Solving Blasius Equation Using RK-4 Numerical method

Solution to Blasius Equation for flat plate , a third order non-linear ordinary differential equation by Rk-4 method

Blasius equation for flat plate is a Third Order Non-Linear Ordinary Differential Equation governing boundary layer flow : f'''(η)+(1/2) f(η) f''(η) = 0 where η is similarity variable. This equation can be solved numerically by converting to three simulatneous Ordinary Linear Differential Equations : { f(η) = f(η) ; g(η) = f'(η) ; h(η) = f''(η) } then f'(η) = g(η) ; g'(η) = h(η) ; h'(η) = -(1/2) f(η) h(η) with f(0) = 0 , g(0) = f'(0) = 0 , and h(0) = ? (to be found) such that g(∞)=1.

We handle this problem as Initial Value Problem approached by numerical methods by Choosing h(0) such that it shoots to g(∞)=1. Initial guesses may give an error: 1- g(∞) ≠ 0 . with subsequent iterations of numerical methods resolves the error. This method is called shooting technique.

Here, Runge Kutta 4rth order (RK4) approximation is used.

Reference : https://nptel.ac.in/content/storage2/courses/112104118/lecture-28/28-7_blasius_flow_contd.htm