Magma flow through elasticwalled dikes
Bokhove, O. and Woods, A.W. and Boer, A. de (2005) Magma flow through elasticwalled dikes. Theoretical and computational fluid dynamics, 19 (4). pp. 261286. ISSN 09354964
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Abstract:  A convection–diffusion model for the averaged flow of a viscous, incompressible magma through an elastic medium is considered. The magma flows through a dike from a magma reservoir to the Earth’s surface; only changes in dike width and velocity over large vertical length scales relative to the characteristic dike width are considered. The model emerges when nonlinear inertia terms in the momentum equation are neglected in a viscous, lowspeed approximation of a magma flow model coupled to the elastic response of the rock.
Stationary and travelingwave solutions are presented in which a Dirichlet condition is used at the magma chamber; and either a (i) freeboundary condition, (ii) Dirichlet condition, or (iii) chokedflow condition is used at the moving free or fixedtop boundary. A chokedflow boundary condition, generally used in the coupled elastic wave and magma flow model, is also used in the convection–diffusion model. The validity of this chokedflow condition is illustrated by comparing stationary flow solutions of the convection–diffusion and coupled elastic wave and magma flow model for parameter values estimated for the Tolbachik volcano region in Kamchatka, Russia. These free and fixedboundary solutions are subsequently explored in a conservative, local discontinuous Galerkin finiteelement discretization. This method is advantageous for the accurate implementation of the choked flow and freeboundary conditions. It uses a mixed Eulerian–Lagrangian finite element with special infinite curvature basis function near the free boundary and ensures positivity of the mean aperture subject to a timestep restriction. We illustrate the model further by simulating magma flow through host rock of variable density, and magma flow that is quasiperiodic due to the growth and collapse of a lava dome. 
Item Type:  Article 
Copyright:  © 2005 Springer 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
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Link to this item:  http://purl.utwente.nl/publications/61962 
Official URL:  http://dx.doi.org/10.1007/s0016200501664 
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