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A fully implicit finite volume scheme for single phase flow with reactive transport in porous media. (English) Zbl 07316717
Summary: Single phase flow and reactive transport modelling involve solving a highly nonlinear coupled system of partial differential equations to algebraic or ordinary differential equations requiring special numerical treatment. In this paper, we propose a fully implicit finite volume method using a direct substitution approach to improve the efficiency and the accuracy of numerical computations for such systems. The approach has been developed and implemented in the framework of the parallel open-source platform DuMu$$^X$$. The object oriented code allows solving reactive transport problems considering different coupling approaches. A number of 2D and 3D numerical tests were performed for verifying and demonstrating the capability of the coupled fully implicit approach for single phase flow and reactive transport in porous media. Numerical results for the reactive transport benchmark of MoMaS and long-term fate of injected $$\mathrm{CO}_2$$ for geological storage including a comparison between the direct substitution approach and the sequential iterative approach are presented. Parallel scalability is investigated for simulations with different grid resolutions.
##### MSC:
 65Y Computer aspects of numerical algorithms 65N Numerical methods for partial differential equations, boundary value problems
##### Software:
DuMuX; DUNE; HYTEC; MIN3P; MoMaS; SPECY
Full Text:
##### References:
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