New Numerical Investigation Using Meshless Methods Applied to the Linear Free Surface Water Waves

Loukili, Mohamed; Mordane, Soumia

doi:10.1007/978-3-319-91192-2_33

Cited by 7 publications

(6 citation statements)

References 7 publications

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“…The case of GABCs without current is found to be the same as the open boundary condition that is proposed by Orlansky [15]. The problem is treated by the Method of Fundamental Solutions MFS that performs strong abilities to resolve the free surface water wave's problem [16][17][18][19][20]. The use of GABCs presented in this work aims to construct an open boundary condition in such a way that the disturbances, caused by different aspects of interactions inside the computational domain, are transmitted without affecting the solutions.…”

Section: Introductionmentioning

confidence: 98%

A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

Loukili

Kotrasová

Bouaine

2021

Civil and Environmental Engineering

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The purpose of this work is to study the feasibility and efficiency of Generating Absorbing Boundary Conditions (GABCs), applied to wave-current interactions using the Method of Fundamental Solutions (MFS) as radial basis function, the problem is solved by collocation method. The objective is modeling wave-current interactions phenomena applied in a Numerical Wave Tank (NWT) where the flow is described within the potential theory, using a condition without resorting to the sponge layers on the boundaries. To check the feasibility and efficiency of GABCs presented in this paper, we verify accurately the numerical solutions by comparing the numerical solutions with the analytical ones. Further, we check the accuracy of numerical solutions by trying a different number of nodes. Thereafter, we evaluate the influence of different aspects of current (coplanar current, without current, and opposing current) on the wave properties. As an application, we take into account the generating-absorbing boundary conditions GABCs in a computational domain with a wavy downstream wall to confirm the efficiency of the adopted numerical boundary condition.

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Section: Introductionmentioning

confidence: 98%

A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

Loukili

Kotrasová

Bouaine

2021

Civil and Environmental Engineering

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“…As a perspective, we endeavor to investigate the limitation of the Hermitian finite differences method to treat the 3D jet flow simulation. Besides, to inspect the capability of spectral methods [38], and meshless methods [39][40][41][42][43] to deal with the jet problem at higher Reynolds number.…”

Section: Discussionmentioning

confidence: 99%

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Loukili

Kotrasová

Dutykh

2021

Fluids

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In this manuscript, the injection of a homogeneous jet in a numerical tank is considered to revolve around discussing the limitation of the direct numerical simulation (DNS), to resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank. The investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the equations governing the problem is made by the compact Hermitian finite differences method (HFDM) high accuracy Oh2,h4 First, the numerical code used in this work is validated by comparing the profiles of the velocity components at the median of the lid-driven cavity with the results of the literature. Furthermore, to confirm the validity of the present numerical code, an evaluation of mesh domain sensitivity is assessed by comparing the numerical vertical velocity profiles for different steps of y-direction (flow direction) with the analytical solution. Afterward, the aim is to perform the nonlinear simulations of the Navier–Stokes equations in a large computational domain. Next, the goal is to characterize the instabilities associated with high Reynolds numbers when a jet is emitted from the bottom of the numerical tank.

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“…In this section, we propose the method of fundamental solutions [10][11][12][13] (MFS) to resolve the equations governing the linear problem of wave-current interactions, by the implementation of the fundamental solution of 2D Laplace equation that is expressed as:…”

Section: Numerical Formulationmentioning

confidence: 99%

“…For these reasons, the generatingabsorbing boundary conditions (GABCs) in the presence of different aspect of currents (coplanar current, opposing current, and without current) is an interesting subject to investigate. Therefore, in this work the generating absorbing boundary conditions (GABCs) for the use of wave-current interactions is studied using the method of fundamental solutions (MFS) [10][11][12][13]. The MFS first proposed by Kupradze and Aleksidze [14] and has been widely used in the numerical solutions for the Laplace, Poisson, biharmonic, Helmholtz and diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Stability Investigations of the Method of Fundamental Solutions Applied to Wave-Current Interactions Using Generating-Absorbing Boundary Conditions

et al. 2021

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In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a Numerical Wave Tank (NWT) within the potential theory where the main regular manifestations are the periodicity, and symmetry of traveling waves. Besides, the investigations cover different aspects of currents (coplanar current, without current, and opposing current), and also different water depths. Furthermore, the accuracy and stability of the numerical method (MFS) used in this work is evaluated for different locations and numbers of source points.

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New Numerical Investigation Using Meshless Methods Applied to the Linear Free Surface Water Waves

Cited by 7 publications

References 7 publications

A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

Numerical Modeling of Jet at the Bottom of Tank at Moderate Reynolds Number Using Compact Hermitian Finite Differences Method

Numerical Stability Investigations of the Method of Fundamental Solutions Applied to Wave-Current Interactions Using Generating-Absorbing Boundary Conditions

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