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A positivity-preserving nonlinear finite volume scheme for radionuclide transport calculations in geological radioactive waste repository

Gang Peng (College of Mathematics and System Sciences, Xinjiang University, Urumqi, China)
Zhiming Gao (Institute of Applied Physics and Computational Mathematics, Beijing, China)
Wenjing Yan (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China)
Xinlong Feng (College of Mathematics and System Sciences, Xinjiang University, Urumqi, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 29 August 2019

Issue publication date: 16 January 2020

Abstract

Purpose

This paper aims to consider numerical simulation for radionuclide transport calculations in geological radioactive waste repository.

Design/methodology/approach

The nonlinear two-point flux approximation is used to discretize the diffusion flux and has a fixed stencil. The cell-vertex unknowns are applied to define the auxiliary unknowns and can be interpolated by the cell-centered unknowns. The approximation of convection flux is based on the second-order upwind method with a slope limiter.

Findings

Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Originality/value

A new positivity-preserving nonlinear finite volume scheme is proposed to simulate the far-field model used in the geological radioactive waste repository. Numerical results illustrate that the positivity-preserving is satisfied in solving this convection-diffusion system and has a second-order convergence rate on the distorted meshes.

Keywords

Acknowledgements

The authors would like to thank the editor and referees for their valuable comments and suggestions, which helped us to improve the results of this paper.

AMS Subject Classification: 65M08, 76S05, 65N12.

Citation

Peng, G., Gao, Z., Yan, W. and Feng, X. (2020), "A positivity-preserving nonlinear finite volume scheme for radionuclide transport calculations in geological radioactive waste repository", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 2, pp. 516-534. https://doi.org/10.1108/HFF-04-2019-0327

Publisher

:

Emerald Publishing Limited

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