Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

Pahar, Gourabananda; Dhar, Anirban

doi:10.1016/j.jhydrol.2017.01.034

Cited by 14 publications

(19 citation statements)

References 39 publications

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“…The most common is for each point to move with its own velocity ∆ x i = v (n) i ∆t , ∀i. Some variants of SPH use movement with the average velocity in the neighbourhood of each particle [19], while others perform two first order movements per time-step: one based on an 'intermediate' velocity, and one based on a 'final' velocity [23]. Some meshfree methods use the average velocity of the current and the previous time step [25], and even refer to the same as a second order method.…”

Section: First Order Movementmentioning

confidence: 99%

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Point cloud movement for fully Lagrangian meshfree methods

Suchde

Kuhnert

2018

Journal of Computational and Applied Mathematics

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In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of points or particles. The movement is most commonly done by a first order method, which assumes the velocity to be constant within a time step. We show that this method is very inaccurate and that it introduces volume and mass conservation errors. We further propose new methods for the same which prescribe an additional ODE system that describes the characteristic velocity. Movement is then performed along this characteristic velocity. The first new way of moving points is an extension of mesh-based streamline tracing ideas to meshfree methods. In the second way, the movement is done based on the difference in approximated streamlines between two time levels, which approximates the pathlines in unsteady flow. Numerical comparisons show these method to be vastly superior to the conventionally used first order method.

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Section: First Order Movementmentioning

confidence: 99%

“…Moving boundary points along this direction will result in the disc to constantly increase in volume. Despite the significant inaccuracies due to this method of movement, it is still used extensively today in almost all Lagrangian meshfree methods (see, for example, recent work in [18,23,25,29]).…”

Section: First Order Movementmentioning

confidence: 99%

Point cloud movement for fully Lagrangian meshfree methods

Suchde

Kuhnert

2018

Journal of Computational and Applied Mathematics

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“…In order to consider incompressibility in the SPH formulation, two approaches based on the projection method introduced by Chorin 74 in 1968 were proposed. 13,18 In 1999, Cummins and Rudman 75 have imposed a divergence free velocity field in the projection method. In 2003, Shao and Lo 17 have imposed an invariance of the fluid density in the projection method.…”

Section: Projection Methodsmentioning

confidence: 99%

“…This SPH method was called weakly compressible SPH (WCSPH) method because the weak form of the density transport equation is enforced through a state equation for pressure based on a numerical speed of sound. [10][11][12][13] The main disadvantage of the WCSPH method is the requirement of small time steps to avoid some numerical errors in the estimation of pressure with the state equation. [13][14][15] To overcome this difficulty, the incompressible SPH (ISPH) methods have been proposed.…”

Section: Introductionmentioning

confidence: 99%

“…The estimation of pressure is obtained thanks to a Poisson solver. 14,16 There are three possibilities to estimate the right hand side of the Poisson equation on the particles used, the density invariant, 17 the divergence free, 13,18 and a mixture of two previous methods. 19,20 The ISPH methods are known to be more accurate and stable than the WCSPH method for the estimation of pressure.…”

Section: Introductionmentioning

confidence: 99%

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Optimized incompressible smoothed particle hydrodynamics methods and validations

Ortega¹,

Beaudoin²,

Huberson³

2020

Numerical Methods in Fluids

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The solution of the Poisson's equation used by the incompressible smoothed particle hydrodynamics (ISPH) methods for estimating the pressure field is expensive in CPU time. The CPU time, consumed by the inversion of the operator ∇(1∕ ∇) and the estimation of the right hand side of the Poisson's equation, increases with the number N of particles used in a purely Lagrangian framework. In this work, this default of ISPH methods is overcome by solving the Poisson's equation on a Cartesian grid. This SPH-mesh coupling is equivalent to the particle in cell method. In a first step, in order to analyze its efficiency, the optimized version of two ISPH methods (divergence free and density invariant) is compared with the standard weakly compressible SPH method through two benchmarks of incompressible bidimensional flows characterized by the Reynolds number Re, Lamb-Oseen vortex (10 ≤ Re ≤ 100) and lid-driven cavity flow (100 ≤ Re ≤ 1000). In a second step, the numerical results obtained by the three SPH methods are compared to laboratory experimental data of a dam break flow in order to show the performance of the SPH-mesh coupling in a practical and complex flow problem. As in the configuration of the experimental setup, the numerical results are obtained for a Reynolds number Re = 3.8 10 6 .

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Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

Ortega

Beaudoin

2021

Numerical Methods in Fluids

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In this work, the ISPHP method proposed by Akbari and Namin in 2013 has been modified by implementing the Taylor expansion of a classical smoothing function. The modified ISPHP method with the Taylor expansion of the smoothing function, the optimization of the solving of Poisson's equation and the wave maker, has been used to simulate the damping of a waves train on an inclined porous structure. The comparison between the numerical results obtained with the modified ISPHP method and the experimental data obtained by Carrasco et al. in 2020 has shown on the one hand that the modified ISPHP method could be used to study the damping of a waves train on an inclined porous structure and on the other hand that the dimensionless number χ could be used to characterize the energy transformations of the interaction of a waves train and an inclined porous structure.

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Robust boundary treatment for open-channel flows in divergence-free incompressible SPH

Cited by 14 publications

References 39 publications

Point cloud movement for fully Lagrangian meshfree methods

Point cloud movement for fully Lagrangian meshfree methods

Optimized incompressible smoothed particle hydrodynamics methods and validations

Modified incompressible smooth particle hydrodynamics in porous media method for modeling the damping of a waves train on an inclined porous structure

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