Issues of an Eulerian/ALE algorithm based on a compatible, staggered-grid, Lagrangian step

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In this paper a number of distinct issues that are of concern in the construction of an Eulerian or ALE algorithm by means of a Lagrangian step and separate remap are explored. First, the common advection test problems usually cited in the literature pertaining to limiter construction are not wholly suitable to accessing the advection quality of an Eulerian scheme. A more appropriate set of test problems are derived to satisfy this need. Next, the basic philosophy of an ALE algorithm is that it should function as close to the Lagrangian limit as possible, and should therefore approach that limit ... continued below

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10 p.

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Caramana, E. J. (Edward J.) January 1, 2001.

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In this paper a number of distinct issues that are of concern in the construction of an Eulerian or ALE algorithm by means of a Lagrangian step and separate remap are explored. First, the common advection test problems usually cited in the literature pertaining to limiter construction are not wholly suitable to accessing the advection quality of an Eulerian scheme. A more appropriate set of test problems are derived to satisfy this need. Next, the basic philosophy of an ALE algorithm is that it should function as close to the Lagrangian limit as possible, and should therefore approach that limit in a uniform manner. Certain difficulties with achieving this using a spatially staggered Lagrangian step (coordinates and velocity are point centered, density, internal energy, stresses, etc. are zone centered), particularly with regard to the update of subzonal pressure forces utilized in the Lagrangian step to control hourglass and other spurious grid motions, are discussed. An additional problem with the Lagrangian step occurs in 2D cylindrical geometry where so-called 'area-weight' differencing is used to obtain the limit of 1D spherical symmetry. Here the nodal mass, and thus the momentum and kinetic energy, is formed by a particular construct that does not have any true volume associated with it. The proper treatment of this pecularity is given. Finally, advection on an unstructured grid may in certain instances be facilitated by means of an underlying structured one; situations where this may be preferred are briefly detailed.

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10 p.

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  • "Submitted to: SIAM-2001, San Diego, CA, July 12, 2001"

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  • Report No.: LA-UR-01-2977
  • Grant Number: none
  • Office of Scientific & Technical Information Report Number: 975360
  • Archival Resource Key: ark:/67531/metadc933541

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  • January 1, 2001

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 4:18 p.m.

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Caramana, E. J. (Edward J.). Issues of an Eulerian/ALE algorithm based on a compatible, staggered-grid, Lagrangian step, article, January 1, 2001; United States. (digital.library.unt.edu/ark:/67531/metadc933541/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.