Computation of Nonlinear Free-Surface Flows Using the Method of Fundamental Solutions

Loukili, Mohamed; Aarabi, Laila El; Mordane, Soumia

doi:10.1007/978-3-319-91186-1_44

Cited by 7 publications

(6 citation statements)

References 9 publications

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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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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 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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“…Furthermore, as the total internal height aspects increases the circulation of the fluid flow becomes slower, which causes to decreases effect of heat transfers rate. As perspectives, we endeavor to study the natural convection flows in H-form cavity using meshless methods [30][31][32][33], and spectral methods [34] that have been proven a strong efficiency in many nonlinear and engineering fields [30][31][32][33].…”

Section: Ra=10mentioning

confidence: 99%

A Computational Simulation of Steady Natural Convection in an H-Form Cavity

Loukili

Kotrasová

Dutykh

2020

Software Engineering Perspectives in Intelligent Systems

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The simulation of natural convection problem based on the Galerkin finite-element method, with the penalty finite-element formulation of the momentum balance equation, is exploited for accurate solutions of equations describing the problem of H-Form cavity differentially heated side walls. The cavity is occupied by the air whose Prandtl number is Pr=0.71, the fluid is assumed to be steady, viscous and incompressible within thermal convection. A numerical investigation has been made for Rayleigh numbers ranging from 10 to 10 6 for three cases of total internal height aspects of H-Form cavity: 0%, 50%, and 85%. Firstly, the goal is to validate the numerical code used to resolve the equations governing the problem of this work. For that, we present a comparison between the profiles at the point (0.5, 0) for the u-component, and u-component obtained in previous work for simple square cavity. Further, a comparison of the averaged Nusselt number with previous works for simple square cavity is realized in order to ensure the numerical accuracy, and the validity of our considered numerical tool. Secondly, the objective is to investigate on the hydrodynamic effects of Rayleigh number for different total internal height aspects of H-Form cavity on the dynamics of natural convection. Shortly after, the ambition is to assess the heat transfer rate for different Rayleigh number for three cases of internal height aspects.

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Computation of Nonlinear Free-Surface Flows Using the Method of Fundamental Solutions

Cited by 7 publications

References 9 publications

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

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

A Computational Simulation of Steady Natural Convection in an H-Form Cavity

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