Numerical Simulations of Silverpit Crater Collapse: A Comparison of TEKTON and SALES 2 Gareth...
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Transcript of Numerical Simulations of Silverpit Crater Collapse: A Comparison of TEKTON and SALES 2 Gareth...
Numerical Simulations of Silverpit Crater Collapse:
A Comparison ofTEKTON and SALES 2
Gareth Collins, Zibi Turtle, and
Jay Melosh
LPL, Univ. of Arizona
Silverpit(Stewart and Allen, 2002)
(Allen and Stewart, 2003)
Objectives
• Understand Silverpit• Ring formation
• Compare 2 modeling techniques to assess:• Consistency• Limitations• Degree to which they are complementary
Finite-Element Method• Model structure as an assemblage of elements
bounded by nodes• Specify:
• Geometry• Material properties and rheologies• Boundary and initial conditions
• Construct system of equations:• Solve simultaneously for displacements at nodes• Calculate stresses using constitutive equations
€
vf = K
v d
Finite-element Method: Rheology• Elastic
• Newtonian
• Power-law
• Plastic• < c: power-law; ≥ c: Newtonian
• Exponential
€
ε =σE
€
˙ ε = Aσ n exp −H
RT
⎛ ⎝ ⎜
⎞ ⎠ ⎟
€
˙ ε = A' exp −H
RT1 −
σ
σ p
⎛
⎝ ⎜
⎞
⎠ ⎟
2 ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
€
˙ ε =σ
η
Lagrangian Hydrocode Method• Model structure as a regular grid of cells
bounded by nodes• Specify:
• Geometry• Material properties• Boundary and initial conditions
• Calculate all forces acting on each cell.• Assuming forces constant for time step,
compute node displacements:
€
vx =
v f i∑
mΔt2
Lagrangian Hydrocode: Rheology
• Elastic
• Newtonian fluid flow
• Plastic• < Y: elastic; ≥ Y: Newtonian• Yield strength Y may be a function of pressure,
pressure vibrations, damage and internal energy.
€
ε =σE
€
˙ ε =σ
η
TEKTON (Finite-Element)
• Lagrangian
• Complex rheology
• Limited strength
• Faults
• No inertia
• Lagrangian
• Limited rheology
• Complex strength
• No faulting
• Inertia
SALES-2 (Hydrocode)
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
TEKTON Silverpit Mesh
SALES-2 Silverpit Mesh
SALES-2 Silverpit Mesh
SALES-2 Silverpit Mesh
SALES-2 Silverpit Mesh
Results
• Central, near-surface, deformation differs• Comparable uplift at depth, few hundred m• Timescales for deformation differ• Magnitudes and orientations of surface
stresses outside of crater are consistent• Stress orientations and consequently fault
types are broadly consistent with Silverpit observations