{"id":{"repo_id":"texas","oai_identifier":"oai:repositories.lib.utexas.edu:2152/129495"},"canonical_url":"https://search.dev.ndltd.org/etd/texas/oai:repositories.lib.utexas.edu:2152/129495","repository":{"repo_id":"texas","name":"University of Texas","base_url":"https://repositories.lib.utexas.edu/server/oai/request"},"display":{"title":"The application of high order finite difference methods to the diffusion-convection equation","abstract":"The one dimensional diffusion-convection equation that describes the miscible displacement process of resident fluid by an invading fluid in a porous medium is approximated numerically with high order finite difference methods using five adjacent space node points by the Crank - Nicolson formulation. This method is referred to as the 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a field size fluid system. Comparisions of the numerical results with the analytical solution of the equation are provided as are the feasibility and validity of the 5PFDM. Based on the numerical results from this method, it can be concluded that the 5PFDM is feasible and valid to simulate the diffusion-convection equation numerically","abstract_html":"The one dimensional diffusion-convection equation that describes the miscible displacement process of resident fluid by an invading fluid in a porous medium is approximated numerically with high order finite difference methods using five adjacent space node points by the Crank - Nicolson formulation. This method is referred to as the 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a field size fluid system. Comparisions of the numerical results with the analytical solution of the equation are provided as are the feasibility and validity of the 5PFDM. Based on the numerical results from this method, it can be concluded that the 5PFDM is feasible and valid to simulate the diffusion-convection equation numerically","abstract_has_math":false,"creators":["Kim, Jeoung Soo"],"institution":"University of Texas at Austin","degree_name":"Master of Science in Engineering","degree_level":"Masters","degree_discipline":"Petroleum Engineering","degree_department":null,"school":null,"contributors":[],"advisors":["Knapp, R. M."],"committee_chairs":[],"committee_members":[],"year":1977,"date_issued":"1977","date_published":"1977","updated_at":"2026-07-24T05:01:02Z","subjects":["Difference equations","Diffusion processes","Finite differences","Oil field flooding","Mathematical models","Numerical solutions","Diffusion-convection equation","Crank-Nicolson","5PFDM"],"languages":["en"],"rights":["Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.26153/tsw/55998"],"render_values":[{"text":"https://doi.org/10.26153/tsw/55998","href":"https://doi.org/10.26153/tsw/55998","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/2152/129495","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Knapp, R. 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It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a field size fluid system. Comparisions of the numerical results with the analytical solution of the equation are provided as are the feasibility and validity of the 5PFDM. Based on the numerical results from this method, it can be concluded that the 5PFDM is feasible and valid to simulate the diffusion-convection equation numerically"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["electronic"]},{"key":"dc:title","label":"Title","values":["The application of high order finite difference methods to the diffusion-convection equation"]}]}],"canonical_facts":{"dc:contributor.advisor":["Knapp, R. M."],"dc:creator":["Kim, Jeoung Soo"],"dc:date.accessioned":["2024-11-16T00:36:13Z"],"dc:date.available":["2024-11-16T00:36:13Z"],"dc:date.issued":["1977"],"dc:description.abstract":["The one dimensional diffusion-convection equation that describes the miscible displacement process of resident fluid by an invading fluid in a porous medium is approximated numerically with high order finite difference methods using five adjacent space node points by the Crank - Nicolson formulation. This method is referred to as the 5PFDM. It has fourth order correctness in space truncation error and shows good approximation to the solution of the equation in a normalized, dimensionless fluid system and also in a field size fluid system. Comparisions of the numerical results with the analytical solution of the equation are provided as are the feasibility and validity of the 5PFDM. Based on the numerical results from this method, it can be concluded that the 5PFDM is feasible and valid to simulate the diffusion-convection equation numerically"],"dc:format.medium":["electronic"],"dc:identifier.uri":["https://hdl.handle.net/2152/129495","https://doi.org/10.26153/tsw/55998"],"dc:language.iso":["en"],"dc:rights":["Copyright © is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works."],"dc:subject":["Difference equations","Diffusion processes","Finite differences","Oil field flooding","Mathematical models","Numerical solutions","Diffusion-convection equation","Crank-Nicolson","5PFDM"],"dc:title":["The application of high order finite difference methods to the diffusion-convection equation"],"dc:type":["Thesis"],"thesis:degree_discipline":["Petroleum Engineering"],"thesis:degree_level":["Masters"],"thesis:degree_name":["Master of Science in Engineering"],"thesis:institution_name":["University of Texas at Austin"]},"updated_at":"2026-07-24T05:01:02Z"}