A particle method for two‐phase flows with large density difference

Luo, Min; Koh, Cheng-Gee; Gao, Minmin; Bai, Wei

doi:10.1002/nme.4884

Cited by 30 publications

(41 citation statements)

References 51 publications

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“…Applying the derivative computation scheme as shown in Equation 3 to the left‐hand side of Equations and leads to a system of linear equations with sparse coefficients, which can be solved effectively by the generalized minimal residual method with incomplete lower upper (LU) factorization . Using the solved fluid pressure, particle velocities and positions are updated as

{boldv}^{(k + 1)} = {boldv}^{*} - ((), \frac{\nabla p}{ρ})^{(k + 1)} normalΔ t

and

{boldr}^{(k + 1)} = {boldr}^{(k)} + {boldv}^{(k + 1)} normalΔ t,

where the pressure gradient term is computed by Equation and the time step Δ t at step k + 1 has to satisfy the Courant condition as

normalΔ t \leq 0.2 \frac{L_{0}}{v_{\max}},

where v max is the maximum particle velocity at step k .…”

Section: Consistent Particle Methodsmentioning

confidence: 99%

“…The first difference is that the proposed method computes spatial derivative (for gradient and Laplacian operators) for two fluids with drastic density difference (e.g., water versus air) on the basis of Taylor series expansion. The computation of first‐order and second‐order derivatives (in the x direction) is as follows (more details are given in and ):

((), \frac{1}{ρ} \frac{∂p}{∂x})_{i} = \sum_{j \neq i} ([], \frac{1}{0.5 (ρ_{i} + ρ_{j})} C_{1 j} ((), p_{j} - p_{i}))

and

((), \frac{\partial}{∂x} ((), \frac{1}{ρ} \frac{∂p}{∂x}))_{i} = \sum_{j \neq i} ([], \frac{1}{0.5 (ρ_{i} + ρ_{j})} C_{3 j} ((), p_{j} - p_{i})),

where ρ i and ρ j are the fluid density at particle i and j , p i and p j are the fluid pressure at particle i and j , and C 1 j and C 3 j are the coefficients (dependent on the relative positions between the reference particle and its neighboring particles) generated by GFD. In a similar way, the derivatives along the y direction are computed.…”

Section: Consistent Particle Methodsmentioning

confidence: 99%

“…Nevertheless, for problems where compression of air is significant, it would be necessary to account for air compressibility while treating water as incompressible. Therefore, the incompressible 2P‐CPM is further improved by accounting for air compressibility in the present study such that water–air flows with air entrapment can be accurately simulated.…”

Section: Introductionmentioning

confidence: 99%

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A particle method for two-phase flows with compressible air pocket

Luo

Koh

Bai

et al. 2016

Int. J. Numer. Meth. Engng

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Summary When using particle methods to simulate water–air flows with compressible air pockets, a major challenge is to deal with the large differences in physical properties (e.g., density and viscosity) between water and air. In addition, the accurate modeling of air compressibility is essential. To this end, a new two‐phase strategy is proposed to simulate incompressible and compressible fluids simultaneously without iterations between the solvers for incompressible and compressible flows. Water is modeled by the recently developed 2‐phase Consistent Particle Method for incompressible flows. For air modeling, a new compressible solver is proposed based on the ideal gas law and thermodynamics. The formulation avoids the problem of determining the actual sound speed that is dependent on the temperature and is therefore not necessarily constant. In addition, the compressible air solver is seamlessly integrated with the incompressible solver 2‐phase Consistent Particle Method because they both use the same predictor–corrector scheme to solve the governing equations. The performance of the proposed method is demonstrated by three benchmark problems as well as an experimental study of sloshing impact with entrapped air pockets in an oscillating tank. Copyright © 2016 John Wiley & Sons, Ltd.

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{boldv}^{(k + 1)} = {boldv}^{*} - ((), \frac{\nabla p}{ρ})^{(k + 1)} normalΔ t

and

{boldr}^{(k + 1)} = {boldr}^{(k)} + {boldv}^{(k + 1)} normalΔ t,

where the pressure gradient term is computed by Equation and the time step Δ t at step k + 1 has to satisfy the Courant condition as

normalΔ t \leq 0.2 \frac{L_{0}}{v_{\max}},

where v max is the maximum particle velocity at step k .…”

Section: Consistent Particle Methodsmentioning

confidence: 99%

((), \frac{1}{ρ} \frac{∂p}{∂x})_{i} = \sum_{j \neq i} ([], \frac{1}{0.5 (ρ_{i} + ρ_{j})} C_{1 j} ((), p_{j} - p_{i}))

and

((), \frac{\partial}{∂x} ((), \frac{1}{ρ} \frac{∂p}{∂x}))_{i} = \sum_{j \neq i} ([], \frac{1}{0.5 (ρ_{i} + ρ_{j})} C_{3 j} ((), p_{j} - p_{i})),

Section: Consistent Particle Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A particle method for two-phase flows with compressible air pocket

Luo

Koh

Bai

et al. 2016

Int. J. Numer. Meth. Engng

Self Cite

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show abstract

“…In the above manners, the acceleration becomes continuous across interfaces. The above approaches to keep acceleration continuity across interfaces are similar to those in the consistent particle method . It is noted that both MMPS and MMPS‐CA can be directly applied to single‐phase flows.…”

Section: Methodsmentioning

confidence: 99%

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Duan

Koshizuka

Yamaji

et al. 2018

Numerical Meth Engineering

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Summary The Lagrangian moving particle semi‐implicit (MPS) method has potential to simulate free‐surface and multiphase flows. However, the chaotic distribution of particles can decrease accuracy and reliability in the conventional MPS method. In this study, a new Laplacian model is proposed by removing the errors associated with first‐order partial derivatives based on a corrected matrix. Therefore, a corrective matrix is applied to all the MPS discretization models to enhance computational accuracy. Then, the developed corrected models are coupled into our previous multiphase MPS methods. Separate stabilizing strategies are developed for internal and free‐surface particles. Specifically, particle shifting is applied to internal particles. Meanwhile, a conservative pressure gradient model and a modified optimized particle shifting scheme are applied to free‐surface particles to produce the required adjustments in surface normal and tangent directions, respectively. The simulations of a multifluid pressure oscillation flow and a bubble rising flow demonstrate the accuracy improvements of the corrective matrix. The elliptical drop deformation demonstrates the stability/accuracy improvement of the present stabilizing strategies at free surface. Finally, a turbulent multiphase flow with complicated interface fragmentation and coalescence is simulated to demonstrate the capability of the developed method.

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“…There is no exact solution for Equation (17). One can only determine its least square error approximation by…”

Section: Methods For Solving the Governing Equationmentioning

confidence: 99%

Simulation of Propagation and Run-Up of Three Dimensional Landslide-Induced Waves Using a Meshless Method

Hsiao

Shih

2018

Water

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Abstract:In this study, a meshless numerical model for the simulation of tsunamis generated by submerged landslides was developed. The phenomena were treated as free surface potential flows governed by the Laplace equation. By using a predictor-corrector time marching approach, the time dependent problem was transformed to a series of boundary value problems (BVP) while at each time step the BVP was solved by a meshless method which employed local polynomial collocation accompanying the weight-least-squares (WLS) approach. The model was validated by comparing the results with experimental data and other numerical results. Then, simulations were carried out in a widened numerical wave flume for the observation of edge waves along the shore.

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A particle method for two‐phase flows with large density difference

Cited by 30 publications

References 51 publications

A particle method for two-phase flows with compressible air pocket

A particle method for two-phase flows with compressible air pocket

An accurate and stable multiphase moving particle semi‐implicit method based on a corrective matrix for all particle interaction models

Simulation of Propagation and Run-Up of Three Dimensional Landslide-Induced Waves Using a Meshless Method

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