Interface Modeling in Incompressible Media using Level Sets in Escript

We use a nite element (FEM) formulation of the level set method to model geo-logical uid ow 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), re-spectively. The implementation of the models is based on Escript which is a Python module for the solution of partial dierential equations (PDEs) using spatial dis-cretization 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 ow problems is the solution of the velocity-pressure problem. We describe how the Escript module can be used for a high{level implementation of an ecient 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. Key words: Partial dierential equations, numerical software, level set method, Uzawa scheme, Rayleigh-Taylor instability, mantle plumes, lava dome modeling Corresponding author