Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation

@article{Belden2019AsymptoticAF,
  title={Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation},
  author={Elizabeth R. Belden and Zachary A. Dickman and Steven J. Weinstein and Alex D. Archibee and Ethan Burroughs and Nathaniel S. Barlow},
  journal={The Quarterly Journal of Mechanics and Applied Mathematics},
  year={2019}
}
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[-0.198837735, 1]$ are considered, and the previously established non-unique solutions for $\beta<0$ having positive and… 
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References

SHOWING 1-10 OF 37 REFERENCES

An asymptotically consistent approximant method with application to soft- and hard-sphere fluids.

A modified Padé approximant is used to construct an equation of state, which has the same large-density asymptotic behavior as the model fluid being described, while still retaining the low-density…

Flow analysis for the Falkner-Skan wedge flow

In this article an analytical technique, namely the homotopy analysis method (HAM), is applied to solve the momentum and energy equations in the case of a two-dimensional incompressible flow passing…

Blasius problem and Falkner–Skan model: Töpfer’s algorithm and its extension

Shooting and parallel shooting methods for solving the Falkner-Skan boundary-layer equation

Critical isotherms from virial series using asymptotically consistent approximants

The low-density equation of state of a fluid along its critical isotherm is considered. An asymptotically consistent approximant is formed having the correct leading-order scaling behavior near the…

A note on the solution of general Falkner-Skan problem by two novel semi-analytical techniques

Further solutions of the Falkner-Skan equation

  • K. Stewartson
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1954
ABSTRACT In an attempt to understand the mechanism governing separation the possibility of there being further solutions to the Falkner-Skan equation f′′′ + ff″ + β(1 − f′2) = 0, in addition to those…

Exact Analytic Solution of a Boundary Value Problem for the Falkner–Skan Equation

The Falkner–Skan equation, subject to appropriate physical boundary conditions arising from boundary layer theory, is exactly solved. The results obtained from this solution are compared with the…

The Blasius Function in the Complex Plane

This work calculates several numerical constants, such as the second derivative of f at the origin and the two parameters of the linear asymptotic approximation to f, to at least eleven digits and derives an expansion in rational Chebyshev functions TL j which converges exponentially fast with the truncation.

On the summation of divergent, truncated, and underspecified power series via asymptotic approximants

A compact and accurate solution method is provided for problems whose infinite power series solution diverges and/or whose series coefficients are only known up to a finite order. The method only…