The Computation of Steady Solutions to the Euler Equations: A Perspective

1989 ◽  
pp. 21-38 ◽  
Author(s):  
Bram van Leer
Keyword(s):  
Euler Equations ◽  
Steady Solutions

Unsteady Solutions of Euler Equations Generated by Steady Solutions

2011 ◽  
Vol 113 (3) ◽  
pp. 289-303 ◽  
Author(s):  
L. Margheriti ◽  
M. P. Speciale
Keyword(s):  
Euler Equations ◽  
Steady Solutions

Variants of Arnold's Stability Results for 2D Euler Equations

2010 ◽  
Vol 53 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Fluid Flow ◽  
Euler Equations ◽  
Stability Estimates ◽  
Planar Domains ◽  
2D Euler Equations ◽  
Steady Solutions ◽  
Stability Results

AbstractWe establish variants of stability estimates in norms somewhat stronger than theH1-norm under Arnold's stability hypotheses on steady solutions to the Euler equations for fluid flow on planar domains.

scholarly journals A characterization of 3D steady Euler flows using commuting zero-flux homologies

2020 ◽  
pp. 1-16
Author(s):  
DANIEL PERALTA-SALAS ◽  
ANA RECHTMAN ◽  
FRANCISCO TORRES DE LIZAUR
Keyword(s):  
Euler Equations ◽  
Vector Fields ◽  
Higher Dimensions ◽  
Riemannian Metric ◽  
Euler Flows ◽  
Homological Characterization ◽  
Steady Solutions ◽  
Volume Preserving

We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a 3-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan’s homological characterization of geodesible flows in the volume-preserving case. As an application, we show that steady Euler flows cannot be constructed using plugs (as in Wilson’s or Kuperberg’s constructions). Analogous results in higher dimensions are also proved.

scholarly journals A Geometry-Preserving Finite Volume Method for Compressible Fluids on Schwarzschild Spacetime

2014 ◽  
Vol 15 (3) ◽  
pp. 827-852 ◽  
Author(s):  
Philippe G. Le Floch ◽  
Hasan Makhlof
Keyword(s):  
Finite Volume Method ◽  
Euler Equations ◽  
Finite Volume ◽  
Late Time ◽  
Spherically Symmetric ◽  
Schwarzschild Spacetime ◽  
Outer Domain ◽  
The Family ◽  
Steady Solutions ◽  
Volume Method

AbstractWe consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild space-time, and we introduce a version of the finite volume method which is formulated from the geometric formulation (and thus takes the geometry into account at the discretization level) and is well-balanced, in the sense that it preserves steady solutions to the Euler equations on the curved geometry under consideration. In order to formulate our method, we first derive a closed formula describing all steady and spherically symmetric solutions to the Euler equations posed on Schwarzschild spacetime. Second, we describe a geometry-preserving, finite volume method which is based from the family of steady solutions to the Euler system. Our scheme is second-order accurate and, as required, preserves the family of steady solutions at the discrete level. Numerical experiments are presented which demonstrate the efficiency and robustness of the proposed method even for solutions containing shock waves and nonlinear interacting wave patterns. As an application, we investigate the late-time asymptotics of perturbed steady solutions and demonstrate its convergence for late time toward another steady solution, taking the overall effect of the perturbation into account.

Toward perfectly absorbing boundary conditions for Euler equations

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 912-918
Author(s):  
M. E. Hayder ◽  
Fang Q. Hu ◽  
M. Y. Hussaini
Keyword(s):  
Boundary Conditions ◽  
Euler Equations ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary
Sign in / Sign up

Export Citation Format

Share Document