Simulation of Red Blood Cell Passing Through Constrictions Using Modified Moving Particle Semi-Implicit Method

2011 ◽  
Author(s):  
K. Firoozbakhsh ◽  
M. T. Ahmadian ◽  
M. Hasanian
Keyword(s):  
Mechanical Behavior ◽  
Experimental Studies ◽  
Small Time ◽  
Implicit Method ◽  
Parallel Plates ◽  
Time Step ◽  
Mps Method ◽  
Time Step Size ◽  
Small Time Step ◽  
Moving Particle

During the circulation of RBC it undergoes elastic deformation as it passes through micro-capillaries where the inner diameter of the constriction can be about 3 micro meters. It means RBC shape must be changed in order to pass through these narrow channels. The role of mechanical behavior of RBC and the deformability traits of RBC are observed with the several experimental studies [1]. Several methods were implemented to simulate the mechanical behavior of RBCs in micro-capillaries [1, 2]. One of the most recent methods is Moving Particle Semi-implicit method (MPS) which is a Lagrangian method with semi-implicit algorithm that guaranties the incompressibility of the fluid. MPS method was implemented for simulation of RBC motion through parallel plates by Tsubota et al. 2006 [3]. Due to small Reynolds number and the Diffusion number restrictions, implementation of small time step size would be necessary which leads to long time simulation. By the way in case of complex geometries or FSI problems, standard MPS method has a delicate pressure solver which leads to diverge the solution. So in these cases using a small time step can help to overcome the problem. Some studies have applied a new approach for time integration and the fractional time step method is employed to overcome the noticed problem. Yohsuke Imai and coworkers (2010) have developed the former studies with two main new approaches [4]. Firstly, evaluation of viscosity is upgraded and secondly boundary condition is assumed to be periodic. Although the developments are really impressive and MPS method has turned into a practical method for simulation of RBC motion in micro-capillaries, but still there are some considerations about using large time steps and error of the velocity profile consequently.

General Formulations for Rhie-Chow Interpolation

2004 ◽  
Author(s):  
Sijun Zhang ◽  
Xiang Zhao
Keyword(s):  
Small Time ◽  
Unsteady State ◽  
Flow Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Relaxation Factor ◽  
Numerical Discretization ◽  
Small Time Step

In this paper, general formulations for Rhie-Chow interpolation on co-located grid are derived. Unlike the standard Rhie-Chow interpolation, the general formulations are applicable for any flow conditions. It has observed that the original momentum-based interpolation due to Rhie and Chow has serious deficiency, such as under-relaxation factor dependence, failure to suppress saw-tooth pressure solutions with small time step size for unsteady state problems and wrong solutions or divergence with discontinuities. Thus the derivation of Rhie-Chow interpolation is first recalled, then the errors of numerical discretization are analyzed, finally, new formulations and some improvements are given.

Simulation of the Mooring Vessels in Tsunamis Using the MPS Method Considers Leading Wave and Backwash

2012 ◽  
Author(s):  
Mitsuhiro Masuda ◽  
Kiyokazu Minami ◽  
Koichi Masuda ◽  
Tomoki Ikoma
Keyword(s):  
Experimental Results ◽  
Implicit Method ◽  
Present Calculation ◽  
Mps Method ◽  
Calculation Results ◽  
Moving Particle

The present paper describes the simulation of behavior of mooring vessels in tsunami using the 3-D MPS (Moving Particle Semi-implicit) Method for considering leading wave and backwash effect. The chain of a disaster is brought about by two kinds of tsunami. The chain of disaster means breaking the mooring tether, grounding on a wharf, drift to continental areas, the collision with building by leading wave and the outflow of the floating matter by backwash. In this research, the 3D-MPS method is applied, and the bore like wave is applied as an assumed tsunami. The expression of backwash is tried by water pillar collapse. The present calculation results are compared with the experimental results and the applicability of the MPS method is discussed. In addition, the vehicle is arranged on a wharf, and the chain of disaster is simulated.

Effects of Wall Condition of a Plunging Body on Splash

2011 ◽  
Author(s):  
Masao Yokoyama ◽  
Yoshihiro Kubota ◽  
Osamu Mochizuki
Keyword(s):  
Numerical Simulation ◽  
Implicit Method ◽  
Water Tank ◽  
Air Cavity ◽  
Slip Ratio ◽  
Mps Method ◽  
Swelling Degree ◽  
Living Things ◽  
Wall Condition ◽  
Moving Particle

Splashes generated by hydrogel sphere were simulated numerically and experimentally for investigating the effects of slip like mucus of living things. Numerical simulation using MPS (Moving Particle Semi-implicit) method was carried out. We defined the slip ratio as the swelling degree of hydrogel and installed the slip ratio into the MPS method. The swelling degree is the ratio of the weight of water against that of hydrogel. We simulated the splashes generated by the hydrogel spheres which had the different swelling degree plunging into water. As the evaluation of swelling degree on the surface of actual hydrogel spheres we also tested by using the hydrogel spheres plunging into water experimentally. The height of splash as a result of reaction of the air cavity became higher according to the increase of the swelling degree. The speed of hydrogel sphere sinking in water tank was also quicker in the numerical simulation. The reason of these results was that the velocity of water around the hydrogel sphere became quicker due to the slip on the surface.

Load Discontinuity and Its Remedy in Step-by-Step Integration

2006 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
Numerical Solution ◽  
Small Time ◽  
Step Size ◽  
Time Step ◽  
Integration Procedure ◽  
Amplitude Distortion ◽  
Small Time Step

The discontinuity at the end of an impulse will lead to an extra impulse and thus an extra displacement. Consequently, an amplitude distortion is introduced in the numerical solution. The difficulty arising from the discontinuity at the end of an impulse can be overcome by using a very small time step to perform the step-by-step integration since it reduces the extra impulse and thus extra displacement. However, computational efforts might be significantly increased since the small time step is performed for a complete step-by-step integration procedure. A remedy is devised to computationally efficiently overcome this difficulty by using a very small time step immediately upon termination of the applied impulse. This is because that the extra impulse caused by the discontinuity is almost proportional to the discontinuity value at the end of the impulse and the step size. The feasibility of this proposed remedy is analytically and numerically confirmed herein.

scholarly journals A diffusion Monte Carlo algorithm with very small time‐step errors

1993 ◽  
Vol 99 (4) ◽  
pp. 2865-2890 ◽  
Author(s):  
C. J. Umrigar ◽  
M. P. Nightingale ◽  
K. J. Runge
Keyword(s):  
Monte Carlo ◽  
Small Time ◽  
Monte Carlo Algorithm ◽  
Diffusion Monte Carlo ◽  
Time Step ◽  
Small Time Step

Stable Moving Particle Semi Implicit Method for Modeling Waves Generated by Submarine Landslides

2014 ◽  
Author(s):  
Mohammad Amin Nabian ◽  
Leila Farhadi
Keyword(s):  
Water Surface ◽  
Surface Profile ◽  
Particle Methods ◽  
Water Tank ◽  
Submarine Landslides ◽  
Fractional Step Method ◽  
Time Step ◽  
Mps Method ◽  
Water Surface Profile ◽  
Moving Particle

A mesh-free numerical formulation, known as Moving Particle Semi Implicit (MPS) Method, is used for modeling waves generated by submarine landslides. In this formulation, approximations are provided to the strong form of PDEs on the basis of integral interpolants. The governing equations, Navier-Stokes equations, are solved in a 2D fully Lagrangian form. This method utilizes a fractional step method and splits each time step in two steps. The fluid is represented with particles and the motion of each particle is calculated through interactions with neighboring particles by means of a kernel function. Landslides in this paper are simulated by a submerged triangle rigid wedge sliding along an inclined plane into a water tank. As the wedge sinks, a wave and a vortex is formed. The water surface profile, velocity field and pressure field are represented at different times. To confirm the accuracy of the model, the water surface profile is compared with the experimental data, showing good agreement. Simulations can continue for a long period of time without any instability occurrence and this is a remarkable competency amongst other particle methods. A discussion on multi-size particle strategy and its ability to increase the efficiency of MPS method is provided at the end of the paper.

Stability Analysis Research of Modified CD-Newmark Numerical Integral Method in Seismic Pseudo-Dynamic Test

2014 ◽  
Vol 638-640 ◽  
pp. 1869-1872
Author(s):  
Xin Jiang Cai ◽  
Shi Zhu Tian
Keyword(s):  
Integral Method ◽  
Dynamic Test ◽  
Stable Condition ◽  
Small Time ◽  
Stability Conditions ◽  
Newmark Method ◽  
Time Step ◽  
Unconditionally Stable ◽  
Small Time Step ◽  
Numerical Integral

The characteristics of explicit numerical integral method is without iteration, and the characteristics of inexplicit numerical integral method is unconditionally stable. The traditional CD-Newmark method has the shortcoming of the bigger upper frequency leads to a small time step, a modified combined integral method named MCD-Newmark release the fixed DOF of numerical substructure, then obtained the parameters range of stable condition of experimental substructure, and the unconditionally stable of numerical substructure is also researched,then the strict stability conditions of the traditional CD-Newmark algorithm is resolved. The study provides reference for structural seismic test.

scholarly journals Investigation of Numerical Conditions of Moving Particle Semi-implicit for Two-Dimensional Wedge Slamming

2022 ◽  
Author(s):  
Takahito Iida ◽  
Yudai Yokoyama
Keyword(s):  
Particle Size ◽  
Poor Performance ◽  
Verification And Validation ◽  
Two Dimensional ◽  
Step Size ◽  
Time Step ◽  
Optimum Time ◽  
Time Step Size ◽  
Tuning Parameters ◽  
Moving Particle

AbstractThe sensitivity of moving particle semi-implicit (MPS) simulations to numerical parameters is investigated in this study. Although the verification and validation (V&V) are important to ensure accurate numerical results, the MPS has poor performance in convergences with a time step size. Therefore, users of the MPS need to tune numerical parameters to fit results into benchmarks. However, such tuning parameters are not always valid for other simulations. We propose a practical numerical condition for the MPS simulation of a two-dimensional wedge slamming problem (i.e., an MPS-slamming condition). The MPS-slamming condition is represented by an MPS-slamming number, which provides the optimum time step size once the MPS-slamming number, slamming velocity, deadrise angle of the wedge, and particle size are decided. The simulation study shows that the MPS results can be characterized by the proposed MPS-slamming condition, and the use of the same MPS-slamming number provides a similar flow.

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