A new finite volume scheme preserving positivity for radionuclide transport calculations in radioactive waste repository

In order to simulate a far field model used in geological radioactive waste repository, a new finite volume scheme preserving positivity on arbitrary convex polygonal meshes with second order accuracy is proposed in this paper. The model problem describes the coupled process of diffusion, convection and chemical reaction, in which the diffusion tensors are highly anisotropic and heterogeneous. The classic implicit and explicit schemes are used in the temporal discretization. The discretization of diffusive flux in Sheng and Yuan (2016) is utilized, and the discretization of convective flux is based on a new corrected upwind scheme that depends on some available informations of diffusive flux. The resulting scheme is positivity-preserving and locally conservative, and has only cell-centered unknowns. Numerical results are presented to show that the performance of our positivity-preserving scheme for the numerical simulation of radionuclide transport problem.