007). [4] M. Bennoune, M. Lemo, and L. Mieussens, J. Comput. Phys. 227, 3781 (2008). [5] K. Xu and J.-C. Huang, J. Comput. Phys. 229, 7747 (2010)