A numerical stability analysis for the two-dimensional incompressible Euler equations

1988 ◽  
Vol 79 (1) ◽  
pp. 70-84 ◽  
Author(s):  
M.G.G Foreman ◽  
A.F Bennett
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Numerical Stability ◽  
Two Dimensional ◽  
Incompressible Euler Equations ◽  
Numerical Stability Analysis ◽  
Incompressible Euler

scholarly journals On the approximation of vorticity fronts by the Burgers–Hilbert equation

2021 ◽  
pp. 1-37
Author(s):  
John K. Hunter ◽  
Ryan C. Moreno-Vasquez ◽  
Jingyang Shu ◽  
Qingtian Zhang
Keyword(s):  
Euler Equations ◽  
Asymptotic Expansions ◽  
Energy Method ◽  
Two Dimensional ◽  
Asymptotic Equation ◽  
Contour Dynamics ◽  
Incompressible Euler Equations ◽  
Incompressible Euler

This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burgers–Hilbert equation derived by Biello and Hunter (2010) using formal asymptotic expansions. The proof uses a modified energy method to show that the contour dynamics equations for vorticity fronts in the Euler equations and the Burgers–Hilbert equation are both approximated by the same cubically nonlinear asymptotic equation. The contour dynamics equations for Euler vorticity fronts are also derived.

scholarly journals Numerical Solution of Two-Dimensional Linear Fuzzy Fredholm Integral Equations by the Fuzzy Lagrange Interpolation

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
H. Nouriani ◽  
R. Ezzati
Keyword(s):  
Integral Equation ◽  
Stability Analysis ◽  
Iterative Method ◽  
Fredholm Integral Equation ◽  
Numerical Stability ◽  
Lagrange Interpolation ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
New Approach ◽  
Numerical Stability Analysis

In this study, at first, we propose a new approach based on the two-dimensional fuzzy Lagrange interpolation and iterative method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equation (2DLFFIE). Then, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm by two theorems. Finally, by some examples, we show the efficiency of the proposed method.

scholarly journals A Characteristic Mapping method for the two-dimensional incompressible Euler equations

2021 ◽  
Vol 424 ◽  
pp. 109781
Author(s):  
Xi-Yuan Yin ◽  
Olivier Mercier ◽  
Badal Yadav ◽  
Kai Schneider ◽  
Jean-Christophe Nave
Keyword(s):  
Euler Equations ◽  
Mapping Method ◽  
Two Dimensional ◽  
Incompressible Euler Equations ◽  
Characteristic Mapping ◽  
Incompressible Euler

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

2009 ◽  
Vol 49 (4) ◽  
pp. 729-742 ◽  
Author(s):  
O. M. Belotserkovskii ◽  
V. V. Denisenko ◽  
A. V. Konyukhov ◽  
A. M. Oparin ◽  
O. V. Troshkin ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Couette Flow ◽  
Numerical Stability ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Taylor Couette ◽  
Taylor Couette Flow

Variety of unsymmetric multibranched logarithmic vortex spirals

2017 ◽  
Vol 30 (1) ◽  
pp. 23-38 ◽  
Author(s):  
V. ELLING ◽  
M. V. GNANN
Keyword(s):  
Euler Equations ◽  
Two Dimensional ◽  
Incompressible Euler Equations ◽  
Incompressible Euler

Building on work of Prandtl and Alexander, we study logarithmic vortex spiral solutions of the two-dimensional incompressible Euler equations. We consider multi-branched spirals that are not symmetric, including mixtures of sheets and continuum vorticity. We find that non-trivial solutions allow only sheets, that there is a large variety of such solutions, but that only the Alexander spirals with three or more symmetric branches appear to yield convergent Biot–Savart integral.

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