A benchmark comparison of spontaneous subduction models – towards a free surface
By H. Schmeling, A. Babeyko, A. Enns, C. Faccenna, F. Funiciello, Taras V. Gerya, G. Golabek, S. Grigull, B. Kaus, Gabriele Morra and 2 more. 2008
422 citations recorded by the source corpus.
Numerically modelling the dynamics of a self-consistently subducting lithosphere is a challenging task because of the decoupling problems of the slab from the free surface. We address this problem with a benchmark comparison between various numerical codes (Eulerian and Lagrangian, Finite Element and Finite Difference, with and without markers) as well as a laboratory experiment. The benchmark test consists of three prescribed setups of viscous flow, driven by compositional buoyancy, and with a low viscosity, zero-density top layer to approximate a free surface. Alternatively, a fully free surface is assumed. Our results with a weak top layer indicate that the convergence of the subduction behaviour with increasing resolution strongly depends on the averaging scheme for viscosity near moving rheological boundaries. Harmonic means result in fastest subduction, arithmetic means produces slow subduction and geometric mean results in intermediate behaviour. A few cases with the infinite norm scheme have been tested and result in convergence behaviour between that of arithmetic and geometric averaging. Satisfactory convergence of results is only reached in one case with a very strong slab, while for the other cases complete convergence appears mostly beyond presently feasible grid resolution. Analysing the behaviour of the weak zero-density top layer reveals that this problem is caused by the entrainment of the weak material into a lubrication layer on top of the subducting slab whose thickness turns out to be smaller than even the finest grid resolution. Agreement between the free surface runs and the weak top layer models is satisfactory only if both approaches use high resolution. Comparison of numerical models with a free surface laboratory experiment shows that (1) Lagrangian-based free surface numerical models can closely reproduce the laboratory experiments provided that sufficient numerical resolution is employed and (2) Eulerian-based codes with a weak surface layer reproduce the experiment if harmonic or geometric averaging of viscosity is used. The harmonic mean is also preferred if circular high viscosity bodies with or without a lubrication layer are considered. We conclude that modelling the free surface of subduction by a weak zero-density layer gives good results for highest resolutions, but otherwise care has to be taken in (1) handling the associated entrainment and formation of a lubrication layer and (2) choosing the appropriate averaging scheme for viscosity at rheological boundaries.
Subfields: Earth-Surface Processes, Geophysics
View Paper: https://www.semanticscholar.org/paper/f0c6359e97be89c4ae7f0d7a5e0932c7dcf080f2
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Citations in the corpus
- High Accuracy Mantle Convection Simulation through Modern Numerical Methods. II: Realistic Models and Problems (2017, methodology): “One can mitigate some of these effects by somehow averaging material properties on each cell (see, for example, [Schmeling et al.(2008), Deubelbeiss & Kaus(2008), Duretz et al.(2011),Thieulot(2015),Thielmann et al.(2014)]).”
- Numerical modelling of spontaneous slab breakoff and subsequent topographic response (2011, methodology): “In order to let the topography build up, a free surface is simulated at the air/ lithosphere interface by setting the viscosity of the air (1019 Pa.s) to be at least two orders ofmagnitude lower than the crust (Schmeling et al., 2008).”
- Subduction styles in the Precambrian: Insight from numerical experiments (2009, background): “The large viscosity contrast caused by these low viscosity boundary layers minimizes shear stresses (b104 Pa) at the top of the lithosphere making it an efficient free surface (cf. Schmeling et al., 2008).”
- Subduction initiation in nature and models: A review (2017, methodology): “In particular, these early models used free upper surface implementation based on “sticky water” approach, which became widespread two decades later (e.g., Gerya and Yuen, 2003; Gerya et al., 2008; Schmeling et al., 2008; Crameri et al., 2012; Crameri and Tackley, 2016).”
- Subduction initiation at passive margins: Numerical modeling (2010, background): “It is known that typical lithospheric mantle beneath continents is compositionally depleted and thus positively buoyant compared to the ambient mantle, which contributes to the stability of continents [Jordan, 1978; Sankaran, 2001; Carlson et al., 2005].”