7/30/2019 Opportunities Montes i

1/15

Magma Dynamics at CIGLaurent G. J. Montsi

University of MarylandContributions from:

Marc Spiegelman (Columbia)

Steve Quenette, David Lee (VPAC)

Wolfgang Bangerth (Texas A&M)

7/30/2019 Opportunities Montes i

2/15

Why Magma Dynamics? Probe into the mantle

Flux influenced bygeodynamics (temperature,flow, pressure)

Composition depends onsource and transport process

Complements geological andgeophysical investigation

Influences mantledynamics

Diferentiation / partitioningof heat producing elements

Buoyancy of melt andresiduum

Melt distributionmodel underneathultraslow ridgesMontsi, Hebert,

Behn, Barry, 2009

7/30/2019 Opportunities Montes i

3/15

A multiphysics problem Two-phase flow McKenzie 1984 formulation

Flow of melt controlled byDarcys law

Compaction of matrixcontrolled by bulk viscosity Stokes flow

Additional complexity Surface tension, grain boundary

processes, viscoelasticity,failure, thermodynamics

Use magma dynamics astestbed for multiphysicssoftware

10 m

Granitic melt in quartz(Laporte et al. 1997)

7/30/2019 Opportunities Montes i

4/15

Magma equations

t+V = 1 ( )

P

+

s

KP+ P

= K

P* + g[ ] +

fs

P*= V+ V

T( ) g

V =P

P = s0gz +P+ P

*

v = VK

P

*+P( )+ g[ ]

K=K0

n

Solve for , V, P, P*

Compute other variables

Spiegelman, Katz, and Simpson, 2007

Mass Conservation

Compressibility

Darcy/Helmholtz

Stokes

Permeability

7/30/2019 Opportunities Montes i

5/15

The MaDDs project Magma Dynamics Demonstration Suite 5 demonstration problems, described in

online document at CIG

1: 2D ridge / 3D segmented ridge (Stokes only) 2: Constant porosity ridge (Stokes + Darcy) 3: Shear bands 4: Solitary wave (Darcy flow + compaction)

5: Coupled ridge, forced melting

Test several software libraries / platforms No Gold Standard code!

7/30/2019 Opportunities Montes i

6/15

MaDDS platforms / software stgMaDDS project

David Lee (VPAC) Based on StGermain

Deal.II Wolgang Bangerth (TAMU) Adaptive mesh refinement

MultiMaDDS: Laurent Montsi (Maryland) COMSOL multiphysics

FEniCS/PETSc hybrid Marc Spiegelman (Columbia) Automatic code generation

MaDDS-2: Stokes flow anduniform porosity melt migration

(COMSOLTM, Montsi.)

7/30/2019 Opportunities Montes i

7/15

Status of stgMaDDS Most problems done

Stokes benchmark Constant porosity

ridge

Solitary wave Ridge with melting

Alpha versionreleased throughCIGs mercurialrepository andStGermain project

Compaction pressure for MaDDS-5: Fullycoupled 3D segmented isoviscous ridgewith melting. (Quenette and Lee one-pager)

7/30/2019 Opportunities Montes i

8/15

7/30/2019 Opportunities Montes i

9/15

Commercial multiphysicssoftware

COMSOL Multiphysics 3D Stokes Flow, Darcy

flow, and Helmholtzequation all implemented

Possibility of adaptivemeshing (steady-state),ALE, other physics

Evaluation Great for small, rapid

applications.

Easy to learn, even withlittle numerical knowledge

Cant tinker with solver

MaDDS-2 with COMSOL

Multiphysics (Montsi)

7/30/2019 Opportunities Montes i

10/15

MultiMaDDS status MaDDS-1: Stokes solver

Higher order element Unstructured mesh (ALE and AMR

possible)

Stress and temperature dependentrheology (with Mark Behn)

MaDDS-2: Stokes coupled withDarcy equation

MaDDS-4: Solitary waves: CustomPDE and Helmholtz equation

2D and 3DStokes flow and uniformporosity melt migration with

COMSOL MultiphysicsTM

7/30/2019 Opportunities Montes i

11/15

FEniCS/PETSc hybrid Developed by Marc Spiegelman Automated code generation (FFC/Dolfin) and

PDE-based block-preconditioners (PETSc)

MaDDS 1, 2, 4 done; Preliminary MaDDS-5

MaDDS-2 with FEniCS/PETSc

_ Stokes flow with cornerflow boundary conditions_ Melt trajectory for constantporosity

7/30/2019 Opportunities Montes i

12/15

MaDDS-4: Solitary wave (FEniCS)

7/30/2019 Opportunities Montes i

13/15

Adaptive refinement Deal.II (Bangerth)

Existing Darcy flow tutorials Stokes flow tutorial complete:

Step 22

Compaction equation underdevelopmentStokes flow forsegmented ridge withadaptive refinement(Burstedde et al.)

Deal.II tutorial step 22

3D Stokes flow underneath a ridge

7/30/2019 Opportunities Montes i

14/15

Summary / Evaluation

StGermain Flexible, but complex

COMSOLMultiphysics

Easy to use butimpossible to modify

Limited to smallproblems

FEniCS/PETSc Newly adopted: Stay

tuned!

Deal.II Flexible library Excellent tutorials

Multiphysics is a challenge! No ideal solution

7/30/2019 Opportunities Montes i

15/15

Possible future goals Multiphysics coupling

Mantle convection Tectonics

Rheology/failure Computational

thermodynamics

Adaptive refinement Deal.ii step 22 adaptively refinedmesh (Bangerth, 2008)

Mid-ocean ridge tectonics influences by dike intrusion

Tucholke, Behn, Buck, 2008