Optimum Approximate-Factorisation schemes for 2D steady potential flows

1981 ◽  
Author(s):  
D. CATHERALL
Keyword(s):  
Potential Flows ◽  
Steady Potential

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.

Finite difference computation for transonic steady potential flows

1981 ◽  
Vol 27 (2) ◽  
pp. 129-138 ◽  
Author(s):  
S.J. Luo ◽  
Y.W. Zheng ◽  
H. Qian ◽  
D.Q. Wang
Keyword(s):  
Finite Difference ◽  
Potential Flows ◽  
Steady Potential

scholarly journals Bound Coherent Structures Propagating on the Free Surface of Deep Water

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 115
Author(s):  
Dmitry Kachulin ◽  
Sergey Dremov ◽  
Alexander Dyachenko
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Nonlinear Models ◽  
Ideal Incompressible Fluid ◽  
Equation Model ◽  
System Of Nonlinear Equations ◽  
Potential Flows ◽  
Deep Water Waves

This article presents a study of bound periodically oscillating coherent structures arising on the free surface of deep water. Such structures resemble the well known bi-soliton solution of the nonlinear Schrödinger equation. The research was carried out in the super-compact Dyachenko-Zakharov equation model for unidirectional deep water waves and the full system of nonlinear equations for potential flows of an ideal incompressible fluid written in conformal variables. The special numerical algorithm that includes a damping procedure of radiation and velocity adjusting was used for obtaining such bound structures. The results showed that in both nonlinear models for deep water waves after the damping is turned off, a periodically oscillating bound structure remains on the fluid surface and propagates stably over hundreds of thousands of characteristic wave periods without losing energy.

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