Studying the influence of a solid shell on lava dome growth and evolution using the level set method

Bourgouin, L., Muhlhaus, H. B., Hale, A. J. and Arsac, A. (2007) Studying the influence of a solid shell on lava dome growth and evolution using the level set method. Geophysical Journal International, 170 3: 1431-1438. doi:10.1111/j.1365-246X.2007.03471.x

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Author Bourgouin, L.
Muhlhaus, H. B.
Hale, A. J.
Arsac, A.
Title Studying the influence of a solid shell on lava dome growth and evolution using the level set method
Journal name Geophysical Journal International   Check publisher's open access policy
ISSN 0956-540X
Publication date 2007
Sub-type Article (original research)
DOI 10.1111/j.1365-246X.2007.03471.x
Open Access Status File (Publisher version)
Volume 170
Issue 3
Start page 1431
End page 1438
Total pages 8
Place of publication Oxford, United Kingdom
Publisher Oxford University Press
Collection year 2008
Language eng
Abstract A finite element formulation of the level set method, a technique to trace flow fronts and interfaces without element distortion, is presented to model the evolution of the free surface of a spreading flow for a highly viscous medium on a horizontal surface. As an example for this class of problem we consider the evolution of an axisymmetric lava dome. Equilibrium configurations of lava domes have been modelled analytically as brittle shells enclosing pressurized magma. The existence of the brittle shell may be viewed as a direct consequence of the strong temperature dependence of the viscosity. The temperature dependence leads to the formation of a thin predominantly elastic-plastic boundary layer along the free surface and acts as a constraint for the shape and flow of the lava dome. In our model, we adopt Iverson's assumption that the thin boundary layer behaves like an ideal plastic membrane shell enclosing the ductile interior of the lava dome. The effect of the membrane shell is then formally identical to a surface tension-like boundary condition for the normal stress at the free surface. The interior of the dome is modelled as a Newtonian fluid and the axisymmetry equations of motion are formulated in a Eulerian framework. We show that the level set is an effective tool to trace and model deforming interfaces for the example of the free surface of a lava dome. We demonstrate that Iverson's equilibrium dome shapes are indeed steady states of a transient model. We also show how interface conditions in the form of surface tension involving higher order spatial derivative (curvature) can be considered within a standard finite element framework.
Keyword Geochemistry & Geophysics
Level set method
Computational volcanology
Surface tension
Q-Index Code C1
Q-Index Status Confirmed Code

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Created: Mon, 18 Feb 2008, 14:48:45 EST