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

doi:10.1007/s42967-023-00289-3

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (3): 1600-1628.doi: 10.1007/s42967-023-00289-3

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

Naren Vohra¹, Konstantin Lipnikov², Svetlana Tokareva²

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

收稿日期:2022-12-03 修回日期:2023-05-13 接受日期:2023-05-15 发布日期:2024-12-20
通讯作者: Naren Vohra,vohran@oregonstate.edu;Konstantin Lipnikov,lipnikov@lanl.gov;Svetlana Tokareva,tokareva@lanl.gov E-mail:vohran@oregonstate.edu;lipnikov@lanl.gov;tokareva@lanl.gov
基金资助:
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.

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

Naren Vohra¹, Konstantin Lipnikov², Svetlana Tokareva²

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:2022-12-03 Revised:2023-05-13 Accepted:2023-05-15 Published:2024-12-20
Contact: Naren Vohra,vohran@oregonstate.edu;Konstantin Lipnikov,lipnikov@lanl.gov;Svetlana Tokareva,tokareva@lanl.gov E-mail:vohran@oregonstate.edu;lipnikov@lanl.gov;tokareva@lanl.gov
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.

摘要/Abstract

摘要： 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.

关键词: Hyperbolic coupled system, Shallow water equations, Linear solute transport, Finite-volume (FV) schemes, Bounds-preservation

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

中图分类号:

65M08
65M12

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.

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

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

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