Improvement of a projection-based particle method in free-surface flows by improved Laplacian model and stabilization techniques

Xu, Tibing; Jin, Yee‐Chung

doi:10.1016/j.compfluid.2019.104235

Cited by 15 publications

(3 citation statements)

References 60 publications

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“…Similar to the collision model suggested in the MPS literature (Shakibaeinia & Jin, 2012; Xu & Jin, 2019a), the adjusted velocity could be accounted for by computing the velocity of each target particle to modify the gradient term. Hence, the dynamic stabilizing force will be

F_{i j}^{D S} = {\begin{matrix} left \\ left 0, u_{i j}^{D S} \leq 0 \\ left \frac{u_{i j}^{D S}}{g normalΔ t}, u_{i j}^{D S} > 0 \end{matrix} & u_{i j}^{D S} = (u_{i} - u_{i j}^{c}) \frac{x_{j} - x_{i}}{| x_{j} - x_{i} |}

where u ij DS is the dynamic stabilizing velocity.…”

Section: Methodsmentioning

confidence: 99%

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MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

Sarkhosh

Jin

2021

Water Resources Research

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Two meshless (or mesh-free) methods that are widely employed in hydrodynamic modeling of problems with steep gradients and large deformation are smoothed particle hydrodynamics (SPH) and moving particle simulation (MPS) that are classified into two categories of incompressible and weakly compressible fluids (Gotoh & Khayyer, 2016). Although SPH was initially introduced for astrophysical applications (Gingold & Monaghan, 1977), in the scope of hydrodynamics, SPH and MPS were developed by Monaghan (1992) and Koshizuka and Oka (1996), respectively, for solving the free-surface incompressible flow using Navier-Stokes equations. Gotoh et al. ( 2001) presented a sub-particle scale closure model for closing large eddy simulation (LES) to simulate turbulence fluctuations in the MPS method. The theory of a weakly compressible flow was adopted by Monaghan (1994) in SPH and Shakibaeinia and Jin (2010) in MPS using a thermodynamic equation of state for calculating the pressure instead of resorting to the Poisson equation.The main difference between SPH and MPS arises from different differential operators employed in the spatial integration of the partial differential equations. In SPH, the differential operators are obtained from the differentiation of a weighted average function, the so-called kernel, without directly applying differencing schemes for flow variables. The superposition of the kernels then computes flow variables' derivatives (Liu & Liu, 2010). In contrast, MPS is the extension of the finite volume method to a mesh-free approach in which the spatial discretization is obtained based on the differentiation of flow variables. The weighted average of physical quantities derivatives of neighboring particles is applied to the target particle. However, unlike the finite volume method in which the velocity divergence is used for pressure calculation, the particle number density is adopted in MPS. The particle number density indicating the number of particles surrounding a particle is a key variable in MPS that is straightforward to fulfill flow incompressibility (Koshizuka et al., 2018).

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F_{i j}^{D S} = {\begin{matrix} left \\ left 0, u_{i j}^{D S} \leq 0 \\ left \frac{u_{i j}^{D S}}{g normalΔ t}, u_{i j}^{D S} > 0 \end{matrix} & u_{i j}^{D S} = (u_{i} - u_{i j}^{c}) \frac{x_{j} - x_{i}}{| x_{j} - x_{i} |}

where u ij DS is the dynamic stabilizing velocity.…”

Section: Methodsmentioning

confidence: 99%

“…Similar to the collision model suggested in the MPS literature (Shakibaeinia & Jin, 2012;Xu & Jin, 2019a), the adjusted velocity could be accounted for by computing the velocity of each target particle to modify the gradient term. Hence, the dynamic stabilizing force will be…”

Section: Stabilization Techniquementioning

confidence: 99%

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

Sarkhosh

Jin

2021

Water Resources Research

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“…Likewise, with the idea of solving the divergence of gradient, Xu and Jin [48,49] introduced an improved Laplacian model (ILM) to enhance the performance in the MPS as follows:…”

mentioning

confidence: 99%

Review of the State-of-Art of MPS Method in Ocean Engineering

Sun

Dou

Tan

et al. 2022

JMSE

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When dealing with the complex deformation of free surface such as wave breaking, traditional mesh-based Computational Fluid Dynamics (CFD) methods often face problems arising alongside grid distortion and re-meshing. Therefore, the meshless method became robust for treating large displaced free surface and other boundaries caused by moving structures. The particle method, which is an important branch of meshless method, is mainly divided into the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods. Different from the SPH method, which involves continuity and treat density as a variable when building kernel functions, the kernel function in the MPS method is a weight function which treats density as a constant, and the spatial derivatives are discretized by establishing the gradient operator and Laplace operator separately. In other words, the first- or second-order continuity of the kernel functions in the MPS method is not a necessity as in SPH, though it might be desirable. At present, the MPS method has been successfully applied to various violent-free surface flow problems in ocean engineering and diverse applications have been comprehensively demonstrated in a number of review papers. This work will focus on algorithm developments of the MPS method and to provide all perspectives in terms of numerical algorithms along with their pros and cons.

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Pressure Distribution in a Dam-Break Flow Simulated by a Mesh-Free Method

Zuo

Huang

2022

Lecture Notes in Civil Engineering

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Improvement of a projection-based particle method in free-surface flows by improved Laplacian model and stabilization techniques

Cited by 15 publications

References 60 publications

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations

Review of the State-of-Art of MPS Method in Ocean Engineering

Pressure Distribution in a Dam-Break Flow Simulated by a Mesh-Free Method

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