Numerical Modeling of Dynamic 3D Processes

Transcription

1 Numerical Modeling of Dynamic 3D Processes Corresponding member of RAS, Professor, Head of Computer Science and Computational Mathematics Department Igor B. Petrov Moscow Institute of Physics and Techology,

2 Contents Numerical modeling of Arctic problems Numerical simulation in geology The numerical solution of collision problems Numerical modeling of composite materials Numerical modeling in Medicine Numerical modeling of seismic stability Numerical modeling of non-destructive railway control Robot-technique Grid-characteristic method

3 Numerical modeling of Arctic problems

4 Migration of iceberg

5 Picture of Ship s Damage R.E. Gagnon, J. Wang Numerical simulations of a tanker collision with a bergy bit incorporating hydrodynamics, a validated ice model and damage to the vessel // Cold regions. Science and Technology, 2012.

6 Collision between the ice-breaker and the ice-hummock

7 Impact of the ice hummock's keel on the seabed and on the underwater pipelines. M.A. Naumov, D.A. Onishchenko, Presentaion Gazprom VNIIGAZ LLC

8 Destruction of the iceberg under intense dynamic impacts

9 Destruction of the iceberg under intense dynamic impacts

10 The flow of ice floes towards the rack of fixed oil-extracting platform

11 Collision between the iceberg and the fixed oil-extracting platform 11

12 Structure of Ice-hummocks A. Marchenko Thermodynamic consolidation and melting of sea ice ridges // Cold regions. Science and Technology, V. 52, N. 3, 2008.

13 Ice-hummock model

14 Seismic exploration in the conditions of the Arctic shelf

15 Strimmer 3D P-waves High performance

16 Seabed stations 3D/4C High price High comprehension of obtained data

17 Geophysical prospecting by electric means seabed stations The leader of volume of work 6 components of the EM field (important for 3D inversion) Not smaller than 50 m EMGS,

18 Geophysical prospecting by electric means - strimmers PGS, High performance No deeper than 300 m One axial component of the field: Ex Frequency and time domain

19 Multilayered geological medium

20 Complicated interfaces

21 Complicated interfaces

22 Complicated interfaces

23 Seismic prospecting at the Arctic shelf

24 Wave pattern in the ice

25 Wave pattern in the water

26 Wave pattern in the ground

27 Wave pattern in the carbon reservoir

28 Problem defintions Source in the ice Source at the seabed Source in the ice, without reservoir Source at the seabed, without reservoir

29 Wave patterns

30 Seismograms from ice receivers, Vy Source in the ice Source at the seabed Source in the ice, without reservoir Source at the seabed, without reservoir

31 Seismograms from seabed receivers, Vy Source in the ice Source at the seabed Source in the ice, without reservoir Source at the seabed, without reservoir

32 Source at the bottom

33 Source at the bottom, without the reservoir

34 Numerical simulation in geology

35 Numerical simulation in geology

36 Cavities of various shape

37 The array of subvertical fluid filled cracks

38 The array of subvertical fluid filled cracks 0,5 The distance between cracks/ the length of craks 1,0 2,0 3,0 1,5 4,0

39 Simple fluid filled cavity Reflected P-wave Wave from the source Reflected wave

40 The numerical solution of collision problems

41 Collision with multilayered barrier

42 Penetration of striker into curved barrier

43 Aircraft collision with the pillar

44 Multilayer barrier

45 Multilayer barrier

46 Numerical modeling of composite materials

47 Composite materials Microstructure Matrix and filler Types of fibers and their orientations 3D structure of fibers 9

48 The impact on the stringer 30

49 The destruction of steel body during ricochet impact

50 Numerical modeling in Medicine

51 Head damage Dependence from the angle = -90 Maximum compression, Па Maximum stretching, Па Maximum shear stress, Па

52 Comparison with clinical results

53 Knee injury

54 Body armour and human chest

55 Numerical modeling of seismic stability

56 Seismic stability of the building Absolute velocity (left) and destruction zones (right) in red

57 Seismic stability of river plant вода земля плотина

58 Seismic stability of the building

59 Love and Rayleigh waves Love waves Rayleigh waves

60 Numerical modeling of non-destructive railway control

61 Dynamic impact on the rail

62 The influence of karst inclusions in the ground above the railway

63 Non-destructive railway control Without crack 1 mm 5 mm 10 mm 40 mm 74 mm

64 Robot-technique

65 Robot-technique

66 Robot-technique

67 Robot-technique

68 Robot-technique

69 Robot-technique

70 Grid-characteristic method

71 Grids Triangular unstructured grid Grids with various average step

72 Grids Curvilinear grids Tetrahedral grids

73 System of equations describing elastic and acoustic waves т v t v σ Elastic waves: v v vт t σ v I v v v v σ tension, density, velocity in the elastic media, stress, Lame s parameters, c p 2 speed of P-waves, 12 cs speed of S-waves. 12 Acoustic waves: v t v p v t pс v v density,v velocity in the acoustic media, p pressure, c 2 speed of sound.

74 Boundary and interface conditions Boundary Given traction r r Given Mixed σp f velocity of boundary r r v V boundary conditions Absorbing boundary contions Interface Continuity ofrthe velocity and traction r r r r va vb V, a b Free sliding conditions r r r r va p vb p, pa pb, a b 0 The interface condition between acoustic and elastic bodies

75 Thank you for your attention!