A 3-D Lagrangian finite element algorithm with remeshing for simulating large-strain hydrodynamic instabilities in power law viscoelastic fluids

摘要

We present a three-dimensional (3-D) numerical algorithm (PINK-3D) that is based on the finite element method. The algorithm is designed to simulate hydrodynamic instabilities in power law viscoelastic fluids under gravity. These instabilities are caused by large and sharp contrasts in mechanical strength and/or density between different materials (e.g., folding, necking, or Rayleigh-Taylor diapirism). The instabilities are controlled by the geometry of the material interfaces and the related intralayer stress distribution when amplitudes of the material interfaces are still low. The presented algorithm combines a deformable Lagrangian mesh with remeshing in order to accurately simulate the low-amplitude stages of the emerging instabilities, and also to simulate the large-strain evolution of the structures emerging from these instabilities. The remeshing is based on material interfaces that accurately track the boundaries between materials with strongly varying material properties (e.g., effective viscosity or power law stress exponent). We describe here the main technical details of the 3-D algorithm. The accuracy of the 3-D algorithm is demonstrated with comparisons between the numerical results and 2-D and 3-D analytical solutions for folding, necking, Rayleigh-Taylor diapirism, and circular inclusions in viscous medium. We also benchmark the 3-D algorithm with results of a different 2-D finite element algorithm to test the accuracy of the large-strain results with remeshing. Furthermore, two tests are presented that show the accuracy of the viscoelasticity implementation. PINK-3D is also used to study 3-D necking applied to lithospheric slab detachment, and 2-D and 3-D folding applied to fold nappe formation. In particular, we apply the 3-D code to quantify and visualize the evolution of the 3-D finite strain ellipsoid for the developing 3-D structures.