2018
DOI: 10.1002/fld.4506
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A high‐order PIC method for advection‐dominated flow with application to shallow water waves

Abstract: Summary A hybrid Eulerian‐Lagrangian particle‐in‐cell–type numerical method is developed for the solution of advection‐dominated flow problems. Particular attention is given over to the high‐order transfer of flow properties from the particles to the grid. For smooth flows, the method presented is of formal high‐order accuracy in space. The method is applied to solve the nonlinear shallow water equations resulting in a new, and novel, shock capturing shallow water solver. The approach is able to simulate compl… Show more

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Cited by 3 publications
(2 citation statements)
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“…Further developments can be found in, for example, Brackbill and Ruppel [10] and Brackbill et al [11], which significantly reduce the numerical dissipation of PIC method. Recently, variations of the PIC method have achieved high-order accuracy (see Edwards and Bridson [12], Maljaars et al [13] and Wang and Kelly [14]).…”
Section: Introductionmentioning
confidence: 99%
“…Further developments can be found in, for example, Brackbill and Ruppel [10] and Brackbill et al [11], which significantly reduce the numerical dissipation of PIC method. Recently, variations of the PIC method have achieved high-order accuracy (see Edwards and Bridson [12], Maljaars et al [13] and Wang and Kelly [14]).…”
Section: Introductionmentioning
confidence: 99%
“…Later, many attempts have been made to improve this method (see Brackbill and Ruppel (1986); Brackbill et al (1988); Yabe (1982, 1983)). More recently, high-order PIC variations have become possible (see Edwards and Bridson (2012), Maljaars et al (2018) and Wang and Kelly (2018)). However, so far this hybrid method has not been very well exploited for use in the ocean engineering field, where modelling complex wavestructure interaction with computational efficiency still remains an important challenge.…”
Section: Introductionmentioning
confidence: 99%