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Center for Nonlinear Studies |
Contaminant transport in porous media constitutes the core of many engineering applications. For example, the design of a robust nuclear waste repository requires modelization of transport of radionuclides around a possible deep deposit in a sedimentary site. Simulations of the 3D contaminant transport are based on the approximate solution of the unsteady singularly perturbed convection-diffusion equation. The diffusion/dispersion tensor may be anisotropic, full, and even heterogeneous. Practical requirements to numerical schemes applied to the equation are well known:
- conservativity (to obey the mass conservation law);
- stability (to afford relatively large time steps);
- monotonicity (to obey the maximum principle to avoid negative concentrations);
- low numerical diffusivity (to recover sharp fronts of the contamination);
- second order accuracy in space and time (to have coarse discretization for smooth data);
- adaptivity (to be flexible to local mesh refinement).
Several schemes on conformal tetrahedral meshes are considered: finite element method, mixed finite element method, finite volume method, and operator splitting. Numerical features of the schemes are examined from the standpoint of the above requirements. We propose a new nonlinear scheme which satisfies the requirements and shows the competitive performance on a set of model test cases. We also discuss the application for a benchmark of Andra, the French agency in charge of studying the possibility of constructing a nuclear waste repository.
This is the joint work with Ivan Kapyrin from the Institute of Numerical Mathematics RAS.
Host: Mikhail Shashkov