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

• Main Authors: C. J. Conroy, E. Lev
• Format: Article
• Language: English
• Published: Copernicus Publications 2021-06-01
• Series: Geoscientific Model Development
• Online Access: https://gmd.copernicus.org/articles/14/3553/2021/gmd-14-3553-2021.pdf

<p>Lava flows present a significant natural hazard to communities around volcanoes and are typically slow-moving (<span class="inline-formula">&lt;1</span> to <span class="inline-formula">5</span> cm s<span class="inline-formula">⁻¹</span>) and laminar. Recent lava flows during the 2018 eruption of Kīlauea volcano, Hawai'i, however, reached speeds as high as <span class="inline-formula">11</span> m s<span class="inline-formula">⁻¹</span> 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M6" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="script">P</mi><mo>+</mo><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="41pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="ed10eee5475468a50927d9ebb450a4c9"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="gmd-14-3553-2021-ie00001.svg" width="41pt" height="14pt" src="gmd-14-3553-2021-ie00001.png"/></svg:svg></span></span> for polynomials of degree <span class="inline-formula">𝒫</span>. 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.</p>