scholarly journals Numerical and asymptotic flow stability analysis of vortex structures

2021 ◽  
Vol 263 ◽  
pp. 03003
Author(s):  
Vadim Akhmetov
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stability Problem ◽  
Swirling Flow ◽  
Viscous Incompressible Fluid ◽  
Kutta Method ◽  
Phase Velocities ◽  
Runge Kutta Method ◽  
Solutions Of Equations ◽  
Orthogonalization Procedure

Stability problem of an axisymmetric swirling flow of a viscous incompressible fluid with respect to nonaxisymmetric perturbations is considered. The system of ordinary differential equations for the amplitude functions is solved numerically by the Runge-Kutta method and orthogonalization procedure. Solutions of equations for perturbations at the neighborhood of singular points are obtained by the Frobenius method. The maximum of amplification coefficients and phase velocities of five unstable modes are calculated.

A New Efficient Ode Solver For Solving Initial Value Problem

1998 ◽  
pp. 47-56
Author(s):  
Nazeeruddin Yaacob ◽  
Bahrom Sanugi
Keyword(s):  
Stability Analysis ◽  
Explicit Formula ◽  
Fourth Order ◽  
Initial Value Problem ◽  
Harmonic Mean ◽  
Kutta Method ◽  
Initial Value ◽  
Order Accuracy ◽  
Runge Kutta Method ◽  
Runge Kutta

In this paper we develop a new three-stage,fourth order explicit formula of Runge-Kutta type based on Arithmetic and Harmonic means.The error and stability analyses of this method indicate that the method is stable and efficient for nonstiff problems.Two examples are given which illustrate the fcurth order accuracy of the method. Keywords: Runge-Kutta method, Harmonic Mean, three-stage, fourth-order, covergence and stability analysis.

scholarly journals Stability Analysis of Symmetrical Rotors Partially Filled with a Viscous Incompressible Fluid

2001 ◽  
Vol 7 (5) ◽  
pp. 301-310 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Damping Ratio ◽  
Navier Stokes ◽  
Fluid Viscosity ◽  
Navier Stokes Equations ◽  
Rotor Systems ◽  
The Stability

On the basis of the linearized fluid forces acting on the rotor obtained directly by using the two-dimensional Navier-Stokes equations, the stability of symmetrical rotors with a cylindrical chamber partially filled with a viscous incompressible fluid is investigated in this paper. The effects of the parameters of rotor system, such as external damping ratio, fluid fill ratio, Reynolds number and mass ratio, on the unstable regions are analyzed. It is shown that for the stability analysis of fluid filled rotor systems with external damping, the effect of the fluid viscosity on the stability should be considered. When the fluid viscosity is included, the adding external damping will make the system more stable and two unstable regions may exist even if rotors are isotropic in some casIs.

scholarly journals ANALISIS DINAMIS MODEL MATEMATIKA PERTUMBUHAN JUMLAH MAHASISWA PROGRAM STUDI PENDIDIKAN MATEMATIKA STKIP PGRI PASURUAN

2018 ◽  
Vol 1 (October) ◽  
pp. 61-66
Author(s):  
Wahyuni Ningsih ◽  
Rif’atul Khusniah
Keyword(s):  
Stability Analysis ◽  
Mathematics Education ◽  
Population Growth ◽  
Dynamic Analysis ◽  
Equilibrium Point ◽  
Education Program ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Completion

Mathematical Models of population growth on the number of students, especially in the mathematics education program STKIP PGRI Pasuruan has been obtained. One of the purposes of this modeling was to find out the behavior of the model or system. To determine the behavior of the systems can be used dynamic analysis of the model. Therefore, a dynamic analysis of the growth model in the number of students, especially in the mathematics education program STKIP PGRI Pasuruan has been done in this article. The dynamic analysis that is used in this article is about a stability analysis around the equilibrium point of the model. Completion of the model using the Runge-Kutta method was simulated so that obtained a graphical completion of the model. Analytical and graphical systems stability analysis showed that the system was asymptotically unstable.   Model matematika pertumbuhan populasi pada jumlah mahasiswa, khususnya di program studi pendidikan matematika STKIP PGRI Pasuruan sudah didapatkan. Salah satu tujuan dilakukan pemodelan ini adalah untuk mengetahui perilaku dari model atau sistem. Untuk mengetahui perilaku sistem dapat digunakan analisis dinamis terhadap model. Oleh karena itu, pada artikel ini dilakukan analisis dinamis terhadap model pertumbuhan jumlah mahasiswa program studi pendidikan matematika STKIP PGRI Pasuruan. Analisis dinamis yang digunakan pada artikel ini berupa analisis kestabilan sistem di sekitar titik setimbang model. Penyelesaian model menggunakan metode Runge-Kutta yang di simulasikan sehingga diperoleh bentuk penyelesaian model secara grafik. Analisis kestabilan sistem secara analitik dan grafik menunjukkan bahwa sistem tidak stabil asimtotik.

scholarly journals Linear Stability Analysis of Runge-Kutta Methods for Singular Lane-Emden Equations

2020 ◽  
pp. 134-140
Author(s):  
M. O. Ogunniran ◽  
O. A. Tayo ◽  
Y. Haruna ◽  
A. F. Adebisi
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Classical Method ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Mind

Runge-Kutta methods are efficient methods of computations in differential equations, the classical Runge-Kutta method of order 4 happens to be the most popular of these methods, and most times it is attached to the mind when Runge-Kutta methods are mentioned. However, there are numerous forms of them existing in lower and higher orders of the classical method. This work investigates the linear stabilities and abilities of some selected explicit members of these Runge-Kutta methods in integrating the singular Lane-Emden differential equations. The results obtained established the ability of the classical Runge-Kutta method and why is mostly used in computations.

scholarly journals Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

2018 ◽  
Vol 173 ◽  
pp. 03004
Author(s):  
Igor Bakholdin
Keyword(s):  
Incompressible Fluid ◽  
Linear Model ◽  
Linear Theory ◽  
Numerical Scheme ◽  
Hyperbolic Equations ◽  
Membrane Model ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Bending Resistance ◽  
Elastic Walls

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

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