{"@context":"http://iiif.io/api/presentation/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/manifest.json","@type":"sc:Manifest","label":"Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes on Unstructured Meshes","metadata":[{"label":"dc.description.sponsorship","value":"This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree."},{"label":"dc.format","value":"Monograph"},{"label":"dc.format.medium","value":"Electronic Resource"},{"label":"dc.identifier.uri","value":"http://hdl.handle.net/11401/77210"},{"label":"dc.language.iso","value":"en_US"},{"label":"dc.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.abstract","value":"Essentially non-oscillatory schemes and their variants, such as ENO and WENO, are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging to design, especially for finite different schemes. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using both finite volume and finite difference methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighed least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present both finite difference and finite volume schemes under the same framework and analyze the accuracy and stability. We show that finite volume WLS-ENO schemes can achieve better accuracy and stability than WENO finite volume schemes, and WLS-ENO finite difference schemes are accurate, stable and more efficient than finite volume schemes. We present numerical results in 1-D, 2-D and 3-D for a number of benchmark problems and also report some comparisons against WENO if applicable."},{"label":"dcterms.available","value":"2017-09-20T16:52:12Z"},{"label":"dcterms.contributor","value":"Glimm, James"},{"label":"dcterms.creator","value":"Liu, Hongxu"},{"label":"dcterms.dateAccepted","value":"2017-09-20T16:52:12Z"},{"label":"dcterms.dateSubmitted","value":"2017-09-20T16:52:12Z"},{"label":"dcterms.description","value":"Department of Applied Mathematics and Statistics"},{"label":"dcterms.extent","value":"102 pg."},{"label":"dcterms.format","value":"Application/PDF"},{"label":"dcterms.identifier","value":"http://hdl.handle.net/11401/77210"},{"label":"dcterms.issued","value":"2016-12-01"},{"label":"dcterms.language","value":"en_US"},{"label":"dcterms.provenance","value":"Made available in DSpace on 2017-09-20T16:52:12Z (GMT). No. of bitstreams: 1\nLiu_grad.sunysb_0771E_13105.pdf: 2918168 bytes, checksum: 06fd4e12d2d5efab720bbe432865aedf (MD5)\n  Previous issue date:    1"},{"label":"dcterms.publisher","value":"The Graduate School, Stony Brook University: Stony Brook, NY."},{"label":"dcterms.subject","value":"Mathematics"},{"label":"dcterms.title","value":"Weighted-Least-Squares Based Essentially Non-Oscillatory Schemes on Unstructured Meshes"},{"label":"dcterms.type","value":"Dissertation"},{"label":"dc.type","value":"Dissertation"}],"description":"This manifest was generated dynamically","viewingDirection":"left-to-right","sequences":[{"@type":"sc:Sequence","canvases":[{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json","@type":"sc:Canvas","label":"Page 1","height":1650,"width":1275,"images":[{"@type":"oa:Annotation","motivation":"sc:painting","resource":{"@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/90%2F63%2F18%2F90631805345589796041903517380628723234/full/full/0/default.jpg","@type":"dctypes:Image","format":"image/jpeg","height":1650,"width":1275,"service":{"@context":"http://iiif.io/api/image/2/context.json","@id":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/90%2F63%2F18%2F90631805345589796041903517380628723234","profile":"http://iiif.io/api/image/2/level2.json"}},"on":"https://repo.library.stonybrook.edu/cantaloupe/iiif/2/canvas/page-1.json"}]}]}]}