High performance mantle convection modeling

Transcription

1 High performance mantle convection modeling Jens Weismüller, Björn Gmeiner, Siavash Ghelichkhan, Markus Huber, Lorenz John, Barbara Wohlmuth, Ulrich Rüde and Hans-Peter Bunge Geophysics Department of Earth- and Environmental Sciences Ludwig-Maximilians-Universität München SPPEXA annual plenary meeting, TERRA Weismüller et al. High performance mantle convection modeling 1/26

2 The Earth s mantle Solid layer between crust and core Makes up about 84% of the Earth s volume Solid, but ductile Creeping, viscous flow Convects on time scales of cm/a Image: mail.colonial.net Weismüller et al. High performance mantle convection modeling 2/26

3 Mantle Convection Regulates the long term thermal evolution of the Earth Controls heat loss of the core Driving force behind plate tectonics Image: mail.colonial.net Weismüller et al. High performance mantle convection modeling 3/26

4 Plate tectonics Earth s magnetic field alternates polarity Solidifying rock takes on the current magnetic field of the Earth Residual magnetization can be used to reconstruct tectonic plate motion history Image: geology.sdsu.edu Weismüller et al. High performance mantle convection modeling 4/26

5 Seismic tomography Seismic tomography images shear velocities in the mantle Using mineralogic models, they can be converted to buoyancies Ritsema et al, S40RTS Weismüller et al. High performance mantle convection modeling 5/26

6 Seismic tomography Seismic tomography images shear velocities in the mantle Using mineralogic models, they can be converted to buoyancies Together with plate velocities: Terminal and boundary conditions Weismüller et al. High performance mantle convection modeling 6/26

7 Brief history of mantle convection modeling Glatzmeier, 1988 Baumgardner, 1985 Global models became available in the late 80s They were parallelized in the 90s Bunge and Baumgardner, 1995 Tackley et al, 1993 Weismüller et al. High performance mantle convection modeling 7/26

8 Convective planform (Earth and other planets) Link to seismology Geodetic observations Mineralogy Rheological effects Thermal evolution... Zhong et al, 2007 Tackley, 2012 Schuberth et al, 2009 Weismüller et al. High performance mantle convection modeling 8/26

9 Towards extreme resolutions Most classic codes scale to 1, 000 processors Current supercomputers have 1,000,000 cores New class of problems: Fluid dynamic inverse models Complex non-linear problems Weismüller et al. High performance mantle convection modeling 9/26

10 Future applications: Adjoint Reconstruct past state of the mantle with inverse models Start from initial guess Iteratively run forward and backwards simulations Ghelichkhan et al, submitted Weismüller et al. High performance mantle convection modeling 10/26

11 Complex, non-linear rheologies Classically, flow laws are linear: η = f(x,t) Non-linear behaviour increasingly in focus: η = f(x,t,v) Conventional stress-strain-relations might not hold: η =? Deformation mechanisms of MgO: Will need to deal with computationally challenging rheologies Cordier et al, 2012 Weismüller et al. High performance mantle convection modeling 11/26

12 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Simplified Navier-Stokes equations Slow deformation by creep Weismüller et al. High performance mantle convection modeling 12/26

13 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Simplified Navier-Stokes equations Slow deformation by creep Force balance between friction and buoyancy Weismüller et al. High performance mantle convection modeling 12/26

14 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Simplified Navier-Stokes equations Slow deformation by creep Force balance between friction and buoyancy Dominated by viscous term η u Global models Weismüller et al. High performance mantle convection modeling 12/26

15 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Simplified Navier-Stokes equations Slow deformation by creep Force balance between friction and buoyancy Dominated by viscous term η u Global models Time derivative only in heat equation Weismüller et al. High performance mantle convection modeling 12/26

16 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Start with initial T Solve Stokes equations for u and p Integrate heat equation for T forward in time Weismüller et al. High performance mantle convection modeling 13/26

17 Governing equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation Start with initial T Solve Stokes equations for u and p Integrate heat equation for T forward in time Weismüller et al. High performance mantle convection modeling 13/26

18 Solving the Stokes equations η u p +RaT = 0 u = 0 } Stokes equations t T = u T κ T } Heat equation So called saddle point problem: ( A B T B 0 )( u p ) = ( f 0 ) Many possible solution schemes Expensive part is solution of Au = f Weismüller et al. High performance mantle convection modeling 14/26

19 Adaptive mesh refinement Flow structures evolve down to the kilometer-scale Refine the mesh where things happen Administrational overhead Burstedde et al, 2013 Kronbichler et al, 2012 Weismüller et al. High performance mantle convection modeling 15/26

20 Extreme resolutions Alternative Concept: Equal resolution throughout the mantle + No administrative overhead Computational overhead in areas that need no high resolution Weismüller et al. High performance mantle convection modeling 16/26

21 Hierarchical Hybrid Grids Discretizing a planet not possible with fully structured grid More efficient solvers on structured grids Block-structured grid: Unstructured input mesh as multigrid s coarse grid Regularly refined Weismüller et al. High performance mantle convection modeling 17/26

22 Hierarchical Hybrid Grids On input mesh: Geometric hierarchy of... Volumes (tetrahedra) Faces (triangles) Edges Nodes Communication reduction by Independent solution within geometric elements Communication of ghost layers Weismüller et al. High performance mantle convection modeling 18/26

23 Hierarchical Hybrid Grids Matrix free stencil code Fully stencil-based for constant viscosity (30FLOPS per grid point and operator evaluation) Efficient on-the-fly stencil assembly for more complex cases Weismüller et al. High performance mantle convection modeling 19/26

24 The asthenosphere Mechanically weak uppermost layer of the mantle Traditionally: plausible depth extent of 660 km Low viscosity: Pas (compared to Pas in the lower mantle) Possible causes: Partial melting, water, mineralogy (p/t) Weismüller et al. High performance mantle convection modeling 20/26

25 Thickness of the asthenosphere from seismology Full waveform seismic tomography studies have imaged a thin horizontal layer of km depth extent Fichtner, 2009 Weismüller et al. High performance mantle convection modeling 21/26

26 Thickness of the asthenosphere from seismology Full waveform seismic tomography studies have imaged a thin horizontal layer of km depth extent Maybe the asthenosphere is only km thick? Fichtner, 2009 Weismüller et al. High performance mantle convection modeling 21/26

27 Fast flow velocities Buried landscape in seismic reflection data on northwest european continental shelf Uplift history hints at passage of sublithospheric material at 35 cm/a Hartley et al, 2011 Weismüller et al. High performance mantle convection modeling 22/26

28 Fast flow velocities Buried landscape in seismic reflection data on northwest european continental shelf Uplift history hints at passage of sublithospheric material at 35 cm/a 35 cm/a: Dynamically plausible? Weismüller et al. High performance mantle convection modeling 22/26

29 Linking channel thickness and flow velocities Model setup: Depth [km] Channel thickness 1000km 660km 410km 200km 100km Viscosity [Pa s] 5 scenarios Viscosity profiles according to observational constraints Computations on JUQUEEN with: degrees of freedom 32numerical layers in the asthenosphere 65536processes Weismüller et al. High performance mantle convection modeling 23/26

30 Linking channel thickness and flow velocities Synthetic simulations (left): with stagnant lid (no-slip) and mobile lid (free slip) Tomography/plate-driven simulations (right) Weismüller et al. High performance mantle convection modeling 24/26

31 Linking channel thickness and flow velocities Viscosity ratio (lower/upper mantle) [-] thick channel low velocity thin channel high velocity Velocities correspond to preditions by a simple Poiseuille flow model Asthenosphere velocity [-] (normalized to 1000 km scenario) , Poiseuille Observation driven Synthetic, stagnant lid Synthetic, mobile lid Channel thickness [km] Weismüller et al. High performance mantle convection modeling 25/26

32 Conclusions Modern computers become faster, but more heterogeneous new software needed Hierarchical Hybrid Grids (HHG) are a promising approach for mantle convection Using HHG, we can explain recent geological observations (fast flow, thin asthenosphere) dynamically Weismüller et al. High performance mantle convection modeling 26/26