1. June 28, 2004AIAA 37th Thermophysics Conference1 Applications of Kinetic Fluxes to Hybrid Continuum-Rarefied Methods Harrison S. Y. Chou Research Scientist Nielsen Engineering & Research, Inc Mountain View, California

2. June 28, 2004AIAA 37th Thermophysics Conference2 Outlines History Difficulties Approaches Applications Concluding Remarks

3. June 28, 2004AIAA 37th Thermophysics Conference3 Research at Stanford (1991~1995) D. Baganoff Particle Method J. McDonald Continuum Method S. Y. Chou L. Dagum B. Hass A. Goswami T. Denery D. Dahlby T. Lou C. D. Duttweiler A. Garcia (Professor at SJSU) Kinetic Theory Study T. Lou D. Dahlby C. D. Duttweiler

4. June 28, 2004AIAA 37th Thermophysics Conference4 References 1.Chou, S. Y. and Baganoff, D., "Kinetic Flux Vector Splitting for the Navier-Stokes Equations," Journal of Computational Physics, 130, Jan. 1997. 2. Garcia, A. and B. Alder, "Generation of the Chapman-Enskog Distribution," Journal of Computational Physics, 140, May 1998. 3. Lou, T.; Dahlby, D. C.; Baganoff, D, “A Numerical Study Comparing Kinetic Flux–Vector Splitting for the Navier–Stokes Equations with a Particle Method,” Journal of Computational Physics, 145, Sep. 1998. 4.Duttweiler, C. R., “Development and Parallelization of a Hybrid particle/Continuum Method for Simulation Rarefied Flow,” Ph.D. Thesis, Stanford University, 1998. 5. Chou, S. Y., "On the Mathematical Properties of Kinetic Split Fluxes," AIAA 2000-0921, AIAA 38 th Aerospace Sciences Meeting & Exhibit, Jan. 2000.

5. June 28, 2004AIAA 37th Thermophysics Conference5 Typical DSMC/NS Hybrid Applications

6. June 28, 2004AIAA 37th Thermophysics Conference6 Difficulties DSMCFVS/FDS (Kinetic Flux) (Viscous Flux ???)

7. June 28, 2004AIAA 37th Thermophysics Conference7 Interfaces From DSMC to continuum methods (a) Sum up particles across boundaries from DSMC domain. (b) Overset grid techniques. From continuum methods to DSMC (a) Convert fluxes into particles back to DSMC domain. (b) Sampling from Chapmann-Enskog PDF. (c) Sampling by acceptance/rejection methods.

8. June 28, 2004AIAA 37th Thermophysics Conference8 Compatibilities Transport Properties (a) Viscosity,… Governing Equations (a) NS/DSMC, High-order Moment Equations. Numerical Methods (a) Steady-state solutions algorithms. (b) Solutions transfer between grids. (c) Boundary conditions at solid walls. (d) Computational stabilities and efficiencies.

9. June 28, 2004AIAA 37th Thermophysics Conference9 Kinetic Approaches Deshpande (1986) Chou & Baganoff (1995) KFVS Scheme For Euler Equations KFVS Scheme For Navier-Stokes Equations Maxwellian PDF Chapman- Enskog PDF

10. June 28, 2004AIAA 37th Thermophysics Conference10 PDFs (1)

11. June 28, 2004AIAA 37th Thermophysics Conference11 PDFs (2) -4-3-201234 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Molecular Thermal Speed Ratio Probability Maxwellian Chapman-Enskog For 1-D Case Mach 2.5

12. June 28, 2004AIAA 37th Thermophysics Conference12 Moment Equations Navier-Stokes Equations where Moment Equations Boltzmann Equation

13. June 28, 2004AIAA 37th Thermophysics Conference13 Mathematical Integrations t1t1 n +n Flux t2

14. June 28, 2004AIAA 37th Thermophysics Conference14 Split Kinetic Fluxes Split Mass Flux Split Normal Momentum Flux Split Tangential Momentum Fluxes (2) Split Energy Fluxes

15. June 28, 2004AIAA 37th Thermophysics Conference15 Split Kinetic Mass Fluxes compression Mach Number

16. June 28, 2004AIAA 37th Thermophysics Conference16 Split Kinetic Momentum Fluxes Mach Number compression

17. June 28, 2004AIAA 37th Thermophysics Conference17 Split Kinetic Energy Fluxes compression Mach Number compression

18. June 28, 2004AIAA 37th Thermophysics Conference18 Properties of Flux Jacobian Split DefineCheck AAA SWSWSW      FAU SWSW      A F U SW SW        Steger-Warming Flux Vector Splitting Algorithm Split DefineCheck FFF VL   A F U      FAU   Van Leer Flux Vector Splitting Algorithm Split DefineCheck FFF kinetic   A F U      FAU   Kinetic Flux Vector Splitting Algorithm

19. June 28, 2004AIAA 37th Thermophysics Conference19 Split Conservative Variables (Mass) Mach Number

20. June 28, 2004AIAA 37th Thermophysics Conference20 Split Conservative Variables (Momentum) Mach Number

21. June 28, 2004AIAA 37th Thermophysics Conference21 Split Conservative Variables (Energy) Mach Number

22. June 28, 2004AIAA 37th Thermophysics Conference22 Sampling Techniques Cumulative Sampling Method Acceptance-Rejection Sampling Method

23. June 28, 2004AIAA 37th Thermophysics Conference23 Kinetic-Based NS Steady-State Solutions Mach Number Contour Plot 2-D Cylinder w/ Isothermal BC (Mach=4.0, AOA=0 degree) Pressure Contour Plot 3-D OSC Taurus Launch Vehicle (Mach=3.98, AOA=10 degree)

24. June 28, 2004AIAA 37th Thermophysics Conference24 Boundary Conditions at Wall (Slip/No Slip) Isothermal Wall (Given Temperature) t1t1 Constrain Equations n flo w wall f ISO-Wall f Chapman-Enskog Accomdation coefficient

25. June 28, 2004AIAA 37th Thermophysics Conference25 DSMC-NS Solutions – Sliding Plate HIGH LOW Pressure (KFVS) x y HIGH LOW x y Pressure (DSMC) (By T. Lou and D. Dahlby)

26. June 28, 2004AIAA 37th Thermophysics Conference26 Applications For NS-DSMC Hybrid (by Craig R. Duttweiler at Stanford)

27. June 28, 2004AIAA 37th Thermophysics Conference27 Concluding Remarks  Compatibilities at different levels.  Efficient Kinetic-based algorithms.  Kinetic-based boundary conditions for all domains.  Dynamic NS/DSMC interfaces.

28. June 28, 2004AIAA 37th Thermophysics Conference28 Future Researches  High-order moment equations algorithms.  Steady-state solution techniques for DSMC.  Dynamic NS-DSMC interfaces