Communications on Applied Mathematics and Computation >

2024 , Vol. 6 >Issue 3: 1600 - 1628

DOI: https://doi.org/10.1007/s42967-023-00289-3

ORIGINAL PAPERS

Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes

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  • 1 Department of Mathematics, Oregon State University, Kidder Hall 368, Corvallis, OR 97331, USA;
    2 Los Alamos National Laboratory, Theoretical Division, MS B284, Los Alamos, NM 87545, USA

Received date: 2022-12-03

  Revised date: 2023-05-13

  Accepted date: 2023-05-15

  Online published: 2024-12-20

Supported by

This work was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. The Los Alamos unlimited release number is LA-UR-22-30864.

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Abstract

We analyze mimetic properties of a conservative finite-volume (FV) scheme on polygonal meshes used for modeling solute transport on a surface with variable elevation. Polygonal meshes not only provide enormous mesh generation flexibility, but also tend to improve stability properties of numerical schemes and reduce bias towards any particular mesh direction. The mathematical model is given by a system of weakly coupled shallow water and linear transport equations. The equations are discretized using different explicit cellcentered FV schemes for flow and transport subsystems with different time steps. The discrete shallow water scheme is well balanced and preserves the positivity of the water depth. We provide a rigorous estimate of a stable time step for the shallow water and transport scheme and prove a bounds-preserving property of the solute concentration. The scheme is second-order accurate over fully wet regions and first-order accurate over partially wet or dry regions. Theoretical results are verified with numerical experiments on rectangular, triangular, and polygonal meshes.

Key words： Hyperbolic coupled system; Shallow water equations; Linear solute transport; Finite-volume (FV) schemes; Bounds-preservation

Cite this article

Naren Vohra, Konstantin Lipnikov, Svetlana Tokareva . Second-Order Accurate Structure-Preserving Scheme for Solute Transport on Polygonal Meshes[J]. Communications on Applied Mathematics and Computation, 2024 , 6(3) : 1600 -1628 . DOI: 10.1007/s42967-023-00289-3

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