hp discontinuous Galerkin methods for parametric, wind-driven water wave models

Conroy, Colton J.; Kubatko, Ethan J.; Nappi, Angela; Sebian, Rachel A.; West, Dustin W.; Mandli, Kyle T.

doi:10.1016/j.advwatres.2018.04.008

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…However, the goal of using high-order polynomial approximations is to use coarser meshes, which results in better computational efficiency in terms of the number of degrees of freedom necessary to achieve a certain level of accuracy (high-order local polynomials produce more accurate results more efficiently than low-order methods). This is explicitly shown in the works of Kubatko et al (2006), Kubatko et al (2009), and Conroy et al (2018).…”

Section: Verificationmentioning

confidence: 84%

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

Conroy

Lev

2021

Geosci. Model Dev.

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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.

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Section: Verificationmentioning

confidence: 84%

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

Conroy

Lev

2021

Geosci. Model Dev.

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“…To quantify air-water interactions over Lake Erie and generate input data for the moment field equations, we apply the nonlinear solution method outlined in § 3.4 to observational atmospheric data obtained from 27 meteorological stations owned and operated by the National Oceanic and Atmospheric Association (NOAA); the positions of the 27 stations are illustrated in figure 7 in Conroy et al (2018). The exponents of the structure functions of the velocity measure (3.51) are shown in figures 2 and 3 while the dimension of the support of the energy measures are shown in table 1.…”

Section: Air-water Interactionsmentioning

confidence: 99%

“…The energy spectrum associated with water waves encompasses a vast range of frequencies. On one end of the spectrum are low-frequency tidal waves generated by the mutual attraction of the Sun, Moon and Earth while on the other end are high-frequency ripples, the periods of which are fractions of a second (see figure 1 in Conroy et al (2018)). A significant portion of energy contained within this spectrum resides in a high-frequency band of water waves generated by air-water interactions known as the wind sea.…”

Section: Introductionmentioning

confidence: 99%