Using the level set method in geodynamical modeling of multi-material flows and Earth's free surface

B Hillebrand,C Thieulot,A P Van Den Berg,W Spakman,T Geenen

doi:10.5194/se-5-1087-2014

B Hillebrand, C Thieulot + Show 3 more

Open Access

https://doi.org/10.5194/se-5-1087-2014

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Abstract

Abstract. The level set method allows for tracking material surfaces in 2-D and 3-D flow modeling and is well suited for applications of multi-material flow modeling. The level set method utilizes smooth level set functions to define material interfaces, which makes the method stable and free of oscillations that are typically observed in case step-like functions parameterize interfaces. By design the level set function is a signed distance function and gives for each point in the domain the exact distance to the interface as well as on which side it is located. In this paper we present four benchmarks which show the validity, accuracy and simplicity of using the level set method for multi-material flow modeling. The benchmarks are simplified setups of dynamical geophysical processes such as the Rayleigh–Taylor instability, post-glacial rebound, subduction and slab detachment. We also demonstrate the benefit of using the level set method for modeling a free surface with the sticky air approach. Our results show that the level set method allows for accurate material flow modeling and that the combination with the sticky air approach works well in mimicking Earth's free surface. Since the level set method tracks material interfaces instead of materials themselves, it has the advantage that the location of these interfaces is accurately known and that it represents a viable alternative to the more commonly used tracer method.

Highlights

Accurate modeling of geodynamical processes involving large deformation, e.g., mantle flow, subduction evolution or slab tearing, is a key research goal in computational geodynamics
For instance multiple materials are important to investigate the influence of an oceanic crust on the decoupling of subducting and overriding plates as well as on the buoyancy of the subducting slab (Behounková and Cižková, 2008; van Hunen and van den Berg, 2008; Androvicová et al, 2013); they are important for research involving subduction termination by continental collision (e.g., Baumann et al, 2010; Magni et al, 2012)
All the benchmarks show the accuracy of the level set method

Summary

Introduction

Accurate modeling of geodynamical processes involving large deformation, e.g., mantle flow, subduction evolution or slab tearing, is a key research goal in computational geodynamics. The level set method is a well-researched interface tracking technique which was originally devised by Osher and Sethian (1988). It tracks an interface by defining it as the zero valued isocontour of a smooth function. If denotes the interface that is to be associated and tracked with a level set function φ, and is a bounded region, bounded by just the interface or the interface and the boundaries of the model domain, φ will be defined as (Osher and Fedkiw, 2001): φ(r, t) > 0 for r ∈.

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