A discontinuous Galerkin finite-element model for fast channelized lava flows v1.0

Abstract

Lava flows present a significant natural hazard to communities around volcanoes and are typically slow-moving (<1 to 5 cm s−1) and laminar. Recent lava flows during the 2018 eruption of Kīlauea volcano, Hawai'i, however, reached speeds as high as 11 m s−1 and were transitional to turbulent. The Kīlauea flows formed a complex network of braided channels departing from the classic rectangular channel geometry often employed by lava flow models. To investigate these extreme dynamics we develop a new lava flow model that incorporates nonlinear advection and a nonlinear expression for the fluid viscosity. The model makes use of novel discontinuous Galerkin (DG) finite-element methods and resolves complex channel geometry through the use of unstructured triangular meshes. We verify the model against an analytic test case and demonstrate convergence rates of P+1/2 for polynomials of degree 𝒫. Direct observations recorded by unoccupied aerial systems (UASs) during the Kīlauea eruption provide inlet conditions, constrain input parameters, and serve as a benchmark for model evaluation.