Nonlinear Monotone FV Schemes for Radionuclide Geomigration and Multiphase Flow Models

We present applications of the nonlinear monotone finite volume method to radionuclide transport and multiphase flow in geological media models. The scheme is applicable for full anisotropic discontinuous permeability or diffusion tensors and arbitrary conformal polyhedral cells. We consider two versions of the nonlinear scheme: two-point flux approximation preserving positivity of the solution and compact multi-point flux approximation that provides discrete maximum principle. We compare the new nonlinear schemes with the conventional linear twopoint and multi-point (O-scheme) flux approximations. Both new nonlinear schemes have compact stencils and a number of important advantages over the traditional linear discretizations. Two industrial applications are discussed briefly: radionuclides transport modeling within the radioactive waste safety assessment and multiphase flow modeling of oil recovery process. Ivan Kapyrin Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia, Institute of Nuclear Safety, B.Tulskaya 52, Moscow, Russia, e-mail: [email protected] Kirill Nikitin Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia, Institute of Nuclear Safety, B.Tulskaya 52, Moscow, Russia, e-mail: [email protected] Kirill Terekhov Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia, e-mail: [email protected] Yuri Vassilevski Institute of Numerical Mathematics, Gubkina 8, Moscow, Russia, Moscow Institute of Physics and Technology, Institutski 9, Dolgoprudny, M.R., Russia, e-mail: [email protected]