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.

Stability Analysis on the Algorithm of Constitutive Relation in Viscoplastic Materials

2016 ◽  
Vol 33 (2) ◽  
pp. 173-181
Author(s):  
M.-T. Liu ◽  
Y.-C. Li ◽  
X.-Z. Hu ◽  
J. Zhang ◽  
T.-G. Tang
Keyword(s):  
Numerical Calculation ◽  
Stability Analysis ◽  
Convergence Rate ◽  
Iterative Algorithm ◽  
Numerical Stability ◽  
Sufficient Condition ◽  
Time Step ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
The Stability

AbstractThe numerical stability of the explicit precise algorithm, which was developed for the viscoplastic materials, was analyzed. It was found that this algorithm is not absolutely stable. A necessary but not sufficient condition for the numerical stability was deduced. It showed that the time step in numerical calculation should be less than a certain value to guarantee the stability of explicit precise algorithm. Through a series of numerical examples, the stability analysis on the explicit precise algorithm was proved to be reliable. At last, an iterative algorithm was presented for viscoplastic materials. Both of the theoretical and numerical results showed that the iterative algorithm is unconditionally stable and its convergence rate is rapid. In practice, the explicit precise algorithm and iterative algorithm can be combined to obtain reliable results with the minimum computing costs.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

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.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Stability Criteria and Analysis of a Monocolumn Concept

2004 ◽  
Author(s):  
Felipe Cruz Rodrigues de Campos ◽  
Marcos Cueva ◽  
Kazuo Nishimoto ◽  
Ana Paula Dos Santos Costa
Keyword(s):  
Stability Analysis ◽  
Offshore Structures ◽  
Oil Fields ◽  
Stability Criteria ◽  
Offshore Drilling ◽  
Steel Catenary Risers ◽  
Special Concern ◽  
The Stability ◽  
Almost All ◽  
Classification Society

To be classified and approved by a classification society, all offshore structures shall be submitted and analyzed according to standard rules. The stability criteria are based on the IMO–MODU (International Maritime Organization–Mobile Offshore Drilling Units) Code which has reference to almost all types of floating units such as surface, column-stabilized and self elevating, but problems were found when dealing with monocolumn concept due to differences between this concept and those presented by the rules. The monocolumn studied is a floating production system (FPS) platform designed to handle steel catenary risers (SCR) in a depth of 1800 m in Brazilian oil fields. In this project, special concern was given to sea keeping behavior, constructability and security. This paper discusses the last item, focusing on subdivision and stability analysis. In order to overcome difficulties in finding the appropriate criteria, the work was developed using a special criteria, discussed with Det Norske Veritas (DNV) and PETROBRAS, which could be implanted in future classifications for this type of hull.

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

scholarly journals The Stability Analyze of KM. Rejeki Baru Kharisma of Tarakan – Tanjung Selor Route

Teknik ◽  
2021 ◽  
Vol 42 (1) ◽  
pp. 52-62
Author(s):  
Alamsyah Alamsyah ◽  
Zen Zulkarnaen ◽  
Suardi Suardi
Keyword(s):  
Stability Analysis ◽  
Stability Criteria ◽  
Load Case ◽  
Ship Stability ◽  
Intact Stability ◽  
Ship Capsize ◽  
The Stability ◽  
Stability Area ◽  
The Ideal

Ship stability that is not according to the IMO standard will make the ship capsize when operating. The purpose of this research is to determine the cause of the overturn in terms of the stability criteria of the ship. The method used is software  of simulation. Stability analysis is carried out with the load case that occurs in the field when an accident occurs and the ideal loadcase according to PM 104 2017 standards about’s the transportation of operation. The results showed is cargo of goods placed on the roof top (loadcase 1) based on the criteria of Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 0.9417 m.deg, area 0° ~ 40° = 1,0200 m.deg, 30° ~ 40° = 0.0783 m.deg, GZ value at heeling 30° = 0.029 m, angle of occurrence of maximum GZ = 21.8°, and the initial GMt value = 0.135 m, the results stated that all did not meet the Intact Stability code A.749 criteria, while in it was obtained cargo of goods placed in the hull (loadcase 2) based on Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 4.5338 m.deg, area 0° ~ 40° = 7.1643 m.deg, area 30° ~ 40° = 2.6305 m.deg, GZ value at heeling 30° = 0.265 m, angle of occurrence of maximum GZ = 34.5°, and the initial GMt value = 0.621 m, the results stated that all met the Intact Stability code A.749 criteria

scholarly journals Stability Analysis of Pulse-Width-Modulated Feedback Systems with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhong Zhang ◽  
Huahui Han ◽  
Qiling Zhao ◽  
Lixia Ye
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Pulse Width ◽  
Time Varying ◽  
Stability Criteria ◽  
Feedback Systems ◽  
Stochastic Perturbations ◽  
Pulse Width Modulated ◽  
The Stability ◽  
Moment Exponential Stability

The stability problem of pulse-width-modulated feedback systems with time-varying delays and stochastic perturbations is studied. With the help of an improved functional construction method, we establish a new Lyapunov-Krasovskii functional and derive several stability criteria aboutpth moment exponential stability.

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.

scholarly journals Numerical approach for solving time fractional diffusion equation

2017 ◽  
Vol 7 (3) ◽  
pp. 281-287
Author(s):  
Dilara Altan Koç ◽  
Mustafa Gülsu
Keyword(s):  
Stability Analysis ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Fractional Diffusion ◽  
Fractional Partial Differential Equations ◽  
Von Neumann ◽  
Liouville Derivative ◽  
Time Fractional Diffusion Equation ◽  
The Stability ◽  
Space Method

In this article one of the fractional partial differential equations was solved by finite difference scheme  based on five point and three point central space method with discretization in time. We use between the Caputo and the Riemann-Liouville derivative definition and the Grünwald-Letnikov operator for the fractional calculus. The stability analysis of this scheme is examined by using von-Neumann method. A comparison between exact solutions and numerical solutions is made. Some figures and tables are included.

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