1. Ali Sami and Clint Dawson
Hybrid Discontinuous Galerkin Methods for Serre-Green-Naghdi Water Wave Models
Ali Sami and Clint Dawson
Ali Samii
Final doctoral exam
Department of ASE/EM UT Austin

2. Acknowledgments

3. Motivation

4. Motivation: Long waves away from the coast

5. Motivation: Dispersive waves

6. Motivation: Dispersive waves

7. The Water Wave Problem: Assumptions

8. Shallow Water Regime

9. Shallow Water Regime

10. Shallow Water Regime

11. Shallow Water Regime

12. The Water Wave Problem: Governing equations

13. The Water Wave Problem: Governing equations

14. The Water Wave Problem: Governing equations

15. The Water Wave Problem: Dirichlet Neumann Operator

16. The Water Wave Problem: Dirichlet Neumann Operator

17. The Water Wave Problem: Dispersive properties

18. The Water Wave Problem: Dispersive properties

19. The Water Wave Problem: Nondimensionalization

20. Water Wave Problem: Asymptotic expansion

21. Water Wave Problem: Asymptotic expansion

22. Asymptotic models:

23. Outline

24. Korteweg de Vries Equation

25. Korteweg de Vries Equation: Solution to linear equation

26. Korteweg de Vries Equation: Solution procedure using HDG

27. Korteweg de Vries Equation: Solution procedure using HDG

28. Korteweg de Vries Equation: Stability of the method

29. Korteweg de Vries Equation: Accuracy of the results

30. Korteweg de Vries Equation: Nonlinear solver

31. Korteweg de Vries Equation: Nonlinear solver

32. Korteweg de Vries Equation: Nonlinear accuracy

33. Korteweg de Vries Equation: Nonlinear examples

34. Korteweg de Vries Equation: Nonlinear examples

35. Korteweg de Vries Equation: Nonlinear examples

36. Outline

37. NSWE: Solution approach

38. NSWE: Solution approach

39. NSWE: Solution approach

40. NSWE: Numerical results

41. NSWE: Numerical results

42. NSWE: Numerical results

43. NSWE: Numerical results

44. NSWE: Numerical results

45. Outline

46. Asymptotic models:

47. Green-Naghdi Equation: Solution approach

48. Green-Naghdi Equation: Strang splitting

49. Green-Naghdi Equation: Solving the dispersive part

50. Green-Naghdi Equation: Solving the dispersive part

51. Green-Naghdi Equation: Solving the dispersive part

52. Green-Naghdi Equation: Numerical results

53. Green-Naghdi Equation: Numerical results

54. Green-Naghdi Equation: Numerical results

55. Green-Naghdi Equation: Numerical results
A. Samii and C. Dawson
SIAM – Computational Science and Engineering
Atlanta 2017

56. Green-Naghdi Equation: Numerical results

57. Green-Naghdi Equation: Numerical results

58. Green-Naghdi Equation: Numerical results

59. Green-Naghdi Equation: Numerical results

60. Green-Naghdi Equation: Numerical results

61. Green-Naghdi Equation: Numerical results

62. Green-Naghdi Equation: Numerical results

63. Green-Naghdi Equation: Numerical results

64. Green-Naghdi Equation: Numerical results

65. Green-Naghdi Equation: Numerical results

66. Concluding remarks

67. Happy Birthday Bernado!!!
Thank You
Happy Birthday Bernado!!!