Interface modeling in incompressible media using level sets in Escript

Abstract

We use a finite element (FEM) formulation of the level set method to model geological fluid flow problems involving interface propagation. Interface problems are ubiquitous in geophysics. Here we focus on a Rayleigh-Taylor instability, namely mantel plumes evolution, and the growth of lava domes. Both problems require the accurate description of the propagation of an interface between heavy and light materials (plume) or between high viscous lava and low viscous air (lava dome), respectively. The implementation of the models is based on Escript which is a Python module for the solution of partial differential equations (PDEs) using spatial discretization techniques such as FEM. It is designed to describe numerical models in the language of PDEs while using computational components implemented in C and C++ to achieve high performance for time-intensive, numerical calculations. A critical step in the solution geological flow problems is the solution of the velocitypressure problem. We describe how the Escript module can be used for a high-level implementation of an efficient variant of the well-known Uzawa scheme (Arrow et al., 1958). We begin with a brief outline of the Escript modules and then present illustrations of its usage for the numerical solutions of the problems mentioned above.

Modelling the lava dome extruded at Soufrière Hills Volcano, Montserrat, August 2005–May 2006

“…However, for simplicity we model the deformation of the entire dome as a ductile fluid, due to the low Deborah number, and vary the viscosity within the core and talus regions, whilst the free surface of the talus is modelled as a purely frictional material that rests at an angle of repose. The model equations are formulated in an Eulerian framework and the parallelised finite element based PDE solver eScript/Finley is utilised (Gross et al, 2007). Modelling the free surface is of primary importance because it is here that the talus develops and large deformations can occur, which requires a reliable and robust technique that can cope with large deformations.…”

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

“…Notable exceptions are Hale et al (2007), Gross et al (2007) and Bourgouin et al (2007) which are focussed on lava dome growth and/or mantle plumes, Suckale et al (2010) on bubbles dynamics in volcanic conduits, Zlotnik et al (2008) on gravitational instabilities and Hale et al (2010) on slab tear faults. In Braun et al (2008) a level set method is presented which is based on a 3-D set of triangulated points, which makes it a hybrid between tracers and level set functions.…”

Efficient solvers for incompressible fluid flows in geosciences

“…In this section we briefly outline the basic idea of escript [5] and show how to implement the evaluation step for the Schur complement (10). The escript module C194 is designed to implement pde based models in python.…”