Introduction to geodynamic modelling Introduction to DOUAR David Whipp and Lars Kaislaniemi Department of Geosciences and Geography, Univ. Helsinki 1
Goals of this lecture Introduce DOUAR, a 3D thermomechanical numerical modelling program for creeping flows Present some of the important features in DOUAR that will be relevant for our use 2
DOUAR in a nutshell DOUAR (Braun et al., 2008) is a 3D finite-element code for modelling geodynamic processes It is designed to be run efficiently in parallel on computer clusters to be able to solve 3D problems at high spatial resolution We don t have time for a complete description of the numerical and computational aspects of DOUAR, but we ll see the highlights DOUAR is the word for Earth in the Breton language www.helsinki.fi/yliopisto May 20, 2018 3
<latexit sha1_base64="gxv2cpy2kibgecpa9euyg71uae0=">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</latexit> <latexit sha1_base64="gxv2cpy2kibgecpa9euyg71uae0=">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</latexit> <latexit sha1_base64="gxv2cpy2kibgecpa9euyg71uae0=">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</latexit> <latexit sha1_base64="gxv2cpy2kibgecpa9euyg71uae0=">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</latexit> Physics of DOUAR DOUAR calculates the flow of a highly viscous flow using the Stokes equation, which we have previously seen r (rv + rv T ) rp = g where η is the fluid viscosity, v is the fluid velocity, p is pressure, ρ is density, and g is the acceleration due to gravity. 4
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<latexit sha1_base64="ijsrrn09blu8bhwxqidf9ieqzqe=">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</latexit> <latexit sha1_base64="ijsrrn09blu8bhwxqidf9ieqzqe=">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</latexit> <latexit sha1_base64="ijsrrn09blu8bhwxqidf9ieqzqe=">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</latexit> <latexit sha1_base64="ijsrrn09blu8bhwxqidf9ieqzqe=">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</latexit> Rheologies Materials in DOUAR are either viscous or plastic (no elasticity) Nonlinear viscosity is modelled using the equation for temperature-dependent nonlinear viscosity = 0 " 1/(n 1) exp (Q/nRT ). where η 0 is the viscosity pre-factor, ε is the strain rate, n is the power law exponent, Q is the activation energy, R is the universal gas constant, and T is temperature in Kelvins 6
<latexit sha1_base64="uwaube5dhfpds3uemonct4aykzi=">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</latexit> <latexit sha1_base64="uwaube5dhfpds3uemonct4aykzi=">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</latexit> <latexit sha1_base64="uwaube5dhfpds3uemonct4aykzi=">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</latexit> <latexit sha1_base64="uwaube5dhfpds3uemonct4aykzi=">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</latexit> Rheologies There are several options for different plasticity criteria The Mohr-Coulomb criterion is what we use most often = c n tan where τ is the shear stress, c is the cohesion, σ n is the normal stress, and φ is the internal angle of friction 7
<latexit sha1_base64="uuf6x3qlzjncpjyncxx0dwz/hqi=">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</latexit> <latexit sha1_base64="uuf6x3qlzjncpjyncxx0dwz/hqi=">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</latexit> <latexit sha1_base64="uuf6x3qlzjncpjyncxx0dwz/hqi=">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</latexit> <latexit sha1_base64="uuf6x3qlzjncpjyncxx0dwz/hqi=">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</latexit> Thermal model The full 3D advection-diffusion equation with heat production is solved in DOUAR @T c @t + v rt = r krt + H where c is the heat capacity, T is temperature, t is time, k is the thermal conductivity, and H is the heat production per unit mass. 8
Numerical approach Braun et al., 2008 The finite-element mesh used in DOUAR is Eulerian and based on the octree division of space An Eulerian mesh is one that is fixed in space with respect to the fluid flowing within/through it The octree division of space is based on subdivisions of a unit cube 9
Numerical approach Braun et al., 2008 The unit cube is at the octree level 0 resolution, meaning that there are 2 0 elements along the width of the cube A mesh at octree level 6 would have 2 6, or 64 x 64 x 64 elements The initial octree resolution is an important setting in the input file 10
The octree division of space Level 2 Level 1 As an example, here is a face of a DOUAR model (2D, not full cube) at octree level 2 This is 2 subdivisions of the unit cube (red) Level 0 11
Other aspects of DOUAR (continued on whiteboard) 12
References Braun, J., Thieulot, C., Fullsack, P., DeKool, M., Beaumont, C. and Huismans, R., 2008. DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems. Physics of the Earth and Planetary Interiors, 171(1-4), pp.76-91. 13