{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/79963"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/79963","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems","abstract":"M.S.","abstract_html":"M.S.","abstract_has_math":false,"creators":["Mishra, Abhishek; 0000-0001-7445-066X"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Bauman, Paul","Mechanical and Aerospace Engineering"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-07-30T15:11:26Z","date_published":"2019-07-30T15:11:26Z","updated_at":"2026-07-27T19:05:21Z","subjects":["aerospace engineering","applied mathematics","computational physics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/79963","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bauman, Paul","Mechanical and Aerospace Engineering"]},{"key":"dc:creator","label":"Author","values":["Mishra, Abhishek; 0000-0001-7445-066X"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-07-30T15:11:26Z","2019","2019-05-15 20:32:43"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["aerospace engineering","applied mathematics","computational physics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/79963"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["M.S.","The Immersed Boundary Method (IBM) was designed by Peskin for modeling fluid-structure interaction (FSI) problems, where a structure is completely immersed in a fluid, in contrast to the arbitrary Lagrangian-Eulerian (ALE) method, which consists of a conforming interface between the fluid and the solid. In the original IBM, the Navier-Stokes equations are considered everywhere and the presence of the immersed solid is taken into account using a Dirac delta distribution term which depends on the position of the solid. Recently, a finite element version of the IBM was developed by Boffi et. al., which avoids explicit treatment of the Dirac delta distribution term. In this approach, equations governing the fluid and solid motion are discretized using finite element method (FEM). The Navier-Stokes equations are solved first using the solid position at previous time step, and then the solid position is updated according to the computed velocity. A modification to this approach was also proposed by Boffi et. al., a fictitious domain formulation of the finite element IBM, that makes use of a distributed Lagrange multiplier, enforcing a constraint on the velocity matching of the solid and the fluid.In this work, we propose a new formulation based on the nonlinear solid mechanics formulations, which properly enforces incompressibility constraints, that corrects any volumetric instabilities that may occur due to discretization of incompressible hyperelastic materials. We numerically investigate some FSI problems using our proposed formulation. The computational algorithm for the implementation of our IBM formulation has been developed using GRINS, a C++ software framework, based on the libMesh finite element library, designed to simulate multiphysics systems of partial differential equations (PDEs) using FEM."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems"]}]}],"canonical_facts":{"dc:contributor":["Bauman, Paul","Mechanical and Aerospace Engineering"],"dc:creator":["Mishra, Abhishek; 0000-0001-7445-066X"],"dc:date":["2019-07-30T15:11:26Z","2019","2019-05-15 20:32:43"],"dc:description":["M.S.","The Immersed Boundary Method (IBM) was designed by Peskin for modeling fluid-structure interaction (FSI) problems, where a structure is completely immersed in a fluid, in contrast to the arbitrary Lagrangian-Eulerian (ALE) method, which consists of a conforming interface between the fluid and the solid. In the original IBM, the Navier-Stokes equations are considered everywhere and the presence of the immersed solid is taken into account using a Dirac delta distribution term which depends on the position of the solid. Recently, a finite element version of the IBM was developed by Boffi et. al., which avoids explicit treatment of the Dirac delta distribution term. In this approach, equations governing the fluid and solid motion are discretized using finite element method (FEM). The Navier-Stokes equations are solved first using the solid position at previous time step, and then the solid position is updated according to the computed velocity. A modification to this approach was also proposed by Boffi et. al., a fictitious domain formulation of the finite element IBM, that makes use of a distributed Lagrange multiplier, enforcing a constraint on the velocity matching of the solid and the fluid.In this work, we propose a new formulation based on the nonlinear solid mechanics formulations, which properly enforces incompressibility constraints, that corrects any volumetric instabilities that may occur due to discretization of incompressible hyperelastic materials. We numerically investigate some FSI problems using our proposed formulation. The computational algorithm for the implementation of our IBM formulation has been developed using GRINS, a C++ software framework, based on the libMesh finite element library, designed to simulate multiphysics systems of partial differential equations (PDEs) using FEM."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/79963"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["aerospace engineering","applied mathematics","computational physics"],"dc:title":["A Variational Implementation of Immersed Boundary Method for Fluid-Structure Interaction Problems"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T19:05:21Z"}