The Blasius Function: Computations before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems

• Published in: SIAM review Vol. 50; no. 4; pp. 791 - 804
• Main Author: Boyd, John P.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.12.2008
• Subjects: Approximation; Boundary layer; Boundary layers; Cauchy problem; Collapse; Computation; Differential equations; Education; Exact sciences and technology; Fluid mechanics; Lists; Mathematical analysis; Mathematical functions; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Power series; Power series coefficients; Radii of convergence; Sciences and techniques of general use; Series convergence; Studies; Theorems; Collapse; Similarity; 76D10; Differential equation; Viscous fluid; Initial value problem; boundary layer; Mathematics; Research; Runge Kutta method; Partial differential equation; Flow; 76-01; Non linear equation; Scientific computation; Numerical solution; Blasius; 65-01; Computer; fluid mechanics; Symmetry

The Blasius flow is the idealized flow of a viscous fluid past an infinitesimally thick, semi-infinite flat plate. The Blasius function is the solution to $2f_{xxx}+ff_{xx}=0$ on x ∈ [0, ∞] subject to $f(0)=f_{x}(0)=0$, $f_{x}(\infty)=1$. We use this famous problem to illustrate several themes. Firs...