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

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.

Implementing nonlinear viscoplasticity in ASPECT: benchmarking and applications to 3D subduction modeling

“…The detachment benchmark involves modeling of a highly nonlinear, power-law viscosity, which is often used in subduction modeling. Our observed model evolution compares well 5 with that of Schmalholz (2011) and other codes (Hillebrand et al, 2014;Thieulot et al, in prep. ) effective splitting of a compositional field into two bodies and how the rheology interacts with the compositional fields through localisation of deformation at the slab hinge.…”

“…Gerya et al, 2004;Andrews and Billen, 2009;Billen, 2009, 2010;van Hunen and Allen, 2011;Duretz et al, 2012Duretz et al, , 2014. Numerical modeling of slab detachment is computationally 20 challenging due to the mesh-resolution dependency of the strain (van Hunen and Allen, 2011) and the gradual decrease in monitoring particle density, the gradual overlapping of level sets (Hillebrand et al, 2014), or the gradual thinning of compositional fields (as is the case here) in the detachment area. Here we test ASPECT with the slab detachment model of Schmalholz …”

Improving Mass Conservation With the Tracer Ratio Method: Application to Thermochemical Mantle Flows

“…To reduce these errors, numerical filters can be applied (Lenardic & Kaula, 1993) as well as flux limiters (Harten, 1984;Roe, 1986;Sweby, 1984) and bound-preserving limiters (He et al, 2017). It is also possible to track the interface between materials through the advection of level sets (e.g., Hillebrand et al, 2014) or a hybrid between particle and level set methods (Samuel & Evonuk, 2010).…”

SEPRAN: A versatile finite-element package for a wide variety of problems in geosciences

“…Non-diffusive material transport has been modelled in several ways: first SEPRAN includes facilities for level set methods (Hillebrand et al, 2014). Besides this several alternative methods have been applied as extensions to SEPRAN such as: (1) marker chain methods similar to Christensen and Yuen (1984) were used in van Keken et a1.…”