\"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate the efficiency and long-time accuracy of the proposed algorithms\"--Abstract, p. iv
","abstract_html":"<p>"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate the efficiency and long-time accuracy of the proposed algorithms"--Abstract, p. iv</p>","abstract_has_math":false,"creators":["Carter, John"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Computational and Applied Mathematics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T03:18:18Z","subjects":["ensemble algorithm","MHD","SAV","Uncertainty Quantification","unconditional stability","Mathematics","Statistics and Probability"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/3267","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Carter, John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Computational and Applied Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ensemble algorithm","MHD","SAV","Uncertainty Quantification","unconditional stability","Mathematics","Statistics and Probability"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/3267"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate the efficiency and long-time accuracy of the proposed algorithms\"--Abstract, p. iv
"]},{"key":"dc:title","label":"Title","values":["Efficient High Order Ensemble for Fluid Flow"]}]}],"canonical_facts":{"dc:creator":["Carter, John"],"dc:description.abstract":["\"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate the efficiency and long-time accuracy of the proposed algorithms\"--Abstract, p. iv
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/3267"],"dc:subject":["ensemble algorithm","MHD","SAV","Uncertainty Quantification","unconditional stability","Mathematics","Statistics and Probability"],"dc:title":["Efficient High Order Ensemble for Fluid Flow"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Computational and Applied Mathematics"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:18:18Z"}