SUMMARYIn this paper, a transient injection flow at low Mach number regime is investigated. Three different methods are used and analyzed. Two of them are based on asymptotic models of the Navier-Stokes equations valid for small Mach numbers, whereas the other is based on the full compressible Navier-Stokes equations, with particular care given to the discretization at low Mach numbers. Numerical solutions are computed both with or without the gravity force. Finally, the performance of the solvers in terms of CPU-time consumption is investigated, and the sensitivity of the solution to some parameters, which affect CPU time is also performed.

We present here results for the Andra Couplex 1 test case, obtained with the code Cast3m. This code is developped at the CEA (Commissariat l'nergie atomique) and is used mainly to solve problems of solid mechanics, fluid mechanics and heat transfers. Different types of discretization are available, among them finite element, finite volume and mixed hybrid finite element method. Cast3m is also a componant of the platteform Alliances (co-developped by Andra, CEA), which will be used by Andra for the safety calculation of an underground waste disposal in year 2004. We solve the Darcy equation for the water flow and a convectiondiffusion transport equation for the Iodine 129 which escapes from a repository cave into the water. The water flow is calculated with a MHFE discretization. It is shown that this method provides sharp results even on relatively coarse grids. The convection-diffusion transport equation is discretized with FE, MHFE and FV methods. In our comparison, we point out the differences of these methods in term of accuracy, respect of the maximum principle and calculations cost. Neither the finite element nor the mixed hybrid finite element approach respects the maximum principle. This results in the presence of negative concentrations near the repository cave, whereas FV calculations respect the monotonicity. We show that mass lumping techniques suppress this problem but with strong restrictions on the grid. FE and MHFE approaches are more accurate than FV for the diffusion equation, but the overall results are equivalent since the advective terms are dominant in the far field and are discretized with centered schemes. We conclude by studying the influence of the grid: a very fine grid near the repository solves almost all the problems of monotonicity, without employing mass lumping techniques. We also observed a very important increase of the accuracy on a structured grid made up of rectangles.

No abstract