{"id":{"repo_id":"sherbrooke","oai_identifier":"oai:usherbrooke.scholaris.ca:11143/4654"},"canonical_url":"https://search.dev.ndltd.org/etd/sherbrooke/oai:usherbrooke.scholaris.ca:11143/4654","repository":{"repo_id":"sherbrooke","name":"Université de Sherbrooke","base_url":"https://usherbrooke.scholaris.ca/server/oai/request"},"display":{"title":"Smoothed particle hydrodynamics","abstract":"Since its introduction in the late 1970s by Lucy [11] and Gingold and Monaghan [4], smoothed particle hydrodynamics (SPH) has been used in many areas. It has grown into a widely-recognized technique with many practical applications. In this thesis, we present a new application of the SPH method: a new algorithm for computing a null divergence velocity field using SPH for incompressible flow - a pure SPH solution of the Helmholtz-Hodge decomposition. Also, a new version of the Laplacian for SPH is proposed and the advantages and disadvantages of different gradient and Laplacian approximation formulas used in SPH are also discussed. A new treatment of boundary conditions is proposed for the whole solution procedure. Throughout the thesis, a brief historical overview is presented, along with some fundamental notions about SPH and computational fluid dynamics.","abstract_html":"Since its introduction in the late 1970s by Lucy [11] and Gingold and Monaghan [4], smoothed particle hydrodynamics (SPH) has been used in many areas. It has grown into a widely-recognized technique with many practical applications. In this thesis, we present a new application of the SPH method: a new algorithm for computing a null divergence velocity field using SPH for incompressible flow - a pure SPH solution of the Helmholtz-Hodge decomposition. 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