Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics pp 1-1 | Cite as

# A numerical method for highly accelerated laminar boundary-layer flows

## Abstract

A second-order-accurate implicit finite difference method is developed to study the boundary-layer flows that occur just upstream of a trailing edge which is attached to a free streamline. An important feature of this technique is the use of an asymptotic expansion to satisfy the boundary condition at the edge of the boundary layer while retaining a rapid algorithm for inverting the system of linear equations for each Newton iteration. The method is applied to the Kirchhoff-Rayleigh flow past a finite flat plate set perpendicular to a uniform stream. Computed velocity profiles are found to be in excellent agreement with those obtained from an asymptotic solution (Ackerberg (1970), (1971a), (1971b)) with pointwise differences being less than 1.2% over two-thirds of the profile. A detailed description of the method is given in Ackerberg and Phillips (1973).

## References

- 1.Ackerberg, R. C. “Boundary-Layer Separation at a Free Streamline. Part 1. Two-dimensional Flow”. J. Fluid Mech. 44, p. 211, (1970).zbMATHCrossRefADSGoogle Scholar
- 2.Ackerberg, R. C. “Boundary-Layer Separation at a Free Streamline. Part 2. Numerical Results”. J. Fluid Mech. 46, p. 727, (1971a).zbMATHCrossRefADSGoogle Scholar
- 3.Ackerberg, R. C. “Boundary-Layer Separation at a Free Streamline — Finite Difference Calculations”. Proceedings of the Second International Conference on Numerical Methods in Fluid Dynamics edited by M. Holt. Published as Lecture Notes in Physics No. 8, Springer-Verlag, p. 170, (1971b).Google Scholar
- 4.Ackerberg, R.C. and Phillips, J.H. “A Numerical Method for Highly Accelerated Laminar Boundary-Layer Flows”. SIAM Journal on Numerical Analysis 10, part 1, (1973).Google Scholar