Numerical simulation of 2D sloshing waves using SPH with diffusive terms

Chowdhury, S. De; Sannasiraj, S. A.

doi:10.1016/j.apor.2014.06.004

Cited by 28 publications

(9 citation statements)

References 35 publications

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“…The dimensions of the fluid domain in the tank are [D × H], and the motion of the tank is represented using the first‐order linear wave theory, as follows:

x(t)=A\cos \left({\omega}_nt\right)

{\omega}_n^2=\mid g\mid {k}_n\tanh \left({k}_nH\right)

where

\mathrm{A}

is the amplitude,

{\upomega}_{\mathrm{n}}

is the angular frequency,

g

is the gravitational acceleration,

{k}_n

is the wave number,

H

is the initial wave depth inside the tank, and

n

is the free surface mode. The amplitude and frequency are 0.03D and

{\upomega}_1

, as in 47 . Same with their study, the initial The LSPH and ELSPH results are compared to the finite element method (FEM) solution 47 in Figure 21.…”

Section: Benchmark Simulationsmentioning

confidence: 98%

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A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

Yoo

Kim

et al. 2022

Numerical Meth Engineering

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In this article, we propose a simple, consistent, and robust Eulerian-Lagrangian weakly compressible smoothed particle hydrodynamics (EL-WCSPH) for the simulation of hydrodynamics and convection heat transfer problems. First, the basic governing equation is formulated using the ALE-SPH framework. The universal formulation is similar to the standard WCSPH, but the degree of Eulerian and Lagrangian schemes can be controlled by inserting a pre-defined arbitrary parameter α ∈ [0, 1]. To alleviate potential numerical errors and inconsistency, particle mass correction is proposed along with particle disorder correction.Then, an algorithm is introduced, in which only a slight modification is necessary compared to the standard WCSPH. Finally, extensive benchmark simulations are conducted to validate the proposed method. As a result, the proposed method is found to perform well in hydrodynamics problems with various flow conditions (pipe flow, lid-driven problem, Taylor-Green vortex, vortex shedding problem, and water sloshing) and thermal-hydraulics problems (natural convection in a square cavity).

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“…The dimensions of the fluid domain in the tank are [D × H], and the motion of the tank is represented using the first‐order linear wave theory, as follows:

x(t)=A\cos \left({\omega}_nt\right)

{\omega}_n^2=\mid g\mid {k}_n\tanh \left({k}_nH\right)

where

\mathrm{A}

is the amplitude,

{\upomega}_{\mathrm{n}}

is the angular frequency,

g

is the gravitational acceleration,

{k}_n

is the wave number,

H

is the initial wave depth inside the tank, and

n

is the free surface mode. The amplitude and frequency are 0.03D and

{\upomega}_1

, as in 47 . Same with their study, the initial The LSPH and ELSPH results are compared to the finite element method (FEM) solution 47 in Figure 21.…”

Section: Benchmark Simulationsmentioning

confidence: 98%

“…The amplitude and frequency are 0.03D and

{\upomega}_1

, as in 47 . Same with their study, the initial The LSPH and ELSPH results are compared to the finite element method (FEM) solution 47 in Figure 21.…”

Section: Benchmark Simulationsmentioning

confidence: 98%

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

Yoo

Kim

et al. 2022

Numerical Meth Engineering

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“…The δ-SPH is a robust, accurate and reliable method in solving several hydrodynamic problems, (see e.g. Antuono et al [2,6], Meringolo et al [45], Zhang et al [43], Sun et al [32], Green and Peiró [65], De Chowdhury and Sannasiraj [61], Zhang et al [63]). Nevertheless, there are still some drawbacks that limit its application in some areas where traditional CFD methods perform well, such as the modelling of shear flows at high Reynolds numbers, vortical flow evolutions characterized by large negative pressure values or viscous flows inside confined domains.…”

Section: Introductionmentioning

confidence: 99%

Theδ-ALE-SPH model: An arbitrary Lagrangian-Eulerian framework for theδ-SPH model with particle shifting technique

et al. 2021

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The behaviour of a weakly-compressible SPH scheme obtained by rewriting the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is studied. Differently from previous works on ALE, which generally adopt conservative variables (i.e. mass and momentum) and rely on the use of Riemann solvers inside the spatial operators, the proposed model is expressed in terms of primitive variables (i.e. density and velocity) and is written by using the standard differential formulations of the weakly-compressible SPH schemes. Similarly to ALE-SPH models, the arbitrary velocity field is obtained by modifying the pure Lagrangian velocity of the material point through a velocity δu given by a Particle Shifting Technique (PST). We show that the above-mentioned ALE-SPH equations are, however, unstable when they are integrated in time. The instability appears in the form of large volume variations in those fluid regions characterised by high velocity strain rates. Nonetheless, the scheme can be stabilised if appropriate diffusion terms are included in both the equations of density and mass. This latter scheme, hereinafter called δ-ALE-SPH scheme, is validated against reference benchmark testcases: the viscous flow around an inclined elliptical cylinder, the lid-driven cavity and a dam-break flow impacting a vertical wall.

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“…Chao et al simulate the phenomenon of sloshing with rectangular tanks to find the optimum kernel [1]. De Chowdhury and Sannasiraj use SPH with rectangular tanks using diffusive terms to reduce pressure oscillation [2], Servan-Camas et al simulate the phenomenon of sloshing employing coupled SPH-FEM using the time-domain method [3], Longshaw and Rogers use SPH to simulate the sloshing of fuel tanks with DualSPHysics [4], Green has used Smoothed Particle Hydrodynamics (SPH) in long-duration simulation at a small filling ratio in 2D with high stretching [5], The applications of SPH in sloshing are carried out by Landrini et al [6] and Chen et al [7] to predict impact pressure in the tanks s sidewall. Recently Trimulyono et.al [8] were used SPH for experimental validation using prismatic tank both 2D and 3D.…”

Section: Introductionmentioning

confidence: 99%

Sloshing Simulation of Single-Phase and Two-Phase SPH using DualSPHysics

Trimulyono

Samuel

Iqbal

2020

Kapal

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The sloshing phenomenon is one of the free surface flow that can endanger liquid cargo carriers such as ships. Sloshing is defined as the resonance of fluid inside a tank caused by external oscillation. When sloshing is close to the natural frequency of the tank it could endanger ships. Particle method has the advantages to be applied because sloshing is dealing with free surface. One of the particle methods is Smoothed Particle Hydrodynamics (SPH). In this study, compressible SPH was used as a result of the pressure oscillation, which exists because of the effect of density fluctuation as nature of weakly compressible SPH. To reduce pressure noise, a filtering method, Low Pass Filter, was used to overcome pressure oscillation. Three pressure sensors were used in the sloshing experiment with a combination of motions and filling ratios. Only one pressure sensor located in the bottom was used to validate the numerical results. A set of SPH parameters were derived that fit for the sloshing problem. The SPH results show a good agreement with the experiment’s. The difference between SPH and experiment is under 1 % for sway, but a larger difference shows in roll. Low pass filter technique could reduce pressure noise, but comprehensive method needs to develop for general implementation.

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Numerical simulation of 2D sloshing waves using SPH with diffusive terms

Cited by 28 publications

References 35 publications

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

Theδ-ALE-SPH model: An arbitrary Lagrangian-Eulerian framework for theδ-SPH model with particle shifting technique

Sloshing Simulation of Single-Phase and Two-Phase SPH using DualSPHysics

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