{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101475"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101475","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Adjoint sensitivity analysis of the two-phase two-fluid model based on an approximate Riemann solver","abstract":"A new shock-capturing upwind numerical solver (i.e. forward solver) and an adjoint sensitivity analysis framework for the two-phase two-fluid model are developed and verified. Both the numerical solver and the adjoint sensitivity analysis framework are based on an analytical analysis of the two-phase two-fluid model. The challenge (due to the arbitrary equation of state) in the analytical analysis of the two-phase system is overcome by introducing several new auxiliary variables. With the help of new auxiliary variables and thermodynamic transformations, the Jacobian matrix of the system can be simplified to a well-structured form, which is convenient for an analytical analysis. Approximate eigenvalues and eigenvectors are obtained using the difference in the thermodynamic properties of liquid and gas phases. The approximate eigenvalues and eigenvectors are essential for constructing the upwind numerical solver, because they provide correct upwind information of the system. Both the numerical solver and the adjoint sensitivity analysis framework are verified with several numerical tests. For the forward tests, the results show that the solver is stable, accurate, and robust. Results from the new solver are in a very good agreement with either analytical solution or measurement data. The grid convergence study shows that the solver using a Roe-type numerical flux is first-order accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint sensitivities (with respect to initial conditions, boundary conditions, or physical model parameters) are verified by either analytical sensitivities or forward sensitivities. A critical and unique feature of the new solver is that the formulation does not depend on the form of equation of state, which ensures that the solver is applicable to practical two-phase flow problems, such as a boiling pipe. The successful application of the solver to a boiling pipe is very encouraging, as it opens up the possibility of applying many other advanced methods to two-phase flow problems.","abstract_html":"A new shock-capturing upwind numerical solver (i.e. forward solver) and an adjoint sensitivity analysis framework for the two-phase two-fluid model are developed and verified. Both the numerical solver and the adjoint sensitivity analysis framework are based on an analytical analysis of the two-phase two-fluid model. The challenge (due to the arbitrary equation of state) in the analytical analysis of the two-phase system is overcome by introducing several new auxiliary variables. With the help of new auxiliary variables and thermodynamic transformations, the Jacobian matrix of the system can be simplified to a well-structured form, which is convenient for an analytical analysis. Approximate eigenvalues and eigenvectors are obtained using the difference in the thermodynamic properties of liquid and gas phases. The approximate eigenvalues and eigenvectors are essential for constructing the upwind numerical solver, because they provide correct upwind information of the system. Both the numerical solver and the adjoint sensitivity analysis framework are verified with several numerical tests. For the forward tests, the results show that the solver is stable, accurate, and robust. Results from the new solver are in a very good agreement with either analytical solution or measurement data. The grid convergence study shows that the solver using a Roe-type numerical flux is first-order accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint sensitivities (with respect to initial conditions, boundary conditions, or physical model parameters) are verified by either analytical sensitivities or forward sensitivities. A critical and unique feature of the new solver is that the formulation does not depend on the form of equation of state, which ensures that the solver is applicable to practical two-phase flow problems, such as a boiling pipe. The successful application of the solver to a boiling pipe is very encouraging, as it opens up the possibility of applying many other advanced methods to two-phase flow problems.","abstract_has_math":false,"creators":["Hu, Guojun"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear, Plasma, Radiolgc Engr","degree_department":null,"school":null,"contributors":["Kozlowski, Tomasz","Brooks, Caleb","Jewett, Brian F.","Stubbins, James F.","Uddin, Rizwan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:22Z","date_published":"2018-09-27T16:17:22Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Riemann solver","adjoint method","two-phase flow"],"languages":["en"],"rights":["Copyright 2018 Guojun Hu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101475","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kozlowski, Tomasz","Brooks, Caleb","Jewett, Brian F.","Stubbins, James F.","Uddin, Rizwan"]},{"key":"dc:creator","label":"Author","values":["Hu, Guojun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:22Z","2018-06-04","2018-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear, Plasma, Radiolgc 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":["Riemann solver","adjoint method","two-phase flow"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Guojun Hu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101475"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A new shock-capturing upwind numerical solver (i.e. forward solver) and an adjoint sensitivity analysis framework for the two-phase two-fluid model are developed and verified. Both the numerical solver and the adjoint sensitivity analysis framework are based on an analytical analysis of the two-phase two-fluid model. The challenge (due to the arbitrary equation of state) in the analytical analysis of the two-phase system is overcome by introducing several new auxiliary variables. With the help of new auxiliary variables and thermodynamic transformations, the Jacobian matrix of the system can be simplified to a well-structured form, which is convenient for an analytical analysis. Approximate eigenvalues and eigenvectors are obtained using the difference in the thermodynamic properties of liquid and gas phases. The approximate eigenvalues and eigenvectors are essential for constructing the upwind numerical solver, because they provide correct upwind information of the system. Both the numerical solver and the adjoint sensitivity analysis framework are verified with several numerical tests. For the forward tests, the results show that the solver is stable, accurate, and robust. Results from the new solver are in a very good agreement with either analytical solution or measurement data. The grid convergence study shows that the solver using a Roe-type numerical flux is first-order accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint sensitivities (with respect to initial conditions, boundary conditions, or physical model parameters) are verified by either analytical sensitivities or forward sensitivities. A critical and unique feature of the new solver is that the formulation does not depend on the form of equation of state, which ensures that the solver is applicable to practical two-phase flow problems, such as a boiling pipe. The successful application of the solver to a boiling pipe is very encouraging, as it opens up the possibility of applying many other advanced methods to two-phase flow problems.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Guojun Hu, accepted the attached license on 2018-05-31 at 19:36.","The student, Guojun Hu, submitted this Dissertation for approval on 2018-05-31 at 19:48.","This Dissertation was approved for publication on 2018-06-04 at 11:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12602 on 2018-09-27 at 10:44:24","Made available in DSpace on 2018-09-27T16:17:22Z (GMT). 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The challenge (due to the arbitrary equation of state) in the analytical analysis of the two-phase system is overcome by introducing several new auxiliary variables. With the help of new auxiliary variables and thermodynamic transformations, the Jacobian matrix of the system can be simplified to a well-structured form, which is convenient for an analytical analysis. Approximate eigenvalues and eigenvectors are obtained using the difference in the thermodynamic properties of liquid and gas phases. The approximate eigenvalues and eigenvectors are essential for constructing the upwind numerical solver, because they provide correct upwind information of the system. Both the numerical solver and the adjoint sensitivity analysis framework are verified with several numerical tests. For the forward tests, the results show that the solver is stable, accurate, and robust. Results from the new solver are in a very good agreement with either analytical solution or measurement data. The grid convergence study shows that the solver using a Roe-type numerical flux is first-order accurate in space and the solver using a WENO-type numerical flux is at least second-order accurate in space. For the adjoint tests, the results show that the adjoint sensitivity analysis framework works well for both steady-state problems and time-dependent problems. The adjoint sensitivities (with respect to initial conditions, boundary conditions, or physical model parameters) are verified by either analytical sensitivities or forward sensitivities. A critical and unique feature of the new solver is that the formulation does not depend on the form of equation of state, which ensures that the solver is applicable to practical two-phase flow problems, such as a boiling pipe. The successful application of the solver to a boiling pipe is very encouraging, as it opens up the possibility of applying many other advanced methods to two-phase flow problems.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Guojun Hu, accepted the attached license on 2018-05-31 at 19:36.","The student, Guojun Hu, submitted this Dissertation for approval on 2018-05-31 at 19:48.","This Dissertation was approved for publication on 2018-06-04 at 11:49.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12602 on 2018-09-27 at 10:44:24","Made available in DSpace on 2018-09-27T16:17:22Z (GMT). No. of bitstreams: 2 HU-DISSERTATION-2018.pdf: 3402853 bytes, checksum: f7ed54347d195c8a9dd7464560e8111a (MD5) LICENSE.txt: 4206 bytes, checksum: 693c9babf52f32a356a61488c56648c6 (MD5) Previous issue date: 2018-06-04"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/101475"],"dc:language":["en"],"dc:rights":["Copyright 2018 Guojun Hu"],"dc:subject":["Riemann solver","adjoint method","two-phase flow"],"dc:title":["Adjoint sensitivity analysis of the two-phase two-fluid model based on an approximate Riemann solver"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear, Plasma, Radiolgc Engr"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:40Z"}