{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/113909"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/113909","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Linear and nonlinear solvers for simulating high-temperature multiphase flow within large-scale engineered subsurface systems","abstract":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","abstract_html":"Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","abstract_has_math":false,"creators":["Park, Heeho Daniel"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Environ Engr in Civil Engr","degree_department":null,"school":null,"contributors":["Valocchi, Albert J","Olson, Luke","Kumar, Praveen","Hammond, Glenn E"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-04-29T21:34:51Z","date_published":"2022-04-29T21:34:51Z","updated_at":"2026-07-22T22:24:53Z","subjects":["Environmental engineering"],"languages":["en","eng"],"rights":["Copyright 2021 Heeho Park"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/113909","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Valocchi, Albert J","Olson, Luke","Kumar, Praveen","Hammond, Glenn E"]},{"key":"dc:creator","label":"Author","values":["Park, Heeho Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-04-29T21:34:51Z","2021-12","2021-12-03"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Environ Engr in Civil Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Environmental engineering"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Heeho Park"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/113909"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","The student, Heeho Park, accepted the attached license on 2021-12-02 at 18:39.","The student, Heeho Park, submitted this Dissertation for approval on 2021-12-02 at 18:52.","This Dissertation was approved for publication on 2021-12-03 at 09:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17374 on 2022-04-06 at 17:10:54","Made available in DSpace on 2022-04-29T21:34:51Z (GMT). No. of bitstreams: 3 PARK-DISSERTATION-2021.pdf: 15274074 bytes, checksum: 94213eb25cdc3cad464f5d7c69557bd8 (MD5) LICENSE.txt: 4207 bytes, checksum: 0ecce96600ecd401814a12df4ba3aaad (MD5) PROQUEST_LICENSE.txt: 4553 bytes, checksum: e37dd9cfd12be59c565a6a0b3e137648 (MD5) Previous issue date: 2021-12-03","Multiphase flow simulation is well-known to be computationally demanding, and modeling large-scale engineered subsurface systems entails significant additional numerical challenges. These challenges arise from: (a) the presence of small-scale discrete features like shafts, tunnels, waste packages, and barriers; (b) the need to accurately represent both the waste form processes at the small spatial scale of the repository and the large-scale transport processes throughout heterogeneous geological formations; (c) the strong contrast in material properties such as porosity and permeability, as well as the nonlinear constitutive relations for multiphase flow; (d) high-temperature heat sources underground (e.g., due to decay of high level nuclear wastes) cause nearby water to boil off into steam, leading to a dry-out condition in porous media, with subsequent re-saturation of the heat source area. Numerical solution is based on discretization of the coupled system of nonlinear governing equations and solving a linear system of equations at each Newton-Raphson iteration. Practical problems require a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. The unique challenges noted above can lead to an ill-conditioned Jacobian matrix and non-convergence with Newton’s method due to discontinuous nonlinearity in constitutive models. Moreover, practical applications such as nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainly in material properties, geological heterogeneity, failure scenarios, or other factors; governmental regulatory agencies can mandate these as part of performance and safety assessments. Finally, some applications like nuclear waste repository require simulations over a million years. Hence there is a need for flexible, robust, and computationally efficient methods for multiphase flow in large-scale engineered subsurface systems. We apply the open-source simulator PFLOTRAN which employs a finite volume discretization and uses the PETSc parallel framework. We evaluate the performance of several preconditioners for the iterative solution of the linearized Jacobian system; these range from stabilized-biconjugate-gradient with block-Jacobi preconditioning (BCGS) to methods adopted from reservoir modeling, such as the constrained pressure residual (CPR) two-stage preconditioner and flexible generalized residual solver (FGMRES). We also implement within PETSc the general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), which truncates the Newton update or modifies the update with a Cauchy solution that is within the quadratic model trust-region of the objective function and Newton trust-region (NTR). We demonstrate the effectiveness with two large-scale simulations for a series of test problems with increasing difficulty. In one numerical experiment, we find that the NTRDC and FGMRES-CPR-ABF (FCA) preconditioners generally perform best for the test problem having the most extreme nonlinear processes, achieving a 50x speed-up compared with BCGS. The most ill-conditioned and extreme nonlinear simulations do not converge with BCGS, but they do complete with NTRDC and FCA. In the other test problem, simulations with high-temperature heat sources causing extreme nonlinear processes with many state changes in the domain do not converge with conventional NR, but they do complete with the trust-region variants. We also investigate the strong scalability of each method and demonstrate the impact of node-packing upon parallel performance on modern processor architectures."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Linear and nonlinear solvers for simulating high-temperature multiphase flow within large-scale engineered subsurface systems"]}]}],"canonical_facts":{"dc:contributor":["Valocchi, Albert J","Olson, Luke","Kumar, Praveen","Hammond, Glenn E"],"dc:creator":["Park, Heeho Daniel"],"dc:date":["2022-04-29T21:34:51Z","2021-12","2021-12-03"],"dc:description":["Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-04-06 without embargo terms","The student, Heeho Park, accepted the attached license on 2021-12-02 at 18:39.","The student, Heeho Park, submitted this Dissertation for approval on 2021-12-02 at 18:52.","This Dissertation was approved for publication on 2021-12-03 at 09:38.","DSpace SAF Submission Ingestion Package generated from Vireo submission #17374 on 2022-04-06 at 17:10:54","Made available in DSpace on 2022-04-29T21:34:51Z (GMT). No. of bitstreams: 3 PARK-DISSERTATION-2021.pdf: 15274074 bytes, checksum: 94213eb25cdc3cad464f5d7c69557bd8 (MD5) LICENSE.txt: 4207 bytes, checksum: 0ecce96600ecd401814a12df4ba3aaad (MD5) PROQUEST_LICENSE.txt: 4553 bytes, checksum: e37dd9cfd12be59c565a6a0b3e137648 (MD5) Previous issue date: 2021-12-03","Multiphase flow simulation is well-known to be computationally demanding, and modeling large-scale engineered subsurface systems entails significant additional numerical challenges. These challenges arise from: (a) the presence of small-scale discrete features like shafts, tunnels, waste packages, and barriers; (b) the need to accurately represent both the waste form processes at the small spatial scale of the repository and the large-scale transport processes throughout heterogeneous geological formations; (c) the strong contrast in material properties such as porosity and permeability, as well as the nonlinear constitutive relations for multiphase flow; (d) high-temperature heat sources underground (e.g., due to decay of high level nuclear wastes) cause nearby water to boil off into steam, leading to a dry-out condition in porous media, with subsequent re-saturation of the heat source area. Numerical solution is based on discretization of the coupled system of nonlinear governing equations and solving a linear system of equations at each Newton-Raphson iteration. Practical problems require a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. The unique challenges noted above can lead to an ill-conditioned Jacobian matrix and non-convergence with Newton’s method due to discontinuous nonlinearity in constitutive models. Moreover, practical applications such as nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainly in material properties, geological heterogeneity, failure scenarios, or other factors; governmental regulatory agencies can mandate these as part of performance and safety assessments. Finally, some applications like nuclear waste repository require simulations over a million years. Hence there is a need for flexible, robust, and computationally efficient methods for multiphase flow in large-scale engineered subsurface systems. We apply the open-source simulator PFLOTRAN which employs a finite volume discretization and uses the PETSc parallel framework. We evaluate the performance of several preconditioners for the iterative solution of the linearized Jacobian system; these range from stabilized-biconjugate-gradient with block-Jacobi preconditioning (BCGS) to methods adopted from reservoir modeling, such as the constrained pressure residual (CPR) two-stage preconditioner and flexible generalized residual solver (FGMRES). We also implement within PETSc the general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), which truncates the Newton update or modifies the update with a Cauchy solution that is within the quadratic model trust-region of the objective function and Newton trust-region (NTR). We demonstrate the effectiveness with two large-scale simulations for a series of test problems with increasing difficulty. In one numerical experiment, we find that the NTRDC and FGMRES-CPR-ABF (FCA) preconditioners generally perform best for the test problem having the most extreme nonlinear processes, achieving a 50x speed-up compared with BCGS. The most ill-conditioned and extreme nonlinear simulations do not converge with BCGS, but they do complete with NTRDC and FCA. In the other test problem, simulations with high-temperature heat sources causing extreme nonlinear processes with many state changes in the domain do not converge with conventional NR, but they do complete with the trust-region variants. We also investigate the strong scalability of each method and demonstrate the impact of node-packing upon parallel performance on modern processor architectures."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/113909"],"dc:language":["en","eng"],"dc:rights":["Copyright 2021 Heeho Park"],"dc:subject":["Environmental engineering"],"dc:title":["Linear and nonlinear solvers for simulating high-temperature multiphase flow within large-scale engineered subsurface systems"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Environ Engr in Civil Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:53Z"}