scholarly journals STABILITY ANALYSIS OF SEIDEL TYPE MULTICOMPONENT ITERATIVE METHOD

2002 ◽  
Vol 7 (1) ◽  
pp. 1-10
Author(s):  
V. N. Abrashin ◽  
R. Čiegis ◽  
V. Pakeniene ◽  
N. G. Zhadaeva
Keyword(s):  
Stability Analysis ◽  
Iterative Method ◽  
Iterative Methods ◽  
Convergence Rates ◽  
Splitting Method ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Discrete Problem ◽  
Smooth Functions ◽  
The Stability

This paper deals with the stability analysis of multicomponent iterative methods for solving elliptic problems. They are based on a general splitting method, which decomposes a multidimensional parabolic problem into a system of one dimensional implicit problems. Error estimates in the L 2 norm are proved for the first method. For the stability analysis of Seidel type iterative method we use a spectral method. Two dimensional and three dimensional problems are investigated. Finally, we present results of numerical experiments. Our goal is to investigate the dependence of convergence rates of multicomponent iterative methods on the smoothness of the solution. Hence we solve a discrete problem, which approximates the 3D Poisson's problem. It is proved that the number of iterations depends weakly on the number of grid points if the exact solution and the initial approximation are smooth functions, both. The same problem is also solved by the Stability Correction iterative method. The obtained results indicate a similar behavior.

Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

2019 ◽  
Vol 1 (1) ◽  
pp. 49-60
Author(s):  
Simon Heru Prassetyo ◽  
Ganda Marihot Simangunsong ◽  
Ridho Kresna Wattimena ◽  
Made Astawa Rai ◽  
Irwandy Arif ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Convergence Rate ◽  
Critical Strain ◽  
Convergence Rates ◽  
Strain Analysis ◽  
Water Diversion ◽  
Tunnel Face ◽  
Tunnel Stability ◽  
The Stability ◽  
Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

Three-dimensional stability analysis for a salt-finger convecting layer

2018 ◽  
Vol 841 ◽  
pp. 636-653
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Grashof Number ◽  
Significant Difference ◽  
The Stability ◽  
Mode A

A three-dimensional linear stability analysis is carried out for a convecting layer in which both the temperature and solute distributions are linear in the horizontal direction. The three-dimensional results show that, for $Le=3$ and 100, the most unstable mode occurs invariably as the longitudinal mode, a vortex roll with its axis perpendicular to the longitudinal plane, suggesting that the two-dimensional results are sufficient to illustrate the stability characteristics of the convecting layer. Two-dimensional results show that the stability boundaries of the transverse mode (a vortex roll with its axis perpendicular to the transverse plane) and the longitudinal modes are virtually overlapped in the regime dominated by thermal diffusion and the regime dominated by solute diffusion, while these two modes hold a significant difference in the regime the salt-finger instability prevails. More precisely, the instability area in terms of thermal Grashof number $Gr$ and solute Grashof number $Gs$ is larger for the longitudinal mode than the transverse mode, implying that, under any circumstance, the longitudinal mode is always more unstable than the transverse mode.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

Stability Analysis of a 3D Vertical Slope with Transverse Earthquake Load and Surcharge

2011 ◽  
Vol 90-93 ◽  
pp. 676-679 ◽  
Author(s):  
Ting Kai Nian ◽  
Ke Li Zhang ◽  
Run Qiu Huang ◽  
Guang Qi Chen
Keyword(s):  
Finite Element ◽  
Stability Analysis ◽  
Failure Mode ◽  
Factor Of Safety ◽  
Three Dimensional ◽  
Strength Reduction ◽  
Reduction Procedure ◽  
Interesting Issue ◽  
Earthquake Load ◽  
The Stability

The stability and failure mode for a 3D vertical slope with transverse earthquake load and surcharge have been an interesting issue, especially in building excavation and wharf engineering. In order to further reveal the seismic and surcharge effect, a three-dimensional elasto-plastic finite element(FE) code combined with a strength reduction procedure is used to yield a factor of safety and failure mode for a vertical slopes under two horizontal direction pseudo-static(PS) coefficient and surcharge on the slope top, respectively. Comparative studies are carried out to investigate the effect of seismic coefficient, surcharge intensity and location on the stability and the failure mechanism for a 3D vertical slope including an inclined weak layer. Several important findings are also achieved.

Three-dimensional stability analysis for slurry-filled trench wall in cohesionless soil

1996 ◽  
Vol 33 (5) ◽  
pp. 798-808 ◽  
Author(s):  
Jiin-Song Tsai ◽  
Jia-Chyi Chang
Keyword(s):  
Stability Analysis ◽  
Stability Problem ◽  
Slip Surface ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Soil Mass ◽  
Cohesionless Soil ◽  
Cohesionless Soils ◽  
Slurry Trench ◽  
The Stability

On the basis of the limiting equilibrium and arching theory, a three-dimensional analysis is proposed for slurry-supported trenches in cohesionless soils. This analytical approach is developed by considering the trench stability problem as a vertical soil cut within a fictitious half-silo with a rough wall surronding. Arching effects are considered not only in the vertical direction but also in the horizontal direction. A shell-shaped slip surface of the sliding soil mass is defined by Mohr-Coulomb criterion. The factor of safety is defines as the ratio of the resisting force induced by slurry pressure to the horizontal force required to maintain the stability of the trench wall. Results of the proposed method have been compared with those of two existing analytical methods for a typical trench stability problem. Key words: stability analysis, slurry trench wall, cohesionless soil.

Stability analysis of three-dimensional (3-D) systems using a wave advanced model (WAM)

2015 ◽  
Vol 39 (6) ◽  
pp. 898-906
Author(s):  
SaeedReza Tofighi ◽  
Masoud Shafiee ◽  
Sayyid Mehdi Alavinia
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Wave Model ◽  
System Stability ◽  
The Stability ◽  
Representation Scheme ◽  
The Given ◽  
Advanced Model ◽  
New Criteria ◽  
D Wave

In this paper, the problem of three-dimensional (3-D) system stability is studied. In order to investigate the stability of 3-D systems, a new representation scheme is introduced based on the local state model proposed by Givone–Roesser for 3-D systems. This representation is obtained from the extended expression of the 1-D wave model proposed by Porter–Aravena. Then, according to the obtained model a new criteria for the stability of 3-D systems is stated. This criteria provides a simpler way to investigate asymptotic stability. Furthermore, an algorithm is performed to illustrate the procedure of analysing stability. Finally, some examples are performed and verified using numerical simulations in order to illustrate the given criteria for the stability.

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