A meshless solution of two-dimensional unsteady flow

Kovářík, Karel; Mužík, Juraj; Mahmood, Mohammed Shuker

doi:10.1016/j.enganabound.2011.12.009

Cited by 22 publications

(11 citation statements)

References 6 publications

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“…where Wðr ij Þ is the multiquadric RBF between points i and j (see [31,19]), r ij is the Euclidean distance between these two points and R is the so-called shape factor of the multiquadric function. The formula of Hardy [32] with a slight modification is applied to the local RBFs (see [31]) to find the optimal value of the shape factor, which can be computed in point i as…”

Section: Meshless Local Integral Formulationmentioning

confidence: 99%

“…A technique described in detail in [19] can be used to obtain a set of RBF shape functions Φ ij , which can be used to express the pressure and its derivatives in the point i as…”

Section: Meshless Local Integral Formulationmentioning

confidence: 99%

“…During the past year, various meshless methods have been developed by different groups. These include smooth particle hydrodynamics (SPH) [8], the least square collocation meshless method [9][10][11], the meshless local Petrov-Galerkin (MLPG) method [12,13], the local boundary integral equation method (LBIEM) [14][15][16], and the radial basis integral equation method (RBIEM) [17][18][19]. Ghasemi et al [20] used SPH to demonstrate the possibility of this method to solve density currents flow.…”

Section: Introductionmentioning

confidence: 99%

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A local boundary integral method for two-dimensional particle-driven gravity currents simulation

Kovářík

Mužík

Masarovičová

et al. 2015

Engineering Analysis with Boundary Elements

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Section: Meshless Local Integral Formulationmentioning

confidence: 99%

“…A technique described in detail in [19] can be used to obtain a set of RBF shape functions Φ ij , which can be used to express the pressure and its derivatives in the point i as…”

Section: Meshless Local Integral Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A local boundary integral method for two-dimensional particle-driven gravity currents simulation

Kovářík

Mužík

Masarovičová

et al. 2015

Engineering Analysis with Boundary Elements

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“…2). To express the local boundary integral form of the governing equations developed in the previous section in a domain Ω s , we apply the weighting residual principle [7] to equations (10), (11), (12), and (13) to obtain the weak form. If the test function w * is chosen to be the fundamental solution of the Laplace equation, then after integration by parts twice the following integral equations can be obtained (see also [8])…”

Section: Local Boundary Integral Formulationmentioning

confidence: 99%

A Meshless Method for Simulation of Particle-Driven Gravity Currents With Obstacles

Kovářík¹,

Mužík²,

Sitányiová³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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A meshless local boundary integral equation method (LBIEM) is used to analyse gravity currents flow in two-dimensional domains. The method solves the incompressible Navier-Stokes equations with a transport equation for the particle concentration. The characteristic-based split scheme is used to solve the governing equations. The LBIEM basic equations are derived via interpolation using radial basis functions. Numerical test cases of the lock-exchange channel flow with obstacles in its bed are presented here.

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“…For other implementations of the DRM meshless approach see Kovarik et al [7] and Dehgam and Shirzadi [4]. These three DRM meshless formulations are based on the DRM approximation of the integral representation formula (4) in terms of superposition of single and double layer potentials, with the fundamental solution and its normal derivative as kernels, instead of the integral formula (10) defined by only superposition of double layer potential, with the Dirichlet Green's function as the kernel, as considered in this work.…”

Section: Mathematical Formulation and Boundary Integral Represention mentioning

confidence: 99%

A note on the use of the Companion Solution (Dirichlet Green's function) on meshless boundary element methods

Power

Caruso

Portapila

2017

Engineering Analysis with Boundary Elements

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A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. AbstractMost implementations of meshless BEMs use a circular integration contours (spherical in 3D) embedded into a local interpolation stencil with the so called Companion Solution (CS) as a kernel, in order to eliminate the contribution of the single layer potential. However, the Dirichlet Green's Function (DGF) is the unique Fundamental Solution that is identically zero at any given close surface and therefore eliminates the single layer potential. One of the main objectives of this work is to show that the CS is nothing else than the DGF for a circle collocated at its origin. The use of the DGF allows the collocation at more than one point, permitting the implementation of a P-adaptive scheme in order to improve the accuracy of the solution without increasing the number of subregions. In our numerical simulations, the boundary conditions are imposed at the interpolation stencils in contact with the problem boundary instead of at the corresponding integration surfaces, permitting always the use of circular integration contours, even in regions near or in contact with the problem domain where the densities of the integrals are reconstructed from the interpolation formulae that already included the problem boundary conditions.

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A meshless solution of two-dimensional unsteady flow

Cited by 22 publications

References 6 publications

A local boundary integral method for two-dimensional particle-driven gravity currents simulation

A local boundary integral method for two-dimensional particle-driven gravity currents simulation

A Meshless Method for Simulation of Particle-Driven Gravity Currents With Obstacles

A note on the use of the Companion Solution (Dirichlet Green's function) on meshless boundary element methods

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