Mixed volume element with characteristic mixed volume element method for compressible contamination treatment from nuclear waste

Abstract

This paper discusses numerical simulation of three-dimensional compressible contamination treatment from nuclear waste in porous media. The mathematical model includes five major unknowns, the pressure, Darcy velocity, brine, radionuclide and the temperature, determined by a parabolic equation, convection-dominated diffusion equations and the heat conductor equation. Considering the physical properties and the characters of equations, a mixed volume element with the characteristics is presented. For the flow equation, a conservative mixed volume element is used to obtain the pressure and Darcy velocity, and improves the accuracy of the latter. The characteristics could solve the convection dominated problems well and confirm the stability and accuracy at the front sharps, thus a characteristic mixed volume element is given for computing the concentrations and temperature. The composite procedures have the nature of conservation. Convergence analysis is discussed. Finally, an experimental system of partial differential equations is carried out and the feasibility and computational efficiency are illustrated. This method could solve such complicated problems well.

Keywords:

• Compressible contamination treatment
• mixed volume element-characteristic mixed volume element
• conservation
• convergence analysis
• numerical experiments

2010 Mathematics Subject Classifications:

• 65M15
• 65N30
• 65N12
• 75S05

Acknowledgments

The authors want to thank the reviewers and editors for their helpful suggestions to improve our work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Tongjun Sun  http://orcid.org/0000-0003-0626-0893

Additional information

Funding

This project was supported by the National Natural Science Foundation of China (Grant No. 11871312), Natural Science Foundation of Shandong Province (Grant No. ZR2016AM08).