smoothed particle hydrodynamics; boundary conditions; shallow water equations; source terms; virtual boundary particles; still waterIn this paper, an approximate modified virtual boundary particle method (MVBP) for solid boundary conditions in a two-dimensional (2-D) smoothed particle hydrodynamics (SPH) model is presented; this is a development of the original VBP method recently proposed by Ferrari et al. (Comput. Fluids 2009; 38(6): 1203–1217). The aim is to maintain the zeroth moment of the kernel function as closely as possible to unity, a property referred to as zero-consistency, for particles close to solid boundaries. The performance of the new method in approximating zero-consistency in the presence of complicated boundaries is demonstrated where we show that the MVBP method improves the accuracy of the zeroth moment by almost an order of magnitude. Shallow-water flows are an important two-dimensional (2-D) application and provide the simple test case of still water. The shallow-water equations (SWEs) are thus considered in SPH form and the zero-consistency approximation is tested for still water in domains with different boundaries: a circle and two squares, one with an additional internal angle of 300∘ and one with four internal angles of 345∘. We demonstrate that for an internal angle of 300∘, the MVBP method demonstrates numerical convergence to still-water conditions whereas both mirror particles and the VBP method cannot. The method is also demonstrated for the dynamic case of a circular dam break interacting with an outer circular wall where conventional mirror particles fail to prevent particles passing through the solid wall. The SPH SWEs are further generalized through a new method for discretizing the bed source term allowing arbitrarily complicated bathymetries. The resulting formulation is tested by considering many different bed shapes in still water: submerged and surface-piercing humps, a submerged step, a submerged and surface-piercing parabolic bed

Smoothed Particle Hydrodynamics: Approximate zero-consistent 2-D boundary conditions and still shallow-water tests / Vacondio, R; Rogers, B.D.; Stansby, P.K.. - In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS. - ISSN 0271-2091. - 69:1(2012), pp. 226-253. [10.1002/fld.2559]

Smoothed Particle Hydrodynamics: Approximate zero-consistent 2-D boundary conditions and still shallow-water tests

VACONDIO, Renato;
2012

Abstract

smoothed particle hydrodynamics; boundary conditions; shallow water equations; source terms; virtual boundary particles; still waterIn this paper, an approximate modified virtual boundary particle method (MVBP) for solid boundary conditions in a two-dimensional (2-D) smoothed particle hydrodynamics (SPH) model is presented; this is a development of the original VBP method recently proposed by Ferrari et al. (Comput. Fluids 2009; 38(6): 1203–1217). The aim is to maintain the zeroth moment of the kernel function as closely as possible to unity, a property referred to as zero-consistency, for particles close to solid boundaries. The performance of the new method in approximating zero-consistency in the presence of complicated boundaries is demonstrated where we show that the MVBP method improves the accuracy of the zeroth moment by almost an order of magnitude. Shallow-water flows are an important two-dimensional (2-D) application and provide the simple test case of still water. The shallow-water equations (SWEs) are thus considered in SPH form and the zero-consistency approximation is tested for still water in domains with different boundaries: a circle and two squares, one with an additional internal angle of 300∘ and one with four internal angles of 345∘. We demonstrate that for an internal angle of 300∘, the MVBP method demonstrates numerical convergence to still-water conditions whereas both mirror particles and the VBP method cannot. The method is also demonstrated for the dynamic case of a circular dam break interacting with an outer circular wall where conventional mirror particles fail to prevent particles passing through the solid wall. The SPH SWEs are further generalized through a new method for discretizing the bed source term allowing arbitrarily complicated bathymetries. The resulting formulation is tested by considering many different bed shapes in still water: submerged and surface-piercing humps, a submerged step, a submerged and surface-piercing parabolic bed
Smoothed Particle Hydrodynamics: Approximate zero-consistent 2-D boundary conditions and still shallow-water tests / Vacondio, R; Rogers, B.D.; Stansby, P.K.. - In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS. - ISSN 0271-2091. - 69:1(2012), pp. 226-253. [10.1002/fld.2559]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2797907
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