Simulation of free‐surface waves in liquid sloshing using a domain‐type meshless method

Wu, Nae‐Lih; Chang, Kuang‐An

doi:10.1002/fld.2346

Cited by 25 publications

(19 citation statements)

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“…In [40], it was reported that 'satisfying the boundary conditions and the governing equations simultaneously at the boundary can provide a more accurate solution to a given problem'. This coincides with what was reported in [21]. Improvements of the approximation for making the governing equation satisfied at the boundaries were also proposed in [40].…”

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confidence: 89%

“…Nevertheless, boundary-type RBF collocation methods are limited to problems governed by some specific equations, such as Laplace or Helmholtz equations. In [21], a modified domain-type RBF collocation method was proposed. With additional satisfaction to the governing equation on boundary collocation points, the gradient of the velocity potential at any free surface node, which represents the velocity vector at that specific node, was accurately estimated.…”

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confidence: 99%

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A robust local polynomial collocation method

Tsay

2012

Numerical Meth Engineering

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In this paper, a robust local polynomial collocation method is presented. Based on collocation, this method is rather simple and straightforward. The present method is developed in a way that the governing equation is satisfied on boundaries as well as boundary conditions. This requirement makes the present method more accurate and robust than conventional collocation methods, especially in estimating the partial derivatives of the solution near the boundary. Studies about the sensitivity of the shape parameter and the local supporting range in the moving least square approach and the convergence of the nodal resolution are carried out by using some benchmark problems. This method is further verified by applying it to a steady-state convectiondiffusion problem. Finally, the present method is applied to calculate the velocity fields of two potential flow problems. More accurate numerical results are obtained. 356N.-J. WU AND T.-K. TSAY methods, in which governing equations are satisfied automatically in the entire domain, are more applicable to problems in which accurate partial derivatives of the solutions around the boundaries are desirable. Typical examples are the application of method of fundamental solutions to water wave problems [18][19][20]. Nevertheless, boundary-type RBF collocation methods are limited to problems governed by some specific equations, such as Laplace or Helmholtz equations. In [21], a modified domain-type RBF collocation method was proposed. With additional satisfaction to the governing equation on boundary collocation points, the gradient of the velocity potential at any free surface node, which represents the velocity vector at that specific node, was accurately estimated. Thus, this method was successfully applied to the simulation of water waves in a swaying tank.Apart from the combination of RBFs, one could use a polynomial to approximate the solution of a PDE and seek the coefficients of all the monomials by applying the collocation technique. However, polynomials have been rarely used globally such as the basis functions being treated in RBF collocation methods. This is because the values of high-order terms could become extremely large at points far from the origin. In most polynomial collocation methods, polynomials are just applied to approximate the solution piecewise around discretized nodes. The moving least square (MLS) approach is always accompanied with the polynomial approximation to transform and combine the local solutions into a global solution form. In each local solution, basis functions are the monomials, and their factors are just the coefficients. In the global solution form, the basis functions are called the shape functions, and their factors are the values of the solution itself. This localizing approach is somewhat like localized RBF collocation methods [22]. Representatives of this family are the hp-meshless cloud method [23] and the finite point method (FPM) [24,25].Being strong-form methods, polynomial collocation methods with MLS approach are reported to ...

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confidence: 89%

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confidence: 99%

A robust local polynomial collocation method

Tsay

2012

Numerical Meth Engineering

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“…This method has been further upgraded to symmetric collocation (Fasshauer, 1996), modified collocation (Šarler, 2005), and indirect collocation (Mai-Duy and Tran-Cong, 2003). Applications of the method can be found for fluid dynamic problems (Mai-Duy and Tran-Cong, 2001), numerical wave tanks (Huang et al, 2014;Tsung et al, 2013;Wu and Chang, 2011), natural convections in porous media (Šarler et al, 2004), solid-liquid phase change problems (Kovacevic et al, 2003), wave problems (Dehghan and Shokri, 2009), stochastic problems (Dehghan and Mohammadi, 2014) and others. The advantage of the GRBFCM is that its effectiveness in dealing with arbitrary and complex domain.…”

Section: Introductionmentioning

confidence: 98%

Using a local radial basis function collocation method to approximate radiation boundary conditions

2015

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“…The numerical results demonstrated that the non-linear effects become obvious as the wave steepness increases, which is in good agreements with experimental observations and physical researches. Wu and Chang Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/enganabound [7] adopted the RBFCM, one kind of meshless methods, and the leapfrog scheme to analyze the sloshing problems in both of twoand three-dimensional numerical tanks. In addition, Chen et al [9] used the MCTM combined with the group-preserving scheme to analyze the two-dimensional sloshing problems and good stability of their approach is observed in the provided comparisons.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, numerical simulation is a good candidate in comparison with mathematical means and experimental study when academic research and engineering design related to sloshing phenomenon are considered. In the past decades, many numerical schemes [1][2][3][4][5][6][7][8][9][10] have been proposed to accurately and efficiently model the non-breaking waves in the sloshing problem, such as the finite difference method (FDM) [3], the finite element method (FEM) [4,5], the boundary element method [6], the radial basis function collocation method (RBFCM) [7], the Trefftz method [8], the modified collocation Trefftz method (MCTM) [9], the meshless local Petrov-Galerkin (MLPG) method [10], etc. For example, Frandsen [3] proposed a FDM scheme, combined with a modified sigma-transformation, to simulate non-linear sloshing wave motion in a two-dimensional tank.…”

Section: Introductionmentioning

confidence: 99%