defmod 1 finite element code for modeling crustal
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Oct 30, 2022 •1.36k likes •2.61k views

Defmod 1 : Finite element code for modeling crustal deformation Tabrez Ali tabrezali@gmail.com 1 https://bitbucket.org/stali/defmod Features Can simulate elastodynamic & quasistatic processes (in 2D or 3D) such as: Coseismic (fault)

  1. Build and Execution $ ssh lonestar.tacc.utexas.edu $ module load petsc $ git clone https://bitbucket.org/stali/defmod $ cd defmod $ make all $ mpirun -np 2 ./defmod -f examples/two quads qs.inp Reading input file ... Partitioning mesh ... Forming [K] ... Forming RHS ... Setting up solver ... Solving ... Recovering stress ... Cleaning up ... Finished

  2. Build and Execution $ ssh lonestar.tacc.utexas.edu $ module load petsc $ git clone https://bitbucket.org/stali/defmod $ cd defmod $ make all $ mpirun -np 2 ./defmod -f examples/two quads qs.inp -ksp monitor Reading input file ... Partitioning mesh ... Forming [K] ... Forming RHS ... Setting up solver ... Solving ... 0 KSP Residual norm 6.484684701823e+00 1 KSP Residual norm 2.983375739070e-15 Recovering stress ... Cleaning up ... Finished

  3. Build and Execution $ ssh lonestar.tacc.utexas.edu $ module load petsc $ git clone https://bitbucket.org/stali/defmod $ cd defmod $ make all $ mpirun -np 2 ./defmod -f examples/two quads qs.inp -ksp monitor Reading input file ... Partitioning mesh ... Forming [K] ... Forming RHS ... Setting up solver ... Solving ... 0 KSP Residual norm 6.484684701823e+00 1 KSP Residual norm 2.983375739070e-15 Recovering stress ... Cleaning up ... Finished By default output is written in VTK format and can be easily visualized using ParaView, VisIt etc.

  4. Result

  5. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  6. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 Constraint Eqn’s 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  7. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 Equation 1 { Ux 5 +Ux 8 -2Ux 13 =0.0 } 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  8. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 Start and end time(s) �

  9. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 Equation 2 { Uy 5 +Uy 8 -2Uy 13 =0.0 } 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  10. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 Equation 9 { Ux 9 =1.0 } 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  11. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1 Equation 10 { Uy 9 =1.0 } 1.0 0.0 5 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 �

  12. Input file with constraints $ cat examples/quadtree qs.inp � implicit quad 12 3 10 19 1 10 0 0 0 0.0 1.0 5 1.0 0.25 1 1 0.0 1.0 8 1 2 5 4 1 0.0 -2.0 13 ... 0.0 0.0 0.0 0.0 0.0 0 0 ... ... 1 7.5E10 0.25 1.0E18 1.0 3000.0 1.0 0.0 9 3 1.0 0.0 1.0 1.0 0.0 5 1 1.0 0.0 8 0.0 1.0 9 -2.0 0.0 13 1.0 0.0 1.0 0.0 0.0 0.0 � Note: Any constraint that is specified remains active throughout the simulation; A zero value is assumed (for u or p ) unless specified otherwise

  13. Result Note: Displacements at hanging nodes are average of their corresponding edge nodes

  14. More examples ... – Displacement BC in 3D Uy 9 =10.0 1 0.0 1.0 0.0 9 10.0 0.0 0.0 – Pressure head BC in 3D (for poroelastic problem) P 9 =1.0E3 1 0.0 0.0 0.0 1.0 9 1.0E3 0.0 0.0 – Fault slip between two coincident nodes (in x-direction) Ux 13 -Ux 81 =10.0 2 1.0 0.0 0.0 13 -1.0 0.0 0.0 81 10.0 0.0 0.0

  15. More examples ... – Displacement BC in 3D Uy 9 =10.0 1 0.0 1.0 0.0 9 10.0 0.0 0.0 – Pressure head BC in 3D (for poroelastic problem) P 9 =1.0E3 1 0.0 0.0 0.0 1.0 9 1.0E3 0.0 0.0 – Fault slip between two coincident nodes (in x-direction) Ux 13 -Ux 81 =10.0 2 1.0 0.0 0.0 13 -1.0 0.0 0.0 81 10.0 0.0 0.0

  16. More examples ... – Displacement BC in 3D Uy 9 =10.0 1 0.0 1.0 0.0 9 10.0 0.0 0.0 – Pressure head BC in 3D (for poroelastic problem) P 9 =1.0E3 1 0.0 0.0 0.0 1.0 9 1.0E3 0.0 0.0 – Fault slip between two coincident nodes (in x-direction) Ux 13 -Ux 81 =10.0 2 1.0 0.0 0.0 13 -1.0 0.0 0.0 81 10.0 0.0 0.0

  17. Fault slip 4 3 8 7 El−1 El−2 1 2 5 6 Element view Nodal view (exploded) To enforce slip we need to specify the relative displacement/opening between coincident nodes { 3 & 8 } and { 2 & 5 } For example the relative displacement (Y coordinate) between nodes { 3 & 8 } can be written as Uy 3 -Uy 8 =1.0 and is specified (between 0 . 1 − 0 . 5 seconds) as: 2 0 1 3 0 -1 8 1.0 0.1 0.5

  18. Fault slip

  19. Example $ cat examples/2d fault dyn.inp explicit quad 12 18796 19036 2 48 0 0 200 75 0.025 40 0 0.0 0.01 ... 2 0 -1 1832 0 1 1619 0.1 0.2 2.7 2 1 0 1832 -1 0 1619 0.1 0.2 2.7 ...

  20. Example $ cat examples/2d fault dyn.inp explicit quad 12 18796 19036 2 48 0 0 200 ABC’s 75 0.025 40 0 0.0 0.01 ... 2 0 -1 1832 0 1 1619 0.1 0.2 2.7 2 1 0 1832 -1 0 1619 0.1 0.2 2.7 ...

  21. Example $ cat examples/2d fault dyn.inp explicit quad 12 18796 19036 2 48 0 0 200 75 0.025 40 0 0.0 0.01 Damping coefficients ... 2 0 -1 1832 0 1 1619 0.1 0.2 2.7 2 1 0 1832 -1 0 1619 0.1 0.2 2.7 ...

  22. Example (Dynamic) T=0.0 sec Displacement Velocity (100x)

  23. Example (Dynamic) T=2.5 sec Displacement Velocity (100x)

  24. Example (Dynamic) T=5.0 sec Displacement Velocity (100x)

  25. Example (Dynamic) T=7.5 sec Displacement Velocity (100x)

  26. Example (Dynamic) T=10.0 sec Displacement Velocity (100x)

  27. Example (Dynamic) T=12.5 sec Displacement Velocity (100x)

  28. Example (Dynamic) T=15.0 sec Displacement Velocity (100x)

  29. Example (Dynamic) T=17.5 sec Displacement Velocity (100x)

  30. Example (Dynamic) T=20.0 sec Displacement Velocity (100x)

  31. Example (Dynamic) T=22.5 sec Displacement Velocity (100x)

  32. Example (Dynamic) T=25.0 sec Displacement Velocity (100x)

  33. Example (Dynamic) T=27.5 sec Displacement Velocity (100x)

  34. Example (Dynamic) T=30.0 sec Displacement Velocity (100x)

  35. Example (Dynamic) T=32.5 sec Displacement Velocity (100x)

  36. Example (Quasistatic) T=0.0 years Displacement Velocity (20x)

  37. Example (Quasistatic) T=5.0 years Displacement Velocity (20x)

  38. Example (Quasistatic) T=10.0 years Displacement Velocity (20x)

  39. Example (Quasistatic) T=15.0 years Displacement Velocity (20x)

  40. Example (Quasistatic) T=20.0 years Displacement Velocity (20x)

  41. Example (3D Quasistatic) T=0.0 years (Rifting starts) Displacement

  42. Example (3D Quasistatic) T=1.0 years (Rifting ...) Displacement

  43. Example (3D Quasistatic) T=2.0 years (Rifting ...) Displacement

  44. Example (3D Quasistatic) T=3.0 years (Rifting ...) Displacement

  45. Example (3D Quasistatic) T=4.0 years (Rifting ...) Displacement

  46. Example (3D Quasistatic) T=5.0 years (Rifting ends) Displacement

  47. Example (3D Quasistatic) T=10.0 years (Postrifting viscous relaxation) Displacement

  48. Example (2D Dynamic with ABCs) Time step 250 Note: Full computational domain is shown

  49. Example (2D Dynamic with ABCs) Time step 500 Note: Full computational domain is shown

  50. Example (2D Dynamic with ABCs) Time step 750 Note: Full computational domain is shown

  51. Example (2D Dynamic with ABCs) Time step 1000 Note: Full computational domain is shown

  52. Example (3D Dynamic) T=3.0 secs Velocity

  53. Example (3D with Traction BCs) Deformation due to lake 3 loading 3 Shoreline is shown in white

  54. Example (2D Poroelasticity) Pore pressure change following an earthquake at time step 0 (i) with a permeable fault zone (ii) with an impermeable fault zone

  55. Example (2D Poroelasticity) Pore pressure change following an earthquake at time step 5 (i) with a permeable fault zone (ii) with an impermeable fault zone

  56. Example (2D Poroelasticity) Pore pressure change following an earthquake at time step 10 (i) with a permeable fault zone (ii) with an impermeable fault zone

  57. Example (2D Poroelasticity) Pore pressure change following an earthquake at time step 15 (i) with a permeable fault zone (ii) with an impermeable fault zone

  58. Example (2D Poroelasticity) Pore pressure change following an earthquake at time step 20 (i) with a permeable fault zone (ii) with an impermeable fault zone

  59. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  60. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  61. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  62. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  63. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  64. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  65. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  66. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production on

  67. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production off

  68. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production off

  69. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production off

  70. Example (2D Poroelasticity) Pore pressure change due to injection (top right) and withdrawl (top left) of fluid in a saturated reservoir Production off

  71. Example (2D Poroelasticity) Fluid velocity vectors (unscaled) during steady production With flow BC

  72. Example (2D Poroelasticity) Fluid velocity vectors (unscaled) during steady production With no-flow BC

  73. Example (3D Poroelasticity) Pore pressure change due to withdrawl of fluid from a confined reservoir; Permeability ratio b/w reservoir and surrounding rock = 1.0E6 Note: In 3D, both (stabilized) linear tet or hex elements can be used

  74. Example (3D Poroelasticity) Pore pressure change due to withdrawl of fluid from a confined reservoir; Permeability ratio b/w reservoir and surrounding rock = 1.0E6 Note: In 3D, both (stabilized) linear tet or hex elements can be used

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