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.

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.

Pseudodynamic Response to Impulsive Loading

2009 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang ◽  
Ching-Hao Yang
Keyword(s):  
Error Propagation ◽  
Small Time ◽  
Impulsive Loading ◽  
Small Displacement ◽  
Step Size ◽  
Time Step ◽  
Pseudodynamic Test ◽  
Experimental Errors ◽  
Small Time Step ◽  
Test Result

The application of a pseudodynamic technique to yield a shock response from an impulse might encounter a difficulty caused by a significant load discontinuity at the end of the impulse since this load discontinuity at the end of an impulse will result in an extra impulse and then an extra amplitude distortion. This extra impulse is linearly proportional to the step size and thus it is natural to consider the use of a very small time step for a whole pseudodynamic test to overcome the difficulty. However, a series of computer simulations reveal that this approach might not be feasible. This is because that the use of a small time step will lead to a very small displacement increment and it may be contaminated by experimental errors as its magnitude is less than or close to the magnitude of the experimental errors. Thus, an inaccurate test result is obtained. A technique is proposed to overcome this difficulty. This novel technique is to perform a single small time step immediately upon the termination of the applied impulse while the other time steps are conducted by using the time step determined from general considerations. This single small time step will not lead to a significant error propagation problem since only this time step is performed by using a very small step size for a complete pseudodynamic test. The feasibility of this technique was confirmed by a series of pseudodynamic tests.

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.

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

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 Convergence Improved Lax-Friedrichs Scheme Based Numerical Schemes and Their Applications in Solving the One-Layer and Two-Layer Shallow-Water Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Xinhua Lu ◽  
Bingjiang Dong ◽  
Bing Mao ◽  
Xiaofeng Zhang
Keyword(s):  
High Resolution ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Small Time ◽  
Numerical Schemes ◽  
Time Step ◽  
Numerical Diffusion ◽  
First Order ◽  
Small Time Step ◽  
The One

The first-order Lax-Friedrichs (LF) scheme is commonly used in conjunction with other schemes to achieve monotone and stable properties with lower numerical diffusion. Nevertheless, the LF scheme and the schemes devised based on it, for example, the first-order centered (FORCE) and the slope-limited centered (SLIC) schemes, cannot achieve a time-step-independence solution due to the excessive numerical diffusion at a small time step. In this work, two time-step-convergence improved schemes, the C-FORCE and C-SLIC schemes, are proposed to resolve this problem. The performance of the proposed schemes is validated in solving the one-layer and two-layer shallow-water equations, verifying their capabilities in attaining time-step-independence solutions and showing robustness of them in resolving discontinuities with high-resolution.

scholarly journals Multi-Degree of Freedom Propeller Force Models Based on a Neural Network and Regression

2020 ◽  
Vol 8 (2) ◽  
pp. 89 ◽  
Author(s):  
Bradford Knight ◽  
Kevin Maki
Keyword(s):  
Neural Network ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Open Water ◽  
Small Time ◽  
Training Data ◽  
Step Size ◽  
Time Step ◽  
Neural Network Approach ◽  
Time Step Size

Accurate and efficient prediction of the forces on a propeller is critical for analyzing a maneuvering vessel with numerical methods. CFD methods like RANS, LES, or DES can accurately predict the propeller forces, but are computationally expensive due to the need for added mesh discretization around the propeller as well as the requisite small time-step size. One way of mitigating the expense of modeling a maneuvering vessel with CFD is to apply the propeller force as a body force term in the Navier–Stokes equations and to apply the force to the equations of motion. The applied propeller force should be determined with minimal expense and good accuracy. This paper examines and compares nonlinear regression and neural network predictions of the thrust, torque, and side force of a propeller both in open water and in the behind condition. The methods are trained and tested with RANS CFD simulations. The neural network approach is shown to be more accurate and requires less training data than the regression technique.

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