{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/12365"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/12365","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Consistency and convergence of SPH approximations","abstract":"This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each.","abstract_html":"This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each.","abstract_has_math":false,"creators":["Penzhorn, Karl"],"institution":"Centre for Research in Computational and Applied Mechanics (CERECAM)","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-22T22:23:00Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/12365","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Penzhorn, Karl"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-02-04T19:06:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-02-04T19:06:43Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Centre for Research in Computational and Applied Mechanics (CERECAM)"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/12365"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references (leaves 58-59).","Includes abstract."]},{"key":"dc:description.abstract","label":"Abstract","values":["This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each."]},{"key":"dc:title","label":"Title","values":["Consistency and convergence of SPH approximations"]}]}],"canonical_facts":{"dc:creator":["Penzhorn, Karl"],"dc:date.accessioned":["2015-02-04T19:06:43Z"],"dc:date.available":["2015-02-04T19:06:43Z"],"dc:date.issued":["2009"],"dc:description":["Includes bibliographical references (leaves 58-59).","Includes abstract."],"dc:description.abstract":["This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each."],"dc:identifier.uri":["http://hdl.handle.net/11427/12365"],"dc:language.iso":["eng"],"dc:publisher.department":["Centre for Research in Computational and Applied Mechanics (CERECAM)"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Consistency and convergence of SPH approximations"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:00Z"}