A multiphase MPS solver for modeling multi-fluid interaction with free surface and its application in oil spill

Duan, Guangtao; Chen, Bin; Zhang, Ximin; Wang, Yechun

doi:10.1016/j.cma.2017.03.014

Cited by 78 publications

(55 citation statements)

References 65 publications

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“…Using the corrective matrix, the first‐order gradient model reads:

{⟨ \nabla P ⟩}_{i} = \frac{d}{n^{0}} \sum_{j \neq i} ({}, \frac{false(P_{j} - P_{i} false)}{false‖ r_{j} - r_{i} false‖} ((), C_{i} \frac{r_{j} - r_{i}}{false‖ r_{j} - r_{i} false‖}) w ((), false‖ r_{j} - r_{i} false‖)) .

…”

Section: Methodsmentioning

confidence: 99%

“…In our previous studies, MPS was extended to the MMPS and MMPS‐CA methods for incompressible multiphase flows. In MMPS, interaction forces are continuous across interfaces, which is consistent with the physics of multiphase flows. However, the produced accelerations are not continuous, owing to the discontinuous density across interfaces.…”

Section: Methodsmentioning

confidence: 99%

“…Specifically, the above viscosity and surface tension terms are calculated explicitly to obtain the temporary velocities and positions. Then, the following multiphase pressure Poisson equation (PPE) is solved implicitly to guarantee incompressibility:

{⟨\nabla \cdot (\frac{1}{ρ} \nabla P)⟩}_{i}^{k + 1} = ((), 1 - γ) \frac{1}{normalΔ t} \nabla \cdot u^{*} - γ \frac{1}{normalΔ t^{2}} ({}, \frac{n^{*} - n_{0}}{n_{0}}) + α \frac{1}{normalΔ t^{2}} P_{i}^{k + 1},

where γ is a relaxation coefficient for the mixed source and α is the artificial compressibility . Typically, γ = 0.0 to 0.1 and α = 0.0 to 10 −7 .…”

Section: Methodsmentioning

confidence: 99%

“…For the free‐surface boundary, the virtual particle method that is proved effective in enhancing accuracy is adopted. In this method, virtual particles with zero pressure are supplemented outside free surface, and thus, the pressure of free‐surface particles is solved from a modified PPE.…”

Section: Methodsmentioning

confidence: 99%

“…For example, the artificial particle displacements based on repulsive forces are also effective for stability. In summary, some particle velocity (eg, PST and background pressure) or position (eg, artificial particle displacement) adjustments are adopted explicitly or implicitly in most Lagrangian particle methods to prevent particles aligning themselves along streamlines . In this manner, stability is guaranteed.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Using the corrective matrix, the first‐order gradient model reads:

{⟨ \nabla P ⟩}_{i} = \frac{d}{n^{0}} \sum_{j \neq i} ({}, \frac{false(P_{j} - P_{i} false)}{false‖ r_{j} - r_{i} false‖} ((), C_{i} \frac{r_{j} - r_{i}}{false‖ r_{j} - r_{i} false‖}) w ((), false‖ r_{j} - r_{i} false‖)) .

…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

{⟨\nabla \cdot (\frac{1}{ρ} \nabla P)⟩}_{i}^{k + 1} = ((), 1 - γ) \frac{1}{normalΔ t} \nabla \cdot u^{*} - γ \frac{1}{normalΔ t^{2}} ({}, \frac{n^{*} - n_{0}}{n_{0}}) + α \frac{1}{normalΔ t^{2}} P_{i}^{k + 1},

where γ is a relaxation coefficient for the mixed source and α is the artificial compressibility . Typically, γ = 0.0 to 0.1 and α = 0.0 to 10 −7 .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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On modeling of MPS‐based multiphase fluid flow with low density ratios

Pahar

Dhar

2018

Numerical Methods in Fluids

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Summary A divergence‐free moving particle semi‐implicit framework has been formulated for modeling of multiple miscible fluids having small density ratios (≤ 1.10) in the presence of free surface. A density‐weighted pressure gradient along with a hybrid free‐surface treatment is specifically adopted to incorporate the effect of marginal density difference through a higher‐order kernel. The hybrid free‐surface treatment reduces error in velocity divergence and resulting spurious velocity fluctuation in the vicinity of free surface for low‐velocity system. Scalar transport equation is resolved to update density associated with the particles at every time step. A total of 9 cases of lock‐exchange flow with different lock positions and density ratios have been utilized to validate the proposed framework. The model performs satisfactorily irrespective of lock positions and low density variations (3%‐9%).

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Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Duan

Matsunaga

Yamaji

et al. 2020

Numerical Methods in Fluids

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Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi-implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.

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A multiphase MPS solver for modeling multi-fluid interaction with free surface and its application in oil spill

Cited by 78 publications

References 65 publications

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

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

On modeling of MPS‐based multiphase fluid flow with low density ratios

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

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