The stability of some numerical schemes for model viscoelastic fluids

1982 ◽  
Vol 10 (1-2) ◽  
pp. 169-174 ◽  
Author(s):  
R.I. Tanner
Keyword(s):  
Viscoelastic Fluids ◽  
Numerical Schemes ◽  
The Stability

On the stability of plane poiseuille flow of viscoelastic fluids

1976 ◽  
Vol 24 (1-2) ◽  
pp. 1-12
Author(s):  
M. J. Crochet ◽  
G. Tackels
Keyword(s):  
Poiseuille Flow ◽  
Viscoelastic Fluids ◽  
Plane Poiseuille Flow ◽  
The Stability

scholarly journals Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Solid Phase ◽  
Viscoelastic Fluids ◽  
Maxwell Fluid ◽  
Base Flow ◽  
Temperature Fields ◽  
Thermal Nonequilibrium ◽  
Interphase Heat Transfer ◽  
Local Thermal Nonequilibrium ◽  
The Stability

The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient Ht, strain retardation parameter Λ2 and diffusivity ratio α portray stabilizing influence on the system while increasing stress relaxation parameter Λ1 and porosity-modified conductivity ratio γ exhibit an opposite trend.

scholarly journals Some Remarks on the Stability Condition of Numerical Scheme of the KdV-type Equation

2017 ◽  
Vol 9 (4) ◽  
pp. 11 ◽  
Author(s):  
Chun-Te Lee ◽  
Jeng-Eng Lin ◽  
Chun-Che Lee ◽  
Mei-Li Liu
Keyword(s):  
Stability Condition ◽  
Numerical Scheme ◽  
Kdv Equation ◽  
Type Equation ◽  
Stability Criteria ◽  
Numerical Schemes ◽  
The Kdv Equation ◽  
The Stability ◽  
Difference Fourier ◽  
Central Finite Difference

This paper has employed a comparative study between the numerical scheme and stability condition. Numerical calculations are carried out based on three different numerical schemes, namely the central finite difference, fourier leap-frog, and fourier spectral RK4 schemes. Stability criteria for different numerical schemes are developed for the KdV equation, and numerical examples are put to test to illustrate the accuracy and stability between the solution profile and numerical scheme.

scholarly journals Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method

2017 ◽  
Vol 27 (11) ◽  
pp. 1993-2030 ◽  
Author(s):  
Xiaofeng Yang ◽  
Jia Zhao ◽  
Qi Wang ◽  
Jie Shen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Approximation Schemes ◽  
Numerical Schemes ◽  
Time Step ◽  
Invariant Energy Quadratization ◽  
The Stability ◽  
2D And 3D ◽  
Well Posed

How to develop efficient numerical schemes while preserving energy stability at the discrete level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper, we develop a set of first- and second-order temporal approximation schemes based on a novel “Invariant Energy Quadratization” approach, where all nonlinear terms are treated semi-explicitly. Consequently, the resulting numerical schemes lead to well-posed linear systems with a linear symmetric, positive definite at each time step. We prove that the developed schemes are unconditionally energy stable and present various 2D and 3D numerical simulations to demonstrate the stability and the accuracy of the schemes.

scholarly journals Physics of ultimate detachment of a tokamak divertor plasma

2017 ◽  
Vol 83 (5) ◽  
Author(s):  
S. I. Krasheninnikov ◽  
A. S. Kukushkin
Keyword(s):  
Experimental Data ◽  
Plasma Physics ◽  
Edge Plasma ◽  
Plasma Transport ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Basic Physics ◽  
Plasma Detachment ◽  
The Stability ◽  
The Impact

The basic physics of the processes playing the most important role in divertor plasma detachment is reviewed. The models used in the two-dimensional edge plasma transport codes that are widely used to address different issues of the edge plasma physics and to simulate the experimental data, as well as the numerical schemes and convergence issues, are described. The processes leading to ultimate divertor plasma detachment, the transition to and the stability of the detached regime, as well as the impact of the magnetic configuration and divertor geometry on detachment, are considered. A consistent, integral physical picture of ultimate detachment of a tokamak divertor plasma is developed.

scholarly journals Stability of rigid body motion through an extended intermediate axis theorem: application to rockfall simulation

2021 ◽  
Author(s):  
Remco I. Leine ◽  
Giuseppe Capobianco ◽  
Perry Bartelt ◽  
Marc Christen ◽  
Andrin Caviezel
Keyword(s):  
Rigid Body ◽  
Direct Method ◽  
Lateral Spreading ◽  
The Body ◽  
Body Motion ◽  
Numerical Schemes ◽  
Stability Properties ◽  
Principal Axes ◽  
Rockfall Simulation ◽  
The Stability

AbstractThe stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.

scholarly journals On the numerical schemes for Langevin-type equations

2020 ◽  
Vol 99 (3) ◽  
pp. 62-74
Author(s):  
M. Akat ◽  
◽  
R. Kosker ◽  
A. Sirma ◽  
◽  
...  
Keyword(s):  
Numerical Scheme ◽  
Numerical Approach ◽  
Linear Case ◽  
Numerical Implementation ◽  
Numerical Schemes ◽  
Variation Of Constants Formula ◽  
Variation Of Constants ◽  
Non Linear ◽  
Numerical Discretization ◽  
The Stability

In this paper, a numerical approach is proposed based on the variation-of-constants formula for the numerical discretization Langevin-type equations. Linear and non-linear cases are treated separately. The proofs of convergence have been provided for the linear case, and the numerical implementation has been executed for the non-linear case. The order one convergence for the numerical scheme has been shown both theoretically and numerically. The stability of the numerical scheme has been shown numerically and depicted graphically.

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