This project proposes a novel approach based on space time adaptive numerical methods to efficiently simulate subsurface flow models, with applications to CO₂ storage.

Tools

The key ingredients are

• The development of a combined Hybrid High-Order / Discontinuous Galerkin (HHO/DG) method
  • Suitable for general meshes (polytopal), high order accuracy
  • Mass conservative method
  • DG : number of degrees of freedom independent of the number of small faces per cell
  • HHO: makes it easy to impose the coupling conditions

• The development of new space-time adaptive algorithms steered by a posteriori error estimates
  • Polytopal mesh refinement/coarsening based on a posteriori estimators
  • To achieve guaranteed accuracy of the solutions
  • To speed up the computations

• The implementation of the proposed algorithms in an open-source library
  • Validate and assess the performance by comparison with available test cases (reproducibility)
  • Expand the series of tests to more complex porous fractured media

This project is funded by the French National Research Agency (ANR): Project-ANR-24-CE56-0127