The mathematical model for the compressible contamination treatment from nuclear waste is defined by a nonlinear system of partial differential equations including a parabolic equation for the pressure, several convection-diffusion equations for the concentrations of different factors, a heat conduction equation for the temperature. Considering the physical nature, the features of model and the computational scale, the authors combine a mixed volume element, the characteristics and fractional step differences together for solving this problem. The conservative physical nature is preserved for the pressure, and the Darcy velocity is computed at the same time. Numerical computations are accomplished quite well at sharp fronts without numerical oscillation or dispersion. Meanwhile, a large step and the speedup algorithm are used, and the computational work is decreased greatly. An optimal second order estimate in  norm is discussed.

mixed volume element, characteristic fractional step, local conservation, error estimates, numerical experiments.

Received: October 8, 2021; Accepted: October 30, 2021; Published: January 4, 2022

How to cite this article: Changfeng Li, Yirang Yuan and Qing Yang, A mixed volume element method with characteristic fractional step differences for compressible contamination treatment from nuclear waste, Far East Journal of Applied Mathematics 111(2) (2021), 59-96. DOI: 10.17654/0972096021002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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