Comparison of two projection methods for modeling incompressible flows in MPM

Kularathna, Shyamini; Soga, Kenichi

doi:10.1016/s1001-6058(16)60750-3

Cited by 22 publications

(7 citation statements)

References 15 publications

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“…The incremental pressure projection method has to satisfy the LBB condition to stably obtain the steady‐state 55,57 . If the LBB condition is violated, the so‐called odd‐even oscillation (checker‐board instability) 58 is observed in the MPM employing the fractional‐step method 59 . To suppress such an oscillation, we employ the sub‐grid method 60,61 in this study, in which two grids with different spatial resolutions are used.…”

Section: Spatial Discretization Using the Materials Point Methodsmentioning

confidence: 99%

“…55,57 If the LBB condition is violated, the so-called odd-even oscillation (checker-board instability) 58 is observed in the MPM employing the fractional-step method. 59 To suppress such an oscillation, we employ the sub-grid method 60,61 in this study, in which two grids with different spatial resolutions are used. One is the pressure grid, and the other is the velocity grid that is supposed to be fine with respect to the pressure grid, as illustrated in Figure 2.…”

Section: Pore Water Pressure Stabilizationmentioning

confidence: 99%

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Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures

Hidano,

Yamaguchi,

Takase

et al. 2024

Num Anal Meth Geomechanics

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This study presents a semi‐implicit MPM to adequately characterize the mechanical behavior of unsaturated soil based on Biot's mixture theory. To represent the dependency of the degree of saturation on the suction, we employ the VG model along with a soil‐water characteristic curve, which determines a functional form of permeability called the Mualem model. Hencky's hyperelastic model and the Drucker‐Prager model assuming nonassociativity are adopted for elastic and plastic deformations, respectively. The novelty of this study is the incorporation of the fractional‐step method into the MPM framework so that the pore water pressure is obtained by implicitly solving the pressure Poisson's equation, which reduces numerical instability and improves computational efficiency. Also, because the drag force between solid and liquid phases is evaluated using the intermediate velocity of pore water relative to the intermediate velocity of solid skeleton, the time increment can be chosen without considering the magnitude of water permeability. In addition, to suppress “odd‐even” oscillation, we employ a sub‐grid method in which two grids with different spatial resolutions are used for the velocities and pore water pressure. Furthermore, considering the advantages and disadvantages of two different interpolation schemes for pore water pressure, we suggest switching the schemes depending on the model conditions. Several numerical examples are presented to demonstrate the performance of the proposed method. Specifically, unidirectional consolidation and leak flow analyses are performed for verification purposes, followed by validation analysis of a model experiment of infiltration‐induced landslides.

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Section: Spatial Discretization Using the Materials Point Methodsmentioning

confidence: 99%

Section: Pore Water Pressure Stabilizationmentioning

confidence: 99%

Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures

Hidano,

Yamaguchi,

Takase

et al. 2024

Num Anal Meth Geomechanics

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show abstract

“…In applying the fractional‐step method, a scalar parameters

β

has been used to generalize different versions of the derivation, wherein

β = 1

represents the incremental fractional step, while

β = 0

denotes the non‐incremental fractional‐step approach as introduced originally by Chorin 29 . A previous study 41 has shown that the non‐incremental version of the fractional step scheme exhibits stable results for the single‐phase MPM formulation. In this paper, a similar comparison of the accuracy and stability of the two schemes implemented in the two‐phase MPM is conducted and discussed.…”

Section: Time Integration and The Application Of Fractional‐step Methodsmentioning

confidence: 99%

A semi‐implicit material point method based on fractional‐step method for saturated soil

Kularathna

Liang

Zhao

et al. 2021

Num Anal Meth Geomechanics

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In this paper, a new formulation of material point method (MPM) to model coupled soil deformation and pore fluid flow problems is presented within the framework of the theory of porous media. The saturated porous medium is assumed to be consisting of incompressible pore fluid and deformable soil skeleton made up of incompressible solid grains. The main difference of the proposed MPM algorithm is the implicit treatment of pore‐water pressure which satisfies its incompressibility internal constraint. The resulting solid‐fluid coupled equations are solved by using a splitting algorithm based on the Chorin's projection method. The splitting algorithm helps to mitigate numerical instabilities at the incompressibility limit when equal‐order interpolation functions are used. The key strengths of the proposed semi‐implicit coupled MPM formulation is its capability to reduce pressure oscillations as well as to increase the time step size, which is independent of the fluid incremental strain level and the soil permeability. The proposed semi‐implicit MPM is validated by comparing the numerical results with the analytical solutions of several numerical tests, including 1D and 2D plane‐strain consolidation problems. To demonstrate the capability of the proposed method in simulating practical engineering problems involving large deformations, a hydraulic process leading to slope failure is studied, and the numerical result is validated by the monitored data.

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“…[16][17][18][19][20][21] The MPM incorporates the advantages of Lagrangian and Eulerian methods, which avoids grid distortion problems and can model history-dependent material behavior. 22 The MPM is an effective method for dealing with large-deformation problems and has been successfully employed in a variety of engineering applications, including solid mechanics, 23,24 solid-fluid interaction problems, [25][26][27][28][29][30][31][32][33] incompressible material flows, 34,35 granular flows, 36,37 dike failure, 29,38,39 and graphics research. 40,41 However, MPM suffers from numerical artifact noise and cell-crossing errors when the material points cross the grid boundaries.…”

Section: Introductionmentioning

confidence: 99%

An improved convected particle domain interpolation material point method for large deformation geotechnical problems

Wang,

Li,

Zhou

et al. 2023

Numerical Meth Engineering

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A novel material point method called the improved convected particle domain interpolation (ICPDI) is proposed in this paper to simulate large‐deformation problems in geotechnical engineering. The ICPDI framework is based on the existing convected particle domain interpolation (CPDI) and employs an adaptive orthogonal improved interpolating moving least square (AOIIMLS) shape functions. The AOIIMLS shape functions prevent computational instability problems caused by singular or ill‐conditioned matrices through avoiding the direct solving of inverse matrices. Additionally, ICPDI adopts the velocity gradient to calculate the velocity field in particle domains and reduces cell‐crossing errors by using AOIIMLS shape functions. To reconstruct the velocity function in the background grid, the velocities of the material points and four related corner points are employed through AOIIMLS shape functions. The bar axis‐aligned vibration, ring radial expansion, slope elasto‐plastic slumping, and post‐failure tunnel collapse behavior examples are used to verify the accuracy and effectiveness of ICPDI by comparing the results with other numerical methods and experiments. Numerical simulation results show that ICPDI outperforms the material point method (MPM) and CPDI in terms of computational accuracy and convergence while reducing cell‐crossing errors. Consequently, this study demonstrates the capability of ICPDI in simulations of large‐deformation geotechnical problems.

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Comparison of two projection methods for modeling incompressible flows in MPM

Cited by 22 publications

References 15 publications

Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures

Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures

A semi‐implicit material point method based on fractional‐step method for saturated soil

An improved convected particle domain interpolation material point method for large deformation geotechnical problems

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