A Mesh-free Lagrangian Fluid Model for Creeping Flow of History-dependant Material with Applications to Extensional Tectonics

A persistent problem in numerical models of tectonic processes is that deformation can be large (suggesting the use of an Eulerian frame) as well as localized and dependent on heterogeneous materials (suggesting the use of a Lagrangian frame). Eulerian fluid models have difficulty tracking material boundaries and histories while Lagrangian grid-based models must undergo regridding when deformation becomes large. Both approaches result in the numerical diffusion of material properties. We have developed a mesh-free Lagrangian fluid model for creeping flow using Smooth Particle Hydrodynamics for the spatial discretization and solving the equations for incompressible Stoke's flow. Strain localization occurs in response to non-linear rheology. Tracking of material properties and deformation history is inherent in this formulation which simplifies the modeling of the large deformation of heterogeneous material. We apply this model to the problem of lithospheric stretching with laminated, non-homogeneous, non-linear rheology designed to simulate a brittle (visco-plastic) upper crust and a fluid (viscous) lower crust. We compare our model with other grid-based and particle models.