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A 3D Two-Phase Conservative Level-Set Method Using an Unstructured Finite-Volume Formulation

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Mathematical and Computational Models of Flows and Waves in Geophysics

Part of the book series: CIMAT Lectures in Mathematical Sciences ((CIMATLMS))

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Abstract

Mathematical and computational modeling of two-phase flows simulations is widely used in many physical and industrial applications. Moreover, a numerical model with an unstructured level-set method allows for flexible applications to geophysical flows of arbitrary domains with the presence of many obstacles. In this work, we introduce a new second-order time- and space-accurate method developed to solve in parallel a conservative level-set equation in three-dimensional geometries. We employ a θ-method for the time integration and a finite-volume method on prisms elements consisting of triangular cells on the horizontal plane and several layers in the vertical direction for the space discretization. We apply an upwind scheme with a Local Extremum Diminishing flux limiter to approximate the convective terms that solves the level-set equation using either the Heaviside function or the regularized characteristic function. Moreover, we present a parallelization strategy using a block domain decomposition technique and Message Passing Interface. The numerical method is initially validated against classical advection test cases and unstructured grids. Finally, several interface-capturing tests, including topology changes, are used to demonstrate the capabilities and performance of the proposed scheme.

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Acknowledgements

The authors gratefully acknowledge the Mexican Council of Science and Technology projects Investigadoras e Investigadores por Mexico and postdoctoral for their financial supports.

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Authors and Affiliations

  1. CONACYT–Centro de Investigación en Matemáticas A. C., CIMAT Unidad Mérida, Mérida, Yucatán, Mexico

    Miguel UhZapata & Reymundo ItzáBalam

Authors
  1. Miguel UhZapata
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  2. Reymundo ItzáBalam
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Correspondence to Miguel UhZapata .

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Editors and Affiliations

  1. Institute of Mathematics, National Autonomous University of Mexico, Juriquilla, Querétaro, Mexico

    Gerardo Hernández-Dueñas

  2. Department of Mathematics, CIMAT, Guanajuato, Mexico

    Miguel Angel Moreles

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UhZapata, M., ItzáBalam, R. (2022). A 3D Two-Phase Conservative Level-Set Method Using an Unstructured Finite-Volume Formulation. In: Hernández-Dueñas, G., Moreles, M.A. (eds) Mathematical and Computational Models of Flows and Waves in Geophysics. CIMAT Lectures in Mathematical Sciences. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-12007-7_3

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