Sino-German Symposium on Advanced Numerical Methods for Compressible Fluid Mechanics and related Problems, May 21-27, 2014, Beijing, china Discrete unified gas-kinetic scheme for compressible flows haoli guo (Huazhong University of Science and Technology Wuhan, China Joint work with Kun Xu and Ruijie Wang(Hong Kong University of Science and Technology
Discrete unified gas-kinetic scheme for compressible flows Zhaoli Guo (Huazhong University of Science and Technology, Wuhan, China) Joint work with Kun Xu and Ruijie Wang (Hong Kong University of Science and Technology) Sino-German Symposium on Advanced Numerical Methods for Compressible Fluid Mechanics and Related Problems, May 21-27, 2014, Beijing, China
Outline ● Motivation Formulation and properties ● Numerical resu|ts Summary
Outline • Motivation • Formulation and properties • Numerical results • Summary
Motivation Non-equilibrium flows covering different flow regimes Re-Entry vehicle Chips Inhalable particles 103 10 101 10 10
Motivation Non-equilibrium flows covering different flow regimes Re-Entry Vehicle Chips Inhalable particles 10 10 -3 10-1 100 10-2
Challenges in numerical simulations Modern cfd: Based on Navier-Stokes equations Efficient for continuum flows does not work for other regimes Particle Methods: (MD, DSMC.) · noise · Small time and cell size Difficult for continuum flows /low-speed non-equilibrium flows Method based on extended hydrodynamic models: Theoretical foundations Numerical difficulties( Stability boundary conditions Limited to weak-nonequilibrium flows
Challenges in numerical simulations • Based on Navier-Stokes equations • Efficient for continuum flows • does not work for other regimes • Noise • Small time and cell size • Difficult for continuumflows / low-speed non-equilibrium flows Modern CFD: Particle Methods: (MD, DSMC… ) • Theoretical foundations • Numerical difficulties (Stability, boundary conditions,……) • Limited to weak-nonequilibrium flows Method based on extended hydrodynamic models :
Lockerby's test (2005, Phys. Fluid) the most common high-order continuum equation sets(Grad's 13 th moment, Burnett, and super-Burnett equations)cannot capture the Knudsen Layer, Variants of these equation families have however, been proposed and some of them can qualitatively describe the Knudsen layer structure. the quantitative agreement with kinetic theory and dSmc data is only slight result from kinetic theory. We find that, for a benchmark case, the most common higher-order continuum equation sets(Grads 13 moment, Burnett, and super-Burnett equations) cannot capture the Knudsen layer. Variants of these equation families have, however, been proposed and some of sm (Pe sul a suin IMt et Nar stles lan ll wats them can qualitatively describe the Knudsen layer structure. To make quantitative comparisons, we f-h artaud lume t- b NGk Biwa i-l Ikale ef the ILN obtain additional boundary conditions(needed for unique solutions to the higher-order equations) from kinetic theory. However, we find the quantitative agreement with kinetic theory and DSMc ata is only slight. o 2005 American Institute of Physics. [ DOI: 10.1063/1.]
Lockerby’s test (2005, Phys. Fluid) = const the most common high-order continuum equation sets (Grad’s 13 moment, Burnett, and super-Burnett equations ) cannot capture the Knudsen Layer, Variants of these equation families have, however, been proposed and some of them can qualitatively describe the Knudsen layer structure … the quantitative agreement with kinetic theory and DSMC data is only slight