Polyhedral Discretisation Methods for Geomechanical Simulation of Faults and Fractures in Poroelastic Media

The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 896616

Understanding subsurface geological processes is crucial for the prevention of environmental damage and the development of renewable alternatives for energy generation. The key for the successful assessment of subsurface activities is the ability to perform accurate numerical simulations able to predict the effects of soil exploitation. The PDGeoFF project focus on the design and analysis of advanced nonconforming polyhedral discretisation methods for geomechanical modelling. The versatility of polyhedral finite element methods allows to successfully tame the main numerical challenges that have to be accounted for in computational geosciences: the geometric complexity arising from the presence of various layers and fractures, the strong coupling between the flow and the mechanics, and the possible rough variations of the physical parameters.

Funder
European Commission
Programme
H2020-MSCA-IF
Grant number
Host istitution

Publications

[1] MB, A. Fumagalli, and A. Scotti. “Uncertainty quantification for mineral precipitation and dissolution in fractured porous media”. Submitted July 2022. Arxiv preprint: 2207.06299.
[2] MB, D. A. Di Pietro, and M. Salah. “A serendipity fully discrete div-div complex on polygonal meshes”. Submitted July 2022. Hal preprint: hal-03723495.
[3] P. F. Antonietti, S. Bonetti, and MB. “Discontinuous Galerkin approximation of the fully-coupled thermo-poroelastic problem”. Accepted for publication on Siam J. Sci. Comput. (October 2022). Arxiv preprint: 2205.04262.
[4] P. F. Antonietti, MB, and I. Mazzieri. “On mathematical and numerical modelling of multiphysics wave propagation with polytopal Discontinuous Galerkin methods: a review”. In: Vietnam J. Math. (July 2022). DOI: 10.1007/s10013-022-00566-3.
[5] P. F. Antonietti, MB, I. Mazzieri, and S. Nati Poltri. “A high-order discontinuous Galerkin method for the poro-elasto-acoustic problem on polygonal and polyhedral grids”. In: SIAM J. Sci. Comput. 44.1 (Sept. 2021), pp. B1-B28. DOI: 10.1137/21M1410919.
[6] L. Botti, MB, and D. A. Di Pietro. “Polyhedral Methods in Geosciences”. In: SEMA-SIMAI. Springer, July 2021. Chap. A Hybrid High-Order method for multiple-network poroelasticity, pp. 227–25. DOI: 10.1007/978-3-030-69363-3_6.
[7] MB, D. Castanon Quiroz, D. A. Di Pietro, and A. Harnist. “A Hybrid High-Order method for creeping flows of non-Newtonian fluids”. In: ESAIM: Math. Model Numer. Anal. (Aug. 20, 2021). Accepted for publication. DOI: 10.1051/m2an/2021051.

Presentations

Congress
ECCOMAS 2022, European Congress on Computational Methods in Sciences and Engineering.
Dates
June 5-9, 2022
Venue
Oslo, Norway.
Title
Polytopal nonconforming methods for multiple-network poroelasticity and thermo-poroelasticity.
Mini symposium
Robust and Reliable Methods in Poromechanics.
PDF

Congress
SIAM-PD 2022, SIAM Conference on Analysis of Partial Differential Equations.
Dates
March 14-18, 2022
Venue
Virtual event, originally planned in Berlin, Germany.
Title
Functional inequalities in broken Sobolev spaces and apllications to polyhedral methods.
Mini symposium
Recent Advances in Polygonal Methods and Their Applications.
PDF

Congress
SIMAI 2020+1, Congress of the Italian Society of Applied and Industrial Mathematics.
Dates
30 August - 3 September 2021
Venue
Universita` di Parma, Italy.
Title
A discontinuous Galerkin method for wave propagation problem in poroelastic-acoustic media.
Mini symposium
Advances in Polygonal and Polyhedral methods.
PDF

Congress
USNCCM 16, 16th U.S. National Congress on Computational Mechanics.
Dates
July 25-29, 2021
Venue
Virtual event, Chicago, USA.
Title
Polyhedral nonconforming discretization methods for multiple-network poroelasticity.
Mini symposium
Polygonal and Polyhedral Discretizations in Computational Mechanics.
PDF

Congress
ICOSAHOM 2020, International Conference on Spectral and High Order Methods.
Dates
July 12-16, 2021
Venue
TU Wien Freihaus, Vienna, Austria.
Title
Hybrid High-Order methods for creeping flows of non-Newtonian fluids.
Mini symposium
High-order face-based discretization methods.
PDF

Congress
INdAM workshop 2021, Polygonal methods for PDEs: theory and applications.
Dates
May 17-19, 2021
Venue
Online event.
Title
Nonconforming monolithic discretizations of multiple-network poroelasticity.
PDF

Invited seminars

Dates
November 9, 2022
Institution
MOX, Dipartimento di Matematica, Politecnico di Milano, Italy.
Title
Multiphysics wave propagation with polytopal Discontinuous Galerkin methods.
Seminar

Dates
July 4, 2022
Institution
MOX, Dipartimento di Matematica, Politecnico di Milano, Italy.
Title
Functional Inequalities in Broken Sobolev Spaces and Applications to Polyhedral Discretization Methods.
Seminar
PDF

Dates
December 7, 2021
Institution
IMAG, Université de Montpellier, France.
Title
On mathematical and numerical modelling of multiphysics wave propagation with polytopal Discontinuous Galerkin methods.
Seminar
PDF

Communication and dissemination activities

Convention
Dates
29 September - October 16, 2022
Venue
Bergamo, Italy
Title
Matematica vs Cambiamento Climatico: dai puzzles alle griglie poligonali per la simulazione numerica.
Presentation

Convention
Dates
November 10-26, 2021
Venue
Online, European Secondary Schools
Title
Mathematical Models vs. Climate Change (in collaboration with European Commission).
Presentation

Organization activities

Congress
POEMs workshop 2022, Polytopal Element Methods in Mathematics and Engineering.
Dates
December 12-14, 2022
Venue
Politecnico di Milano, Italy.
Role
Member of the Organizing Commitee.

Congress
GIMC-SIMAI 2022, joint workshop for young scientist.
Dates
September 29-30, 2022
Venue
Pavia, Italy.
Role
Organizer of the Mini symposium: Polygonal and Polyhedral Methods: Theory and Applications (with L. Mascotto).

Congress
ECCOMAS 2022, 8th European Congress on Computational Methods in Applied Sciences and Engineering.
Dates
June 5-9, 2022
Venue
Oslo, Norway.
Role
Organizer of the Mini symposium: Polygonal and Polyhedral Discretizations for PDEs (with J. Bishop, G. Manzini, and N. Sukumar).

Congress
SIMAI 2020, Congress of the Italian Society of Applied and Industrial Mathematics.
Dates
30 August - 3 September 2021
Venue
Universita` di Parma, Italy.
Role
Organizer of the Mini symposium: Advances in Polygonal and Polyhedral methods (with A. Borio, I. Mazzieri, and G. Vacca).

Congress
SIAM-GS 2021, SIAM Conference on Mathematical and Computational Issues in the Geosciences.
Dates
June 21-24, 2021
Venue
Virtual event, Politecnico di Milano, Italy..
Role
Organizer of the Mini symposium: Polyhedral discretization methods for geomechanical simulation (with D.A. Di Pietro and G. Manzini).