Some free boundary problems in potential flow regime usinga based level set method

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Recent advances in the field of fluid mechanics with moving fronts are linked to the use of Level Set Methods, a versatile mathematical technique to follow free boundaries which undergo topological changes. A challenging class of problems in this context are those related to the solution of a partial differential equation posed on a moving domain, in which the boundary condition for the PDE solver has to be obtained from a partial differential equation defined on the front. This is the case of potential flow models with moving boundaries. Moreover the fluid front will possibly be carrying some material substance ... continued below

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Garzon, M.; Bobillo-Ares, N. & Sethian, J.A. December 9, 2008.

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Recent advances in the field of fluid mechanics with moving fronts are linked to the use of Level Set Methods, a versatile mathematical technique to follow free boundaries which undergo topological changes. A challenging class of problems in this context are those related to the solution of a partial differential equation posed on a moving domain, in which the boundary condition for the PDE solver has to be obtained from a partial differential equation defined on the front. This is the case of potential flow models with moving boundaries. Moreover the fluid front will possibly be carrying some material substance which will diffuse in the front and be advected by the front velocity, as for example the use of surfactants to lower surface tension. We present a Level Set based methodology to embed this partial differential equations defined on the front in a complete Eulerian framework, fully avoiding the tracking of fluid particles and its known limitations. To show the advantages of this approach in the field of Fluid Mechanics we present in this work one particular application: the numerical approximation of a potential flow model to simulate the evolution and breaking of a solitary wave propagating over a slopping bottom and compare the level set based algorithm with previous front tracking models.

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  • Journal Name: Nova

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  • Report No.: LBNL-1460E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 948033
  • Archival Resource Key: ark:/67531/metadc899541

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  • December 9, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:21 p.m.

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Garzon, M.; Bobillo-Ares, N. & Sethian, J.A. Some free boundary problems in potential flow regime usinga based level set method, article, December 9, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc899541/: accessed September 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.