Modeling Mantle Flow at the Subduction Zones on

Modeling Mantle Flow at the Subduction Zones on Earth Minjin Baek AMSC 689 A – Finite Element Modeling Student Project May 16, 2011

Motivation – Why deal. II? Adaptive Mesh Refinement (AMR) Advantages of AMR Start with solving on coarse grid Compute error Refine mesh until error < tolerance Same accuracy with less cost (uniformly fine meshes are expensive!) Achieve much higher resolution at areas of interest Great for solving geophysical problems since the action is localized Flexibility C++ program library, not software Can be written from scratch for complex work Well documented tutorials www. dealii. org - step 22

Subduction Model Subduction zone is a region where two tectonic plates collide and one sinks beneath the other Compute mantle flow field and pressure in the interior of Earth at subduction zones by solving Stokes flow equations This simplified model includes two trapezoidal geometries, each representing the oceanic corner and arc corner Not coupled – two systems are treated separately Dip angle of 45° Arc corner Oceanic corner Turcotte and Schubert (2002)

Stokes Flow Equations Non-dimensional model μ = 1 (uniform viscosity) bx 2 + by 2 = 1 (constant plate velocity) Incompressible flow No external forces, thus flow is entirely driven by subducting plate velocity (f = 0) Fluid velocity (u) is set equal to plate velocity (b) on Γ 1 Natural boundary conditions of σ n = 0 everywhere else

Model Geometry Oceanic Corner Arc Corner

Weak Formulation

Solving with Schur Complement

Flow Field in Oceanic Corner

Flow Field in Arc Corner

Pressure in Oceanic Corner

Pressure in Oceanic Corner

Pressure in Arc Corner

“Coupled” Subduction Model Coupling two sides Solve stokes flow equations for the “oceanic corner” as previously done Instead of prescribing a moving wall condition at the ramp (Γ 3) of the “arc corner” geometry, set the normal stress at the boundary equal to the external pressure in normal direction, which is obtained from the “oceanic corner” solution

“Coupled” Subduction Model Oceanic Corner Arc Corner

Flow Field in Arc Corner