{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106377"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106377","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A discontinuous Galerkin spectral element method compressible flow solver","abstract":"We develop and implement algorithms for highly-scalable high-order compressible flow simulation using the discontinuous Galerkin spectral element method. The algorithms are designed for simulation of compressible turbulence in realistic engineering geometries that are relevant to a broad range of mechanical engineering applications. Such problems are difficult because of high computational costs and stringent requirements for accurate integration over a wide range of space- and time-scales. Features of this solver include exponential spatial convergence, fast matrix-free operator evaluation, implicit time-stepping schemes, highly-scalable iterative solvers, effective stabilization techniques, and moving-mesh capabilities. Novel nonlinear filter-based artificial viscosity methods have been developed for effective regularization of challenging scalar transport problems in high-order methods and have found application in shock-capturing for the compressible flow solver. Moving-mesh capabilities via the arbitrary Lagrangian-Eulerian method are verified and have enabled simulation of complex engineering applications with moving geometries such as flows in internal combustion engines. Spatial (exponential) and temporal (up to fourth-order) convergence rates of the underlying numerical methods are established. Scalability of the solver, up to realizable strong-scale limits, establishes that the code is suitable for large-scale parallel computing applications. Several proposed preconditioning strategies are evaluated. The solver is demonstrated on a variety of flow problems, such as nearly-incompressible flows, supersonic flows, high Reynolds number flows, shock problems, and moving-geometry problems.","abstract_html":"We develop and implement algorithms for highly-scalable high-order compressible flow simulation using the discontinuous Galerkin spectral element method. The algorithms are designed for simulation of compressible turbulence in realistic engineering geometries that are relevant to a broad range of mechanical engineering applications. Such problems are difficult because of high computational costs and stringent requirements for accurate integration over a wide range of space- and time-scales. Features of this solver include exponential spatial convergence, fast matrix-free operator evaluation, implicit time-stepping schemes, highly-scalable iterative solvers, effective stabilization techniques, and moving-mesh capabilities. Novel nonlinear filter-based artificial viscosity methods have been developed for effective regularization of challenging scalar transport problems in high-order methods and have found application in shock-capturing for the compressible flow solver. Moving-mesh capabilities via the arbitrary Lagrangian-Eulerian method are verified and have enabled simulation of complex engineering applications with moving geometries such as flows in internal combustion engines. Spatial (exponential) and temporal (up to fourth-order) convergence rates of the underlying numerical methods are established. Scalability of the solver, up to realizable strong-scale limits, establishes that the code is suitable for large-scale parallel computing applications. Several proposed preconditioning strategies are evaluated. The solver is demonstrated on a variety of flow problems, such as nearly-incompressible flows, supersonic flows, high Reynolds number flows, shock problems, and moving-geometry problems.","abstract_has_math":false,"creators":["Lu, Li"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Fischer, Paul F","Pearlstein, Arne J","Matalon, Moshe","Olson, Luke N"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-03-02T22:15:08Z","date_published":"2020-03-02T22:15:08Z","updated_at":"2026-07-22T22:24:45Z","subjects":["Discontinuous Galerkin, compressible flow solver, high-order"],"languages":["en"],"rights":["Copyright 2019 Li Lu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106377","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Fischer, Paul F","Pearlstein, Arne J","Matalon, Moshe","Olson, Luke N"]},{"key":"dc:creator","label":"Author","values":["Lu, Li"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-03-02T22:15:08Z","2022-03-03T10:15:19Z","2019-12-05","2019-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"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":["Discontinuous Galerkin, compressible flow solver, high-order"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 Li Lu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/106377"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We develop and implement algorithms for highly-scalable high-order compressible flow simulation using the discontinuous Galerkin spectral element method. The algorithms are designed for simulation of compressible turbulence in realistic engineering geometries that are relevant to a broad range of mechanical engineering applications. Such problems are difficult because of high computational costs and stringent requirements for accurate integration over a wide range of space- and time-scales. Features of this solver include exponential spatial convergence, fast matrix-free operator evaluation, implicit time-stepping schemes, highly-scalable iterative solvers, effective stabilization techniques, and moving-mesh capabilities. Novel nonlinear filter-based artificial viscosity methods have been developed for effective regularization of challenging scalar transport problems in high-order methods and have found application in shock-capturing for the compressible flow solver. Moving-mesh capabilities via the arbitrary Lagrangian-Eulerian method are verified and have enabled simulation of complex engineering applications with moving geometries such as flows in internal combustion engines. Spatial (exponential) and temporal (up to fourth-order) convergence rates of the underlying numerical methods are established. Scalability of the solver, up to realizable strong-scale limits, establishes that the code is suitable for large-scale parallel computing applications. Several proposed preconditioning strategies are evaluated. The solver is demonstrated on a variety of flow problems, such as nearly-incompressible flows, supersonic flows, high Reynolds number flows, shock problems, and moving-geometry problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-12-01","The student, Li Lu, accepted the attached license on 2019-12-05 at 10:25.","The student, Li Lu, submitted this Dissertation for approval on 2019-12-05 at 10:38.","This Dissertation was approved for publication on 2019-12-05 at 13:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14713 on 2020-02-28 at 17:23:31","Made available in DSpace on 2020-03-02T22:15:08Z (GMT). No. of bitstreams: 2 LU-DISSERTATION-2019.pdf: 16816874 bytes, checksum: 9fa57050e06a045525200a0a817ebf93 (MD5) LICENSE.txt: 4202 bytes, checksum: 13ce14ecb0e6a35fb1dc2d5dea6d8892 (MD5) Previous issue date: 2019-12-05","Embargo set by: Seth Robbins for item 113919 Lift date: 2022-03-02T22:15:21Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 113919 Lift date: 2022-03-02T22:18:25Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 113919 on 2022-03-03T10:15:19Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["A discontinuous Galerkin spectral element method compressible flow solver"]}]}],"canonical_facts":{"dc:contributor":["Fischer, Paul F","Pearlstein, Arne J","Matalon, Moshe","Olson, Luke N"],"dc:creator":["Lu, Li"],"dc:date":["2020-03-02T22:15:08Z","2022-03-03T10:15:19Z","2019-12-05","2019-12"],"dc:description":["We develop and implement algorithms for highly-scalable high-order compressible flow simulation using the discontinuous Galerkin spectral element method. The algorithms are designed for simulation of compressible turbulence in realistic engineering geometries that are relevant to a broad range of mechanical engineering applications. Such problems are difficult because of high computational costs and stringent requirements for accurate integration over a wide range of space- and time-scales. Features of this solver include exponential spatial convergence, fast matrix-free operator evaluation, implicit time-stepping schemes, highly-scalable iterative solvers, effective stabilization techniques, and moving-mesh capabilities. Novel nonlinear filter-based artificial viscosity methods have been developed for effective regularization of challenging scalar transport problems in high-order methods and have found application in shock-capturing for the compressible flow solver. Moving-mesh capabilities via the arbitrary Lagrangian-Eulerian method are verified and have enabled simulation of complex engineering applications with moving geometries such as flows in internal combustion engines. Spatial (exponential) and temporal (up to fourth-order) convergence rates of the underlying numerical methods are established. Scalability of the solver, up to realizable strong-scale limits, establishes that the code is suitable for large-scale parallel computing applications. Several proposed preconditioning strategies are evaluated. The solver is demonstrated on a variety of flow problems, such as nearly-incompressible flows, supersonic flows, high Reynolds number flows, shock problems, and moving-geometry problems.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2021-12-01","The student, Li Lu, accepted the attached license on 2019-12-05 at 10:25.","The student, Li Lu, submitted this Dissertation for approval on 2019-12-05 at 10:38.","This Dissertation was approved for publication on 2019-12-05 at 13:19.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14713 on 2020-02-28 at 17:23:31","Made available in DSpace on 2020-03-02T22:15:08Z (GMT). No. of bitstreams: 2 LU-DISSERTATION-2019.pdf: 16816874 bytes, checksum: 9fa57050e06a045525200a0a817ebf93 (MD5) LICENSE.txt: 4202 bytes, checksum: 13ce14ecb0e6a35fb1dc2d5dea6d8892 (MD5) Previous issue date: 2019-12-05","Embargo set by: Seth Robbins for item 113919 Lift date: 2022-03-02T22:15:21Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 113919 Lift date: 2022-03-02T22:18:25Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 113919 on 2022-03-03T10:15:19Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/106377"],"dc:language":["en"],"dc:rights":["Copyright 2019 Li Lu"],"dc:subject":["Discontinuous Galerkin, compressible flow solver, high-order"],"dc:title":["A discontinuous Galerkin spectral element method compressible flow solver"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:45Z"}