scholarly journals The Euler Equations in Planar Domains with Corners

2019 ◽  
Vol 234 (1) ◽  
pp. 57-79 ◽  
Author(s):  
Christophe Lacave ◽  
Andrej Zlatoš
Keyword(s):  
Euler Equations ◽  
Planar Domains ◽  
Domains With Corners

scholarly journals Euler Equations on General Planar Domains

Annals of PDE ◽  
2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Zonglin Han ◽  
Andrej Zlatoš
Keyword(s):  
Euler Equations ◽  
Planar Domains

scholarly journals Uniqueness for the 2-D Euler equations on domains with corners

2014 ◽  
Vol 63 (6) ◽  
pp. 1725-1756 ◽  
Author(s):  
Christophe Lacave ◽  
Evelyne Miot ◽  
Chao Wang
Keyword(s):  
Euler Equations ◽  
Domains With Corners

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 Lightning Solvers for Potential Flows

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 227
Author(s):  
Peter J. Baddoo
Keyword(s):  
Convergence Rates ◽  
Mathematical Basis ◽  
New Class ◽  
Planar Domains ◽  
Potential Flows ◽  
Rational Function Approximation ◽  
Novel Algorithms ◽  
High Degree ◽  
Domains With Corners ◽  
Steady Potential

We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms.

scholarly journals On a Helmholtz transmission problem in planar domains with corners

2018 ◽  
Vol 371 ◽  
pp. 315-332 ◽  
Author(s):  
Johan Helsing ◽  
Anders Karlsson
Keyword(s):  
Transmission Problem ◽  
Planar Domains ◽  
Domains With Corners
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