A study of localization limiters and mesh dependency in earthquake rupture

Abstract

No complete physically consistent model of earthquake rupture exists that can fully describe the rich hierarchy of scale dependencies and nonlinearities associated with earthquakes. We study mesh sensitivity in numerical models of earthquake rupture and demonstrate that this mesh sensitivity may provide hidden clues to the underlying physics generating the rich dynamics associated with earthquake rupture. We focus on unstable slip events that occur in earthquakes when rupture is associated with frictional weakening of the fault. Attempts to simulate these phenomena directly by introducing the relevant constitutive behaviour leads to mesh-dependent results, where the deformation localizes in one element, irrespective of size. Interestingly, earthquake models with oversized mesh elements that are ill-posed in the continuum limit display more complex and realistic physics. Until now, the mesh-dependency problem has been regarded as a red herringbut have we overlooked an important clue arising from the mesh sensitivity? We analyse spatial discretization errors introduced into models with oversized meshes to show how the governing equations may change because of these error terms and give rise to more interesting physics.

Mesh dependence and slip complexity in earthquake fault models

“…We showed in detail in Reference [16] that only considering discretization errors up to order O( 2 2 ) in Equation (3) will remove the largest contribution to the spatial discretization error. Thus, the reason we get more complex soliton-like behaviour occurring in the numerical solution of the 1-D nonlinear wave equation using coarser meshes is because the spatial discretization errors present lead to the solution of the soliton wave equation not a shock wave equation.…”

Numerical modelling of damage evolution and fracture propagation in brittle materials

“…Additionally, three-dimensional simulations in a homogeneous material can show mesh-dependency [113]. Different researchers have discussed effects of mesh dependence in different fields such as earthquake rupture [114], finite element blast structural analysis induced by non-uniform pressure distribution from high explosive blast wave [115] and two-mesh coupled gas flow-solid interaction model for 2-D blast analysis in fractured media [116]. In the literature, it is widely acknowledged that local continuum damage models lead to mesh dependency, [117,118].…”