Unified Solution Algorithm for Solids and Fluids.

Fujieda, Tadaomi; Wada, Soji; Tanahashi, Takahiko

doi:10.1299/kikaib.65.3891

Cited by 1 publication

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“…Moreover, the movement of a drop due to the Marangoni e ect [19][20][21][22][23][24] has not been analysed with the relevant methods yet. The governing equations are discretized by the ÿnite element method (FEM), in which the velocity ÿeld is solved by the generalized simpliÿed marker and cell (GSMAC) scheme [25][26][27][28] and the cubic interpolated pseudo-particle (CIP) method [29] is applied to the reinitialization of the level set function. The outline of the paper is as follows: ÿrst the governing equations and their discretization are described with a review of the level set method.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement

Kohno

Tanahashi

2004

Numerical Methods in Fluids

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SUMMARYA novel numerical scheme is developed by coupling the level set method with the adaptive mesh reÿnement in order to analyse moving interfaces economically and accurately. The ÿnite element method (FEM) is used to discretize the governing equations with the generalized simpliÿed marker and cell (GSMAC) scheme, and the cubic interpolated pseudo-particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh reÿnement is implemented in the quadrangular grid systems and easily embedded in the FEM-based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two-dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its e ectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni e ect is ÿrst simulated e ciently with the present scheme.

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