Feedback Control of Cumuliform Cloud Formation based on Computational Fluid Dynamics

1. Feedback Control of Cumuliform Cloud Formation based on Computational Fluid Dynamics Yoshinori Dobashi (Hokkaido University) Katsutoshi Kusumoto (Hokkaido University) Tomoyuki Nishita (The University of Tokyo) Tsuyoshi Yamamoto (Hokkaido University)

2. Overview • Introduction • Previous Work • Overview of Our Method • Details of Our Method • Results • Conclusions

3. Introduction • Visual simulation of natural phenomena • Fire, smoke , water, clouds, etc.. • Computational Fluid Dynamics • Realistic shape and motion [Miyazaki 02] [Enright 02] [Nguyen 02] [Fedkiw 01]

4. Introduction • Applications include movies and commercial films • Requiring desired shapes and motion • Controlling fluid simulation • for smoke and water Our research focuses on clouds [Miyazaki 02] [Enright 02] [Nguyen 02] [Fedkiw 01]

5. Introduction • Clouds simulation using CFD [Miyazaki 02] • Realistic clouds • Many physical parameters(temperature, water vapor, etc..) • Difficult to generate desired shape Goal：Generation of clouds with desired shape • Controlling cloud formation process • Naturally-looking clouds with desired shape

6. Features of Our Method video

7. Overview • Introduction • Previous Work • Overview of Our Method • Details of Our Method • Results • Conclusions

8. Controlling fluid simulation Previous Work • Keyframe Control of Smoke Simulation • [Treuille et al 03] • Fluid Control Using the Adjoint Method • [McNamara et al 04] • Target driven smoke animation • [Fattal et al 04]

9. Previous Work • Controlling fluid simulation • Controlling Fluid Animation with Geometric Potential [Kim and Hong 04] • No methods for cloud simulation • Intended for unnatural shape • No considerations for physical processes for cloud formation • phase transition, adiabatic cooling... • Taming liquids for rapidly changing targets [Shi et al 05] • Detail-Preserving Fluid Control [Thürey et al 06]

10. Overview • Introduction • Previous Work • Overview of Our Method • Details of Our Method • Results • Conclusions

11. density, velocity, etc Overview of Our Method • Simulation of cloud formation • Atmospheric fluid dynamics [Miyazaki et al 02] • Cumuliform cloud formation • No wind • Control method • Feedback control • Geometric potential field

12. Simulation of Cloud Formation Ground is heated by the sun.

13. buoyancy force air parcels Simulation of Cloud Formation Air parcels start to move upward.

14. Simulation of Cloud Formation Temperature of air parcels decreases. adiabatic expansion/ cooling

15. (vapor cloud) Simulation of Cloud Formation Clouds are generated due to phase transition phase transition

16. (vapor cloud) Simulation of Cloud Formation latent heatis liberated due to phase transition phase transition

17. (vapor cloud) Simulation of Cloud Formation latent heatis liberated due to phase transition phase transition additional buoyancy

18. (vapor cloud) Simulation of Cloud Formation latent heat is liberated due to phase transition phase transition additional buoyancy further cloud growth

19. (vapor cloud) Simulation of Cloud Formation latent heat is liberated due to phase transition phase transition The cloud growth is controlled by adjusting the amount of latent heat additional buoyancy further cloud growth

20. Simulation of cloud formation • Atmospheric fluid dynamics [Miyazaki et al 02] • Cumuliform cloud formation • No wind • Control method • Feedback control • Geometric potential field density, velocity, etc Overview of Our Method

21. center of simulation space 3D Target Shape from Contours • Drawing contours target shape plane including center • Projecting contours • Creating target shape [Igarashi et al 99] desired contour screen viewpoint simulation space

22. minimize Our Control Method • Feedback control • Geometric potential field target shape difference from the highest point simulated clouds

23. Feedback Control • Latent heat controller • Water vapor supplier Htarget Hc / Htarget Hc

24. Feedback Control • Latent heat controller • Water vapor supplier Htarget Hc / Htarget Hc latent heat controller

25. Feedback Control • Latent heat controller • Water vapor supplier No latent heat without phase transitions from vapor to clouds Hc / Htarget increase latent heat latent heat controller

26. Feedback Control • Latent heat controller • Water vapor supplier water vapor supplier Hc / Htarget increase latent heat latent heat controller

27. Feedback Control • Latent heat controller • Water vapor supplier water vapor supplier add water vapor • Generation of clouds • Cloud development Hc / Htarget increase latent heat latent heat controller

28. water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller Feedback Control • Latent heat controller • Water vapor supplier

29. water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier water vapor supplier latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller latent heat controller Feedback Control • Latent heat controller • Water vapor supplier

30. potential horizontal component of gradient Geometric Potential Field • Horizontal force around boundaries of target shape • Preventing clouds from growing outside target shape

31. potential horizontal component of gradient Geometric Potential Field • Horizontal force around boundaries of target shape • Preventing clouds from growing outside target shape • Feedback controller: vertical extent • Geometric potential field: horizontal extent

32. Overview • Introduction • Previous Work • Overview of Our Method • Details of Our Method • Results • Conclusions

33. Details of Our Method • Formulation of our feedback controller • Feedback controller • Geometric potential field

34. Details of Our Method • Formulation of our feedback controller • Feedback controller • Geometric potential field

35. Details of Our Method • Formulation of our feedback controller • Feedback controller • Geometric potential field

36. Cloud Formation • Velocity of atmosphere • NS equation + buoyancy force • Temperature of atmosphere • Adiabatic cooling, latent heat, heat from ground • Water vapor and water droplet (clouds) • Phase transition between vapor and droplets

37. : time : external force : velocity : pressure Velocity of Atmosphere • Incompressible Navier-Stokes Equation (buoyancy force)

38. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector

39. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector • Temperature : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

40. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector • Temperature : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

41. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector • Temperature : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

42. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector • Temperature amount of latent heat : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

43. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector • Temperature control (latent heat controller) : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

44. Buoyancy and Temperature • Thermal buoyancy : temperature : ambient temperature ： buoyancy coeff. : upward vertical vector change in buoyancy • Temperature control (latent heat controller) : latent heat coeff. : amount of generated clouds : adiabatic lapse rate : vertical component of velocity : heat supplied from ground

45. Phase transition : cloud density : vapor density : clouds generated by phase transition Water vapor and Water Droplet water droplet: water vapor:

46. Phase transition : cloud density : vapor density : clouds generated by phase transition Water vapor and Water Droplet water droplet: water vapor: control (water vapor supplier)

47. Details of Our Method • Formulation of our controller • Feedback controller • latent heat controller • water vapor supplier • Geometric potential field

48. Details of Our Method • Formulation of our controller • Feedback controller • latent heat controller • water vapor supplier • Geometric potential field

49. Latent Heat Controller • PI Control (Proportional Integral Control) • Proportional control updates latent heat according to difference • Integral control updates latent heat according to accumulated difference difference latent heat coefficient P controller I controller ( KP: proportional gain, KI: integral gain )

50. Latent Heat Controller • PI Control (Proportional Integral Control) • PI Control height of clouds target shape P controller target height difference small gaps are left clouds time