{"id":{"repo_id":"whiterose","oai_identifier":"oai:etheses.whiterose.ac.uk:1343"},"canonical_url":"https://search.dev.ndltd.org/etd/whiterose/oai:etheses.whiterose.ac.uk:1343","repository":{"repo_id":"whiterose","name":"White Rose University Consortium","base_url":"https://etheses.whiterose.ac.uk/cgi/oai2"},"display":{"title":"Applications of the Discrete Adjoint Method in Computational Fluid Dynamics","abstract":"The discrete adjoint method allows efficient evaluation of the derivative of a function I(s) with respect to parameters s in situations where I depends on s indirectly, via an intermediate variable w(s), which is computationally expensive to evaluate. In this thesis two applications of this method in the context of computational fluid dynamics are considered. The first is shape optimisation, where the discrete adjoint approach is employed to compute the derivatives with respect to shape parameters for a performance functional depending on the solution of a mathematical flow model which has the form of a discretised system of partial differential equations. In this context particular emphasis is given to efficient solution strategies for the linear systems arising in the discretisation of the flow models. Numerical results for two example problems are presented, demonstrating the utility of the approach. The second application, in adaptive mesh design, allows efficient evaluation of the derivatives of an a posteriori error estimate with respect to the positions of the nodes in a finite element mesh. This novel approach makes additional information available which may be utilised to guide the automatic design of adaptive meshes. Special emphasis is given to problems with anisotropic solution features, for which adaptive anisotropic mesh refinement can deliver significant performance improvements over existing adaptive hrefinement approaches. Two adaptive solution algorithms are presented and compared to existing approaches by applying them to a reaction-diffusion model problem.","abstract_html":"The discrete adjoint method allows efficient evaluation of the derivative of a function I(s) with respect to parameters s in situations where I depends on s indirectly, via an intermediate variable w(s), which is computationally expensive to evaluate. In this thesis two applications of this method in the context of computational fluid dynamics are considered. The first is shape optimisation, where the discrete adjoint approach is employed to compute the derivatives with respect to shape parameters for a performance functional depending on the solution of a mathematical flow model which has the form of a discretised system of partial differential equations. In this context particular emphasis is given to efficient solution strategies for the linear systems arising in the discretisation of the flow models. Numerical results for two example problems are presented, demonstrating the utility of the approach. The second application, in adaptive mesh design, allows efficient evaluation of the derivatives of an a posteriori error estimate with respect to the positions of the nodes in a finite element mesh. This novel approach makes additional information available which may be utilised to guide the automatic design of adaptive meshes. Special emphasis is given to problems with anisotropic solution features, for which adaptive anisotropic mesh refinement can deliver significant performance improvements over existing adaptive hrefinement approaches. Two adaptive solution algorithms are presented and compared to existing approaches by applying them to a reaction-diffusion model problem.","abstract_has_math":false,"creators":["Schneider, Rene"],"institution":"University of Leeds","degree_name":"Ph.D","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Jimack, P.K."],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-04","date_published":"2006-04","updated_at":"2026-07-24T06:04:32Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.431992"],"render_values":[{"text":"uk.bl.ethos.431992","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jimack, P.K."]},{"key":"dc:creator","label":"Author","values":["Schneider, Rene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2006-04"]},{"key":"dc:date.issued","label":"Date","values":["2006-04"]},{"key":"dc:publisher.commercial","label":"Dc Publisher Commercial","values":["University of Leeds"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Computing (Leeds)"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Leeds"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://etheses.whiterose.ac.uk/id/eprint/1343/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Ph.D"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["uk.bl.ethos.431992"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://etheses.whiterose.ac.uk/id/eprint/1343/1/schneider.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The discrete adjoint method allows efficient evaluation of the derivative of a function I(s) with respect to parameters s in situations where I depends on s indirectly, via an intermediate variable w(s), which is computationally expensive to evaluate. In this thesis two applications of this method in the context of computational fluid dynamics are considered. The first is shape optimisation, where the discrete adjoint approach is employed to compute the derivatives with respect to shape parameters for a performance functional depending on the solution of a mathematical flow model which has the form of a discretised system of partial differential equations. In this context particular emphasis is given to efficient solution strategies for the linear systems arising in the discretisation of the flow models. Numerical results for two example problems are presented, demonstrating the utility of the approach. The second application, in adaptive mesh design, allows efficient evaluation of the derivatives of an a posteriori error estimate with respect to the positions of the nodes in a finite element mesh. This novel approach makes additional information available which may be utilised to guide the automatic design of adaptive meshes. Special emphasis is given to problems with anisotropic solution features, for which adaptive anisotropic mesh refinement can deliver significant performance improvements over existing adaptive hrefinement approaches. Two adaptive solution algorithms are presented and compared to existing approaches by applying them to a reaction-diffusion model problem."]},{"key":"dc:format","label":"Dc Format","values":["text"]},{"key":"dc:title","label":"Title","values":["Applications of the Discrete Adjoint Method in Computational Fluid Dynamics"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jimack, P.K."],"dc:creator":["Schneider, Rene"],"dc:date":["2006-04"],"dc:date.issued":["2006-04"],"dc:description.abstract":["The discrete adjoint method allows efficient evaluation of the derivative of a function I(s) with respect to parameters s in situations where I depends on s indirectly, via an intermediate variable w(s), which is computationally expensive to evaluate. 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Special emphasis is given to problems with anisotropic solution features, for which adaptive anisotropic mesh refinement can deliver significant performance improvements over existing adaptive hrefinement approaches. Two adaptive solution algorithms are presented and compared to existing approaches by applying them to a reaction-diffusion model problem."],"dc:format":["text"],"dc:identifier":["uk.bl.ethos.431992"],"dc:identifier.uri":["https://etheses.whiterose.ac.uk/id/eprint/1343/1/schneider.pdf"],"dc:publisher.commercial":["University of Leeds"],"dc:publisher.department":["School of Computing (Leeds)"],"dc:publisher.institution":["University of Leeds"],"dc:relation.isreferencedby":["https://etheses.whiterose.ac.uk/id/eprint/1343/"],"dc:title":["Applications of the Discrete Adjoint Method in Computational Fluid Dynamics"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["Ph.D"]},"updated_at":"2026-07-24T06:04:32Z"}