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...term proposed by Morris (Advance online publication: 17 February 2009)Engineering Letter, 16:3, EL_17_1_05 ____________________________________________________________________________________ et al. =-=[7]-=-. In order to investigate the accuracy of the modified algorithm, a poiseuille flow is simulated and velocity profile is compared with analytical solution. Moreover, the method is used to simulate an ...

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...which were consisted of fixed or moving rigid boundaries, in FSI problems deformable boundaries are of interest. A simple technique to implement no-slip boundary condition is usage of image particles =-=[13]-=-. Nevertheless, this method is usually limited to straight boundaries and simple geometries. In this paper, the velocity extrapolation method proposed by Morris et al. [7] is used. According to this m...

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...the summation index b denotes a particle label and particle b carries a mass mb at the position r b . The value of A at b − th particle is shown by A b . Derivative of A with respect to x is given by =-=[10]-=- ⎛ ∂A ⎞ 1 Φ b ∂Wab ⎜ ⎟ = ∑ mb ( A b − A a ) , (14) ⎝ ∂x ⎠ a Φ a b ρb ∂x where Φ is any differentiable function. IV. SOLUTION ALGORITHM Solution algorithm consists of a prediction-correction scheme whi...

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...combination of the pressure gradient term of the momentum equation and continuity equation, a Poisson equation is formulated by which a trade off between deviation of density and pressure is produced =-=[12]-=-. i f ~ j 1 ρ0 − ρ ∂uˆ + = 0 , (24) j ρ 0 Δt ∂x u P t i ⎛ ⎞ = −⎜ ∇ ⎟Δ ⎝ ρ ⎠ ~ 1 ˆ , (25) ⎛ 1 ⎞ ρ ~ 0 − ρ ∇. ⎜ ~ ∇P⎟ = . (26) 2 ⎝ ρ ⎠ ρ0 Δt Pressure of each particle is calculated according to the foll...

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...) u ⎞ ab i Tf = ⎜ m j b xab ⋅∇ aWab x ⎟ = ∑ ⎜ b a b ( ab ) ⎟ (20) 2 2 ⎝ ρ ∂ ⎠a ⎝ ρ ρ r + η ⎠ where η is a small number to avoid singularities. Although equation (20) does not satisfy angular momentum =-=[11]-=-, no-slip boundary condition can be imposed accurately. Finally, the vector i T which is equal to T for fluid particles, and i Ts for solid particles is used to calculate a provisional velocity filed....

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...as A ( r ) ≈ ∫ A( r′ ) W ( r − r′ , h) dr′ , (10) Ω where h is smoothing length proper to kernel function W which represents the effective width of the kernel. The kernel has the following properties =-=[9]-=- ⎧ ( ) ⎪∫W r − r′ , h dr′ = 1 V ⎨ . (11) ⎪limW ( r − r′ , h) = δ ( r − r′ ) ⎩ h→0 There are many possible choices for the kernel function. A quintic kernel normalized for two-dimensions is used in the...

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...uring two past decades, SPH has employed to simulate incompressible fluids as well as elastic-plastic deformations. Recently, some researches have been devoted to utilize SPH to simulate FSI problems =-=[3,4,5]-=-. Antoci et al. [3] used standard SPH along with an incremental hypoelastic relation to simulate FSI problems. On the other hand, Hosseini et al. [4] developed a three-step SPH algorithm, which had al...

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...rming-grid methods [1]. Deforming-grid methods usually need remeshing, particularly when large deformation is of great interest; however, remeshing strategy can be a difficult and time consuming task =-=[1,2]-=-. On the other hand, fixed-grid methods often require an interpolation to the immersed boundary, which results in inaccurate computations in vicinity of these boundaries [2]. Smoothed particle hydrody...

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...long with an incremental hypoelastic relation to simulate FSI problems. On the other hand, Hosseini et al. [4] developed a three-step SPH algorithm, which had already been proposed by Hosseini et al. =-=[6]-=-, to simulate FSI problems. In addition, viscosity was taken into account in their simulations; whereas, neither artificial viscosity nor artificial stress was used. Comparing these two methods illust...

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...uring two past decades, SPH has employed to simulate incompressible fluids as well as elastic-plastic deformations. Recently, some researches have been devoted to utilize SPH to simulate FSI problems =-=[3,4,5]-=-. Antoci et al. [3] used standard SPH along with an incremental hypoelastic relation to simulate FSI problems. On the other hand, Hosseini et al. [4] developed a three-step SPH algorithm, which had al...

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...f field variables on deformable boundaries considerably affects the accuracy of the result. Generally, there are two classes of grid-based methods namely fixed-grid methods and deforming-grid methods =-=[1]-=-. Deforming-grid methods usually need remeshing, particularly when large deformation is of great interest; however, remeshing strategy can be a difficult and time consuming task [1,2]. On the other ha...