The Method of Fundamental Solutions for Stokes flows with a free surface

Poullikkas, Andreas; Karageorghis, Andréas; Georgiou, Georgios C.; Ascough, J.

doi:10.1002/num.10500

Cited by 14 publications

(9 citation statements)

References 16 publications

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“…For a two-dimensional problem, the unknown variable of the streamfunction formulation is only the streamfunction, and the number of unknown variables is minimum among these formulations. Poullikkas et al [3] successfully used the method of fundamental solutions (MFS), which is free from mesh generation and numerical quadrature, and the streamfunction formulation to simulate the Stokes flow with a free surface. The velocity-vorticity formulation can be derived by introducing the vorticity vector.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solutions of Direct and Inverse Stokes Problems by the Method of Fundamental Solutions and the Laplacian Decomposition

Fan

2015

Numerical Heat Transfer, Part B: Fundamentals

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In this study, both of direct and inverse Stokes problems are stably and accurately analyzed by the method of fundamental solutions (MFS) and the Laplacian decomposition. In order to accurately resolve the Stokes problem, the Laplacian decomposition is adopted to convert the Stokes equations into three Laplace equations, which will be solved by the MFS, with an augmented boundary condition. To enforce the satisfactions of continuity equation along whole boundary as an augmented boundary condition will guarantee the satisfactions of mass conservation inside the computational domain. The MFS is one of the most promising boundary-type meshless methods, since the time-consuming tasks of mesh generation and numerical quadrature can be avoided as well as only boundary nodes are needed for numerical implementations. The numerical solutions of the MFS are expressed as linear combinations of fundamental solutions of Laplace equation and the sources are located out of the computational domain to avoid numerical singularity. The numerical solutions for velocity components, pressure and their gradient terms can be obtained by simple summation due to the simplicity of the MFS. Several numerical examples of direct and inverse Stokes problems are analyzed by the proposed boundarytype meshless numerical scheme. The simplicity and the accuracy of the proposed method are verified by numerical experiments and comparisons. Moreover, different levels of noise are added into boundary conditions of inverse Stokes problems to validate the stability of the proposed numerical scheme.

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Section: Introductionmentioning

confidence: 99%

“…For Stokes flow, there are various formulations of the governing equations, such as the primary-variable formulation [2], the streamfunction formulation [3,4], the velocity-vorticity formulation [5], the Laplacian decomposition [6], etc. The unknown variables in the primary-variable formulation are the velocity components and the pressure.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Direct and Inverse Stokes Problems by the Method of Fundamental Solutions and the Laplacian Decomposition

Fan

2015

Numerical Heat Transfer, Part B: Fundamentals

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“…Prior to this study, the MFS has been applied to solve free boundary problems [14,25] and direct Signorini potential problems in both two and three dimensions [23,24], using the FORTRAN NAG routine E04UPF [22]. The novelty of this paper is twofold.…”

Section: Introductionmentioning

confidence: 99%

The method of fundamental solutions for solving direct and inverse Signorini problems

Karageorghis

Lesnic

Marin

2015

Computers & Structures

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“…Based on a set of scattered nodes, mesh-less methods overcome certain limitations of grid methods. The Kansa method [9], the boundary knot method (BKM) [10], the backward substitution method [11,12], and the method of fundamental solutions (MFS) [13][14][15] are such methods. Nevertheless, the MFS shows superiority of stability over the LRBF.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Steady-State Free Boundary Problems Using the Singular Boundary Method

sci¹

2021

AAMM

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In this paper, the recently-developed singular boundary method is applied to address free boundary problems. This mesh-less numerical method is based on the use of the origin intensity factors with fundamental solutions. Three numerical examples and their results are compared with the results obtained using traditional methods. The comparisons indicate that the proposed scheme yields good results in determining the position of the free boundary.

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The Method of Fundamental Solutions for Stokes flows with a free surface

Cited by 14 publications

References 16 publications

Numerical Solutions of Direct and Inverse Stokes Problems by the Method of Fundamental Solutions and the Laplacian Decomposition

Numerical Solutions of Direct and Inverse Stokes Problems by the Method of Fundamental Solutions and the Laplacian Decomposition

The method of fundamental solutions for solving direct and inverse Signorini problems

Numerical Solution of Steady-State Free Boundary Problems Using the Singular Boundary Method

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