Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements
<p dir="ltr">This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner,...
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2023
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| _version_ | 1864513530938523648 |
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| author | Stefano Nardean (14151900) |
| author2 | Massimiliano Ferronato (14151903) Ahmad Abushaikha (17148349) |
| author2_role | author author |
| author_facet | Stefano Nardean (14151900) Massimiliano Ferronato (14151903) Ahmad Abushaikha (17148349) |
| author_role | author |
| dc.creator.none.fl_str_mv | Stefano Nardean (14151900) Massimiliano Ferronato (14151903) Ahmad Abushaikha (17148349) |
| dc.date.none.fl_str_mv | 2023-07-28T03:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1007/s10596-023-10238-x |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Block_constrained_pressure_residual_preconditioning_for_two-phase_flow_in_porous_media_by_mixed_hybrid_finite_elements/24981210 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Engineering Fluid mechanics and thermal engineering Resources engineering and extractive metallurgy Mathematical sciences Applied mathematics Numerical and computational mathematics Constrained pressure residual Block preconditioning Two-phase flow in porous media Mixed hybrid finite element |
| dc.title.none.fl_str_mv | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3\times 3$$ 3 × 3 block-structured Jacobian matrix with a $$2\times 2$$ 2 × 2 inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2\times 2$$ 2 × 2 structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.</p><h2>Other Information</h2><p dir="ltr">Published in: Computational Geosciences<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s10596-023-10238-x" target="_blank">https://dx.doi.org/10.1007/s10596-023-10238-x</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_c265f0665dba59a7c78f88c06a0a4629 |
| identifier_str_mv | 10.1007/s10596-023-10238-x |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/24981210 |
| publishDate | 2023 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elementsStefano Nardean (14151900)Massimiliano Ferronato (14151903)Ahmad Abushaikha (17148349)EngineeringFluid mechanics and thermal engineeringResources engineering and extractive metallurgyMathematical sciencesApplied mathematicsNumerical and computational mathematicsConstrained pressure residualBlock preconditioningTwo-phase flow in porous mediaMixed hybrid finite element<p dir="ltr">This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $$3\times 3$$ 3 × 3 block-structured Jacobian matrix with a $$2\times 2$$ 2 × 2 inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $$2\times 2$$ 2 × 2 structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.</p><h2>Other Information</h2><p dir="ltr">Published in: Computational Geosciences<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s10596-023-10238-x" target="_blank">https://dx.doi.org/10.1007/s10596-023-10238-x</a></p>2023-07-28T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1007/s10596-023-10238-xhttps://figshare.com/articles/journal_contribution/Block_constrained_pressure_residual_preconditioning_for_two-phase_flow_in_porous_media_by_mixed_hybrid_finite_elements/24981210CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/249812102023-07-28T03:00:00Z |
| spellingShingle | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements Stefano Nardean (14151900) Engineering Fluid mechanics and thermal engineering Resources engineering and extractive metallurgy Mathematical sciences Applied mathematics Numerical and computational mathematics Constrained pressure residual Block preconditioning Two-phase flow in porous media Mixed hybrid finite element |
| status_str | publishedVersion |
| title | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| title_full | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| title_fullStr | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| title_full_unstemmed | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| title_short | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| title_sort | Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements |
| topic | Engineering Fluid mechanics and thermal engineering Resources engineering and extractive metallurgy Mathematical sciences Applied mathematics Numerical and computational mathematics Constrained pressure residual Block preconditioning Two-phase flow in porous media Mixed hybrid finite element |