A Precise Calculation Method of the Gradient Operator in Numerical Computation with the MPS

Iribe, Tsunakiyo; Nakaza, Eizo

doi:10.2208/kaigan.66.46

Cited by 10 publications

(7 citation statements)

References 1 publication

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“…regular particle distribution is assumed), varied correction techniques have been proposed in order to enhance the accuracy of the MPS method. For instance, Khayyer-Gotoh gradient operator anti-symmetrization [42], Khayyer-Gotoh divergence operator correction [43], Khayyer-Gotoh Laplace operator correction [44], Khayyer-Gotoh gradient operator correction [45], and Suzuki gradient operator correction [39,91] are proposed. Only Suzuki method based on weighted least squares technique can achieve 1st order consistency for gradient operator; however, others do not hold differential completeness/reproducing conditions in general case.…”

Section: Theorem 23 ( Pth Order Differential Completeness/ Reproducimentioning

confidence: 99%

Least squares moving particle semi-implicit method

2014

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In this paper, a consistent meshfree Lagrangian approach for numerical analysis of incompressible flow with free surfaces, named least squares moving particle semi-implicit (LSMPS) method, is developed. The present methodology includes arbitrary high-order accurate meshfree spatial discretization schemes, consistent time integration schemes, and generalized treatment of boundary conditions. LSMPS method can resolve the existing major issues of widely used strong-form particle method for incompressible flow-particularly, the lack of consistency condition for spatial discretization schemes, difficulty in enforcing consistent Neumann boundary conditions, and serious instability like unphysical pressure oscillation. Applications of the present proposal demonstrate remarkable enhancements of stability and accuracy. Keywords Least squares moving particle semi-implicit method · LSMPS method · High order scheme · Meshfree compact scheme · Moving particle semi-implicit method

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Section: Theorem 23 ( Pth Order Differential Completeness/ Reproducimentioning

confidence: 99%

Least squares moving particle semi-implicit method

2014

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“…The reason is that when the two space vectors are introduced to the Taylor expansion of the gradient equation, the nonzero assumption of each vector is guaranteed but the product of the two vectors is not. This problem also exists in predecessor's gradient operators that are derived from the Taylor series expansion . To resolve this problem, an integrated pressure gradient model is constituted as follows:

\nabla p true|_{i} = ({,, \begin{array}{l} {[\frac{1}{n_{0}} \underset{i \neq j}{false\sum} w ({boldr}_{j} - {boldr}_{i}) \frac{((),, r_{j} - r_{i})}{| {boldr}_{j} - {boldr}_{i} |} \otimes \frac{{({boldr}_{j} - {boldr}_{i})}^{T}}{| {boldr}_{j} - {boldr}_{i} |}]}^{- 1} ([],, \frac{1}{n_{0}} \sum_{i \neq j} w (()||, r_{j} - r_{i}) \frac{p_{j} - {\overset{truê}{p}}_{i}}{true| r_{j} - r_{i} true|} \frac{({boldr}_{j} - {boldr}_{boldi})}{true| r_{j} - r_{i} true|}) det ((),, C_{i}) \geq 0.05 \\ \frac{D_{s}}{n_{0}} \sum_{i \neq j} w (()||, r_{j} - r_{i}) \frac{p_{j} - {\overset{truê}{p}}_{i}}{true| r_{j} - r_{i} true|} \frac{({boldr}_{j} - {boldr}_{boldi})}{true| r_{j} - r_{i} true|} det ((),, C_{i}) < 0.05 \end{array})

…”

Section: Methodsmentioning

confidence: 99%

“…The reason is that when the two space vectors are introduced to the Taylor expansion of the gradient equation, the nonzero assumption of each vector is guaranteed but the product of the two vectors is not. This problem also exists in predecessor's gradient operators that are derived from the Taylor series expansion [20,25,33]. To resolve this problem, an integrated pressure gradient model is constituted as follows:…”

mentioning

confidence: 99%

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Wang

Jiang

Zhang

2017

Numerical Methods in Fluids

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Summary Precise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.

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“…where ⊗ is the tensor product. This model was applied by Iribe and Nakaza [13] to the analysis of incompressible fluid. By this Equation, the calculation accuracy around a boundary is maintained and the calculation accuracy is improved more than the previous method.…”

Section: The High Accuracy Gradient Model and The High Accuracy Laplamentioning

confidence: 99%

“…The high accuracy divergence model is applied as shown in Eq. (13). In these models, the primary convergent is ensured by Tamai et al [14]…”

Section: The High Accuracy Gradient Model and The High Accuracy Laplamentioning

confidence: 99%

Use of the Mps method to estimate the energy conversion efficiency of the owc-wec (first report)

et al. 2019

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In recent years, ocean renewable energy has been increasingly in the spotlight due to global warming and energy issues etc. Research on ocean renewable energy devices is being carried out by many researchers, companies and countries. Additionally, many sea tests are being carried out by countries with real sea test sites. Ocean renewable energy devices still need to research about a power generation method, an energy conversion efficiency and costs etc. In this paper, Authors focus on the oscillating water column type wave energy converter (called below OWC-WEC). It is considered that the OWC-WEC is useful because a movable part which becomes a cause of trouble is few and can also be used as a breakwater device. In this study, the MPS (Moving Particle Semi-implicit) method is applied to the performance analysis of the OWC-WEC. It is because the performance analysis by various parameters and the reduction of an experimental cost is needed. In this paper, these following items are shown; 1) the development of analysis program code which can simulate the multiphase flow by three phases of gas, liquid and solid, 2) the development of air duct model, 3) verification of the usefulness of the improved MPS program code and 4) verification of the applicability to the performance analysis of the OWC-WEC. This program code was applied to the simulation of the fixed type OWC-WEC. Following this, the reproducibility of the primary conversion efficiency of the fixed type OWC-WEC by this program code was verified and discussed. Finally, the usefulness and applicability of this program code were discussed and recommendations for future work were made.

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A Precise Calculation Method of the Gradient Operator in Numerical Computation with the MPS

Cited by 10 publications

References 1 publication

Least squares moving particle semi-implicit method

Least squares moving particle semi-implicit method

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

Use of the Mps method to estimate the energy conversion efficiency of the owc-wec (first report)

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