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A scalable well-balanced Taylor-Galerkin scheme for a lava flow depth-integrated model with point source vents

by F. Gatti and C. de Falco and M. Fois and L. Formaggia

(Report number 2025-07)

Abstract
We propose a scalable well-balanced numerical method to efficiently solve a modified set of shallow water equations targeting the dynamics of lava flows. The governing equations are an extension of a depth-integrated model already available in the literature and proposed to model lava flows. Here, we consider the presence of vents that act as point sources in the mass and energy equations. Starting from a scheme developed in the framework of landslide simulation, we prove its capability to deal with lava flows. We show its excellent performances in terms of parallel scaling efficiency while maintaining good results in terms of accuracy. To verify the reliability of the proposed simulation tool, we first assess the accuracy and efficiency of the scheme on ideal scenarios. In particular, we investigate the well-balancing property, we simulate benchmarks taken from the literature in the framework of lava flow simulations, and provide relevant scaling results for the parallel implementation of the method. Successively, we challenge the scheme on a real configuration taken from the available literature.

Keywords: Taylor-Galerkin scheme, Depth-integrated models, Parallel simulations, Lava flows, Quadtree mesh, Path-conservative method.

@Techreport{GdFF25_1128,
  author = {F. Gatti and C. de Falco and M. Fois and L. Formaggia},
  title = {A scalable well-balanced Taylor-Galerkin scheme for a lava flow depth-integrated model with point source vents},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2025-07},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2025/2025-07.pdf },
  year = {2025}
}

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