scholarly journals Study on divergence approximation formula for pressure calculation in particle method

2018 ◽  
Vol 10 (4) ◽  
pp. 159-169
Author(s):  
Zhu Yue ◽  
Jiang Shengyao ◽  
Yang Xingtuan ◽  
Duan Riqiang
Keyword(s):  
Pressure Oscillation ◽  
Particle Method ◽  
Free Surface Flows ◽  
Implicit Method ◽  
Approximation Formula ◽  
Pressure Poisson Equation ◽  
Pressure Calculation ◽  
Approximation Formulas ◽  
Moving Particle ◽  
Dam Breaking

The moving particle semi-implicit method is a meshless particle method for incompressible fluid and has proven useful in a wide variety of engineering applications of free-surface flows. Despite its wide applicability, the moving particle semi-implicit method has the defects of spurious unphysical pressure oscillation. Three various divergence approximation formulas, including basic divergence approximation formula, difference divergence approximation formula, and symmetric divergence approximation formula are proposed in this paper. The proposed three divergence approximation formulas are then applied for discretization of source term in pressure Poisson equation. Two numerical tests, including hydrostatic pressure problem and dam-breaking problem, are carried out to assess the performance of different formulas in enhancing and stabilizing the pressure calculation. The results demonstrate that the pressure calculated by basic divergence approximation formula and difference divergence approximation formula fluctuates severely. However, application of symmetric divergence approximation formula can result in a more accurate and stabilized pressure.

An Improved Moving Particle Semi-Implicit Method for Free Surface Flows

2014 ◽  
Vol 571-572 ◽  
pp. 682-687
Author(s):  
Qiao Rui Wu ◽  
Xiong Liang Yao
Keyword(s):  
Free Surface ◽  
Hydrostatic Pressure ◽  
Large Deformation ◽  
Pressure Oscillation ◽  
Free Surface Flows ◽  
Dam Break ◽  
Implicit Method ◽  
Surface Flows ◽  
Collision Model ◽  
Moving Particle

The objective of this study is to make some improvements to the original Moving Particle Semi-implicit method (MPS) for free surface flows. Compared to traditional mesh methods, MPS is feasible to simulate surface flows with large deformation, however, during the simulation; the pressure oscillation is quite violent, duo to misjudgment of surface particles as well as particles gathering together. To modify this problem, a new arc method is applied to judge free surface particles, and a collision model is introduced to avoid particles from gathering together. Hydrostatic pressure and classical dam break are investigated by original and improved MPS. The results verify that improved MPS method is more effective for free surface flows.

Multi-Resolution MPS Method for Free Surface Flows

2016 ◽  
Vol 13 (04) ◽  
pp. 1641018 ◽  
Author(s):  
Zhenyuan Tang ◽  
Youlin Zhang ◽  
Decheng Wan
Keyword(s):  
Free Surface ◽  
Pressure Field ◽  
Fine Particles ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Mps Method ◽  
Time Simulation ◽  
Long Time ◽  
Moving Particle ◽  
Dam Breaking

A multi-resolution moving particle semi-implicit (MPS) method is applied into two-dimensional (2D) free surface flows based on our in-house particle solver MLParticle-SJTU in the present work. Considering the effect of different size particles, both the influence radiuses of two adjacent particles are replaced by the arithmetic mean of their interaction radiuses. Then the modifications for kernel function of differential operator models are derived, respectively. In order to validate the present multi-resolution MPS method, two cases are carried out. Firstly, a hydrostatic case is performed. The results show that the contour of pressure field by multi-resolution MPS is quite in agreement with that by single resolution MPS. Especially, the multi-resolution MPS can still provide a relative smooth pressure together with the single resolution MPS in the vicinity of the interface between the high resolution and low resolution particles. For a long time simulation, the kinetic energy of particles by multi-resolution MPS can decrease quickly to the same level as that of single resolution MPS. In addition, a 2D dam breaking flow is simulated and the multi-resolution case can run stably during the whole simulation. The pressure by the multi-resolution MPS is in agreement with experimental data together with single resolution MPS. The contour of pressure field by the former is also similar to that by the later. Finally, the simulation by multi-resolution MPS is as accurate as the traditional MPS with fine particles distributed in the whole domain and the corresponding CPU time can be reduced.

scholarly journals Improved pressure calculation for the moving particle semi-implicit method

2015 ◽  
Vol 2 (1) ◽  
pp. 91-108 ◽  
Author(s):  
Kazuya Shibata ◽  
Issei Masaie ◽  
Masahiro Kondo ◽  
Kohei Murotani ◽  
Seiichi Koshizuka
Keyword(s):  
Implicit Method ◽  
Pressure Calculation ◽  
Moving Particle

Study on Kernel Functions of Pressure Oscillation in MPS Method

2017 ◽  
Author(s):  
Zhu Yue ◽  
Sun Chen ◽  
Jiang Shengyao ◽  
Yang Xingtuan ◽  
Duan Riqiang
Keyword(s):  
Pressure Distribution ◽  
Kernel Function ◽  
Compact Support ◽  
Pressure Oscillation ◽  
Kernel Functions ◽  
Implicit Method ◽  
Computational Time ◽  
Simulation Process ◽  
Moving Particle ◽  
Approach Zero

In this paper,we studied the characteristic of four kernel functions of Moving Particle Semi-implicit method (MPS).In order to find the dependence of pressure oscillation on kernel functions, the dam break problem was selected for as a benchmark.Results showed that proper value of a kernel function was required in the compact support region to smooth the pressure distribution. The value of the kernel function should approach zero when the particle distance was close to the edge of compact support region to avoid large replusive force.When the distance between particles was close to zero,the value of kernel function should be large enough to avoid particle clustering. At the same time,the kernel function should be simple to stabilize the simulation process and decrease the computational time.

scholarly journals Particle Based Visualization of Stress Distribution Caused by the Aortic Valve Deformation

1970 ◽  
Vol 6 (1) ◽  
pp. 33-39
Author(s):  
Masashi Nakagawa ◽  
Nobuhiko Mukai ◽  
Kiyomi Niki ◽  
Shuichiro Takanashi
Keyword(s):  
Aortic Valve ◽  
Stress Distribution ◽  
Particle Method ◽  
Blood Stream ◽  
Free Surfaces ◽  
Surgical Simulators ◽  
Virtual Particles ◽  
Pressure Calculation ◽  
Operative Planning ◽  
Moving Particle

Medical and engineering technologies have developed the surgical simulators, which allow users to train for surgical skills. To perform the aortic valve replacement, which is one of the cardiovascular surgeries, it is necessary to examine not only the timing of the heart pulsating but also the stress distribution on the aortic valve. For pre-operative planning, wehave visualized the stress on the aortic valve due to the deformation of the aorta and blood stream. In our research, simulations of the deformation of the aortic valve and blood stream have been performed with 3D aorta and aortic valve models, which are composed of particles. In the simulation, the aortic valve and blood models are treated as an elastic body and Hershel-Bulkley fluid, respectively. We have used MPS (Moving Particle Semi-implicit) as the particle method; however, it is known that MPS method cannot specify the stress because the pressure among the particles on the free surfaces is zero. Then, in this paper, we propose more stable pressure calculation by considering virtual particles. As a result, visualization of the stress distribution on the aortic valve has been achieved.

scholarly journals A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Mitsuteru Asai ◽  
Abdelraheem M. Aly ◽  
Yoshimi Sonoda ◽  
Yuzuru Sakai
Keyword(s):  
Poisson Equation ◽  
Pressure Fluctuations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Invariance Condition ◽  
Pressure Poisson Equation ◽  
Relaxation Coefficient ◽  
Particle Hydrodynamics ◽  
Moving Particle ◽  
Dam Breaking

A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper.

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