{"id":{"repo_id":"uno","oai_identifier":"oai:scholarworks.uno.edu:td-1057"},"canonical_url":"https://search.dev.ndltd.org/etd/uno/oai:scholarworks.uno.edu:td-1057","repository":{"repo_id":"uno","name":"University of New Orleans","base_url":"https://scholarworks.uno.edu/do/oai/"},"display":{"title":"Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation","abstract":"The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work.","abstract_html":"The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work.","abstract_has_math":false,"creators":["Voonna, Kiran"],"institution":null,"degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Guillot, Martin","Hall, Carsie","Akyuzlu, Kazim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-12-19T08:00:00Z","date_published":"2003-12-19T08:00:00Z","updated_at":"2026-07-24T05:27:57Z","subjects":["Courant Number","Finite Element Methods","Euler's Method","Runge-Kutta Method","DG Method","Burgers Equation","Hyperbolic Equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uno.edu/td/58","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Guillot, Martin","Hall, Carsie","Akyuzlu, Kazim"]},{"key":"dc:creator","label":"Author","values":["Voonna, Kiran"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Courant Number","Finite Element Methods","Euler's Method","Runge-Kutta Method","DG Method","Burgers Equation","Hyperbolic Equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uno.edu/td/58"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work."]},{"key":"dc:title","label":"Title","values":["Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation"]}]}],"canonical_facts":{"dc:contributor":["Guillot, Martin","Hall, Carsie","Akyuzlu, Kazim"],"dc:creator":["Voonna, Kiran"],"dc:description.abstract":["The main objective of this research work is to apply the discontinuous Galerkin method to a classical partial differential equation to investigate the properties of the numerical solution and compare the numerical solution to the analytical solution by using discontinuous Galerkin method. This scheme is applied to 1-D non-linear conservation equation (Burgers equation) in which the governing differential equation is simplified model of the inviscid Navier-stokes equations. In this work three cases are studied. They are sinusoidal wave profile, initial shock discontinuity and initial linear distribution. A grid and time step refinement is performed. Riemann fluxes at each element interfaces are calculated. This scheme is applied to forward differentiation method (Euler's method) and to second order Runge-kutta method of this work."],"dc:identifier":["https://scholarworks.uno.edu/td/58"],"dc:subject":["Courant Number","Finite Element Methods","Euler's Method","Runge-Kutta Method","DG Method","Burgers Equation","Hyperbolic Equations"],"dc:title":["Development of Discontinuous Galerkin Method for 1-D Inviscid Burgers Equation"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."]},"updated_at":"2026-07-24T05:27:57Z"}