Investigation Into Stability and Accuracy in Predicting Slender Bodies’ Hydroelasticity Using Loose Coupling Methods

2015 ◽  
Author(s):  
Leixin Ma ◽  
Shixiao Fu ◽  
Ke Hu ◽  
Qian Shi ◽  
Runpei Li
Keyword(s):  
Time Integration ◽  
Hydrodynamic Forces ◽  
Mass Force ◽  
Loose Coupling ◽  
Time Step ◽  
Time Saving ◽  
Coupling Methods ◽  
The Stability ◽  
Stability And Accuracy ◽  
Hydroelastic Response

Problems concerning fluid-structure-interaction are often encountered in aquaculture engineering. For a moving slender structure like fishing net or floater in currents and waves, modified Morison Equation is a widely employed formula to estimate its hydrodynamic loads. The hydrodynamic forces are closely dependent on the structures’ velocity and acceleration, and quadratic relative velocity in the equation even adds nonlinearity in the forces. To study the hydroelastic response, two time-saving loosely coupling methods, calculating the hydrodynamic forces based on the structure’s response in the previous time step without iteration, are proposed in this paper. The loose coupling methods were proved to affect the traditional stability criteria for time integration. Based on the two loose coupling methods, the stability and accuracy of a slender beam’s hydroelasticity undergoing large deformation were studied. The calculated responses were compared against strong coupling results. It was found that if loose coupling is assumed in added mass force, unconditional instability is likely to occur. On the other hand, the accuracy of numerical results can be improved with smaller time increments set if loose coupling is only assumed in the quadratic relative drag force.

Second Order Errors Related to Geometric Nonlinearity in Explicit Central Difference Operator

2008 ◽  
Author(s):  
Don R. Metzger ◽  
Young-Suk Kim
Keyword(s):  
Difference Method ◽  
Difference Operator ◽  
Time Integration ◽  
General Nature ◽  
Time Step ◽  
Central Difference ◽  
Central Difference Method ◽  
Dynamic Structures ◽  
The Stability ◽  
Stability And Accuracy

Numerical analysis of nonlinear dynamic structures frequently makes use of the central difference method to step the transient forward in time. The method is particularly robust, accommodating material and geometric nonlinearities as well as contact surfaces and constraints of a very general nature. The implementation of the method is most usually performed according to [1], where velocity terms (or more generally rate quantities) are taken half a time step from the displacement and acceleration terms. It was recognized that a proper check of energy balance, requires that velocity must also be interpolated to the integer steps [2]. The stability and accuracy of the central difference method is well established, and decades of experience including its use in numerous commercial finite element codes confirms why it is the method of choice for explicit time integration of transients.

Numerical Simulation of Transient Flow in Products Pipeline

2013 ◽  
Vol 732-733 ◽  
pp. 487-490
Author(s):  
Zhen Ye Wang ◽  
Jiang Fei Li ◽  
Lian Yuan ◽  
Zhi Zhong Fu ◽  
Bo Li ◽  
...  
Keyword(s):  
Difference Scheme ◽  
Large Time ◽  
Transient Flow ◽  
Implicit Difference Scheme ◽  
Time Step ◽  
Characteristics Method ◽  
Large Time Step ◽  
The Stability ◽  
Products Pipeline ◽  
Stability And Accuracy

In this paper, explicit difference scheme, implicit difference scheme and characteristics method are separately used to simulate the transient flow in products pipeline. The simulation result can be used to prevent water hammer in the pipeline of unsteady situation and to improve the efficiency and safety in oil transmission systems. And then, the stability and accuracy of the three methods are compared by adopting different time steps. For explicit difference method, large fluctuation may occur in case of large time step. For implicit method, the result is weakly affected by time step, only if the relaxation factor selected is reasonable. For characteristics method, the results have a high convergence speed and precision. The results show that, in the situation of valve shut down in terminal, it takes about 1.1×104 seconds to return to a new steady state.

scholarly journals A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

2007 ◽  
Vol 7 (3) ◽  
pp. 227-238 ◽  
Author(s):  
S.H. Razavi ◽  
A. Abolmaali ◽  
M. Ghassemieh
Keyword(s):  
Fourth Order ◽  
Initial Conditions ◽  
Time Integration ◽  
Critical Time ◽  
Linear Acceleration ◽  
Time Step ◽  
Time Integration Method ◽  
Acceleration Method ◽  
The Stability ◽  
Critical Time Step

AbstractIn the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

Stability analysis of implicit semi-Lagrangian methods for numerical solution of non-hydrostatic atmospheric dynamics equations

2021 ◽  
Vol 36 (4) ◽  
pp. 239-253
Author(s):  
Vladimir V. Shashkin
Keyword(s):  
Fixed Point ◽  
Potential Temperature ◽  
Time Integration ◽  
Buoyancy Frequency ◽  
Time Step ◽  
Reference Profile ◽  
Maximum Time ◽  
Pressure Variable ◽  
Thermodynamic Variables ◽  
The Stability

Abstract The stability of implicit semi-Lagrangian schemes for time-integration of the non-hydrostatic atmosphere dynamics equations is analyzed in the present paper. The main reason for the instability of the considered class of schemes is the semi-Lagrangian advection of stratified thermodynamic variables coupled to the fixed point iteration method used to solve the implicit in time upstream trajectory computation problem. We identify two types of unstable modes and obtain stability conditions in terms of the scheme parameters. Stabilization of sound modes requires the use of a pressure reference profile and time off-centering. Gravity waves are stable only for an even number of fixed point method iterations. The maximum time step is determined by inverse buoyancy frequency in the case when the reference profile of the potential temperature is not used. Generally, applying time off-centering and reference profile to pressure variable is necessary for stability. Using reference profile for potential temperature and an even number of the iterations allows one to significantly increase the maximum time-step value.

Transient Analysis of a Cylindrical Heat Pipe Considering Different Wick Structures

2016 ◽  
Author(s):  
Mehdi Famouri ◽  
M. Mahdi Abdollahzadeh ◽  
Ahmed Abdulshaheed ◽  
GuangHan Huang ◽  
Gerardo Carbajal ◽  
...  
Keyword(s):  
Heat Pipe ◽  
Experimental Studies ◽  
Simple Algorithm ◽  
Heat Pipes ◽  
Working Fluid ◽  
Time Step ◽  
Base Scheme ◽  
The Stability ◽  
Stability And Accuracy ◽  
Energy Equations

Heat pipes have been shown to be one of the most efficient passive cooling devices for electronic cooling. Only a handful of studies were capable of solving transient performances of heat pipes based on realistic assumptions. A segregated finite volume base scheme using SIMPLE algorithm is used along with system pressurization and overall mass balance to solve mass transfer at the interface, continuity, momentum and energy equations. The fluid flow and heat transfer are solved throughout the wick and vapor core and no assumptions are made at the locations where evaporation and condensations occur. Water is the working fluid and variable densities are used for both liquid and vapor phases to account for continuity at the interface as well as inside of wick and vapor core. The wick is modeled as a non-homogeneous porous media and the effective thermal conductivities and viscous properties are calculated for each type of structure separately using the available relations from the literature. In this study, an axisymmetric two-dimensional solver for cylindrical heat pipe is developed using FLUENT package with the help of User Defined Functions (UDFs) and User Defined Scalar (UDS). The model is tested for grid and time step independency and the results show the stability and accuracy of the proposed method. The numerical results of the present study were in good agreement with the data from previous numerical and experimental studies available in the literature. Additionally, two different wick structures were studied to determine its effect on the thermal performance of heat pipes.

A Taylor Series Integration Method with Coupling in Structural Dynamics

2012 ◽  
Vol 166-169 ◽  
pp. 9-13
Author(s):  
Ze Ying Guo
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Integration Method ◽  
Damping Ratio ◽  
Time Integration ◽  
Taylor Series Expansion ◽  
Time Step ◽  
Structural Dynamic ◽  
Precise Time Integration ◽  
Stability And Accuracy

Based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family, implicit series solution of structural dynamic equation is put forward by introducing the Taylor series expansion. Relevant time step integration formulas were designed. Stability and accuracy of the method were analyzed. Stability analyses show that the coupling implicit method is stable when damping ratio is equal to 0, and is conditionally stable when damping ratio are other values. The results show that the accuracy of the algorithm can be controlled by choosing the number of truncation order of Taylor series expansion and is better than that of traditional scheme with the increase of time step. Number examples are given to demonstrate the validity of the proposed method.

A Mixed and Multi-Step Higher-Order Implicit Time Integration Family

2010 ◽  
Vol 224 (10) ◽  
pp. 2097-2108 ◽  
Author(s):  
M Rezaiee-Pajand ◽  
S R Sarafrazi
Keyword(s):  
Time Integration ◽  
Higher Order ◽  
Trapezoidal Rule ◽  
Implicit Time ◽  
Benchmark Problems ◽  
Integration Schemes ◽  
Implicit Time Integration ◽  
Time Integration Schemes ◽  
The Stability ◽  
Stability And Accuracy

This article develops a new time integration family for second-order dynamic equations. A combination of the trapezoidal rule and higher-order Newton backward extrapolation functions are utilized in the formulation. Five members of the suggested family are extensively studied in this article. Most members of the presented time integration family are new. The stability and accuracy of the proposed time integration schemes are investigated by solving some benchmark problems. Numerical results are checked and compared with well-known strategies. The findings of the article show the efficiency, accuracy and robustness of the suggested techniques.

A FAST AND ACCURATE STEP-BY-STEP SOLUTION PROCEDURE FOR DIRECT INTEGRATION

2011 ◽  
Vol 11 (03) ◽  
pp. 473-493 ◽  
Author(s):  
SHYH-RONG KUO ◽  
J. D. YAU
Keyword(s):  
Time Integration ◽  
Closed Form Solution ◽  
Solution Procedure ◽  
Small Time ◽  
Form Solution ◽  
Dynamic Problems ◽  
Sdof System ◽  
Linear Dynamic ◽  
The Stability ◽  
Stability And Accuracy

Very small time steps are usually needed in numerical computation as conventional time integration methods are used to compute the response of a structure subjected to a dynamic loading with rapid changes or load discontinuity. To overcome this drawback, this study proposed a fast, fourth-order accurate step-by-step time integration (FASSTI) algorithm that is unconditionally stable and allows larger time steps for linear dynamic problems. From the stability and accuracy analysis, it is shown that the FASSTI algorithm retains the features of unconditional stability, accuracy, and fast convergence than the Newmark method. As a first test, a closed-form solution of an excited single degree of freedom (SDOF) system is derived and used to verify the reliability of the present algorithm in solving linear dynamic problems. In the numerical examples, the accuracy and efficiency of the proposed method is demonstrated in the solution of the dynamic response of an SDOF system under a series of impulse-type forces.

scholarly journals Conditional stability of Larkin methods with non-uniform grids

2010 ◽  
Vol 37 (2) ◽  
pp. 139-159 ◽  
Author(s):  
Kazuhiro Fukuyo
Keyword(s):  
Stability Analysis ◽  
Conditional Stability ◽  
Dimensionless Time ◽  
Stability Criteria ◽  
Time Step ◽  
Unconditionally Stable ◽  
Von Neumann ◽  
Uniform Grids ◽  
The Stability ◽  
Stability And Accuracy

Stability analysis based on the von Neumann method showed that the Larkin methods for two-dimensional heat conduction with non- uniform grids are conditionally stable while they are known to be unconditionally stable with uniform grids. The stability criteria consisting of the dimensionless time step ?t, the space intervals ?x, ?y, and the ratios of neighboring space intervals ?, ? were derived from the stability analysis. A subsequent numerical experiment demonstrated that solutions derived by the Larkin methods with non-uniform grids lose stability and accuracy when the criteria are not satisfied.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

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