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, Newton Raphson approximation is used to refine values of h0 then using ODE45 or Rk4 method to find solution.
Reference : https://nptel.ac.in/content/storage2/courses/112104118/lecture-28/28-7_blasius_flow_contd.htm
引用格式
Raghu Karthik Sadasivuni (2024). Solving Blasius Equation using Newton Raphson method (https://www.mathworks.com/matlabcentral/fileexchange/102199-solving-blasius-equation-using-newton-raphson-method), MATLAB Central File Exchange. 检索来源 .
MATLAB 版本兼容性
创建方式
R2021b
兼容任何版本
平台兼容性
Windows macOS Linux标签
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!版本 | 已发布 | 发行说明 | |
---|---|---|---|
1.0.0 |