A semi-implicit SPH scheme for the two-dimensional shallow water equations

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Erscheinungsjahr:
2015
Medientyp:
Text
Beschreibung:
  • This work focuses on the extension of the semi-
    implicit SPH scheme to two dimensions for the shallow water
    equations. The scheme in was first presented at last year’s
    SPHERIC workshop, following the semi-implicit finite volume
    and finite difference approach of Casulli. In standard explicit
    numerical methods, there is often a severe limitation on the
    time step due to the stability restriction imposed by the CFL
    condition. To this end, a new semi-implicit SPH scheme is derived,
    which leads to an unconditionally stable method. The discrete
    momentum equation is substituted into the discrete continuity
    equation to obtain a symmetric positive definite linear system
    for the free surface elevation. The resulting system can be easily
    solved by a matrix-free conjugate gradient method. Once the
    new free surface location is known, the velocity at the new time
    level can be directly computed and the particle positions can
    subsequently be updated. The method is validated on a smooth
    inviscid hydrostatic free surface flow for the two dimensional
    shallow water equations.
Lizenz:
  • info:eu-repo/semantics/restrictedAccess
Quellsystem:
Forschungsinformationssystem der UHH

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oai:www.edit.fis.uni-hamburg.de:publications/d0bd368c-47bd-4d02-817d-930e5b88eea5