README.md

🚀 Boundary Layer Inflation Calculator

A C++ numerical tool designed to calculate the precise geometric growth ratio required for CFD boundary layer meshing. This tool ensures the total inflation layer thickness matches the target aerodynamic boundary layer height ($\delta$) while maintaining a specific first-cell height ($y_H$) for $y^+$ requirements.

🧮 Theoretical Background

In Computational Fluid Dynamics (CFD), capturing the boundary layer requires a series of prism layers growing geometrically from the wall.

• $y_H$: First cell height (determined by desired $y^+$ value, e.g., $y^+ \approx 1$ for SST $k-\omega$).
• $N$: Number of prism layers.
• $\delta$ ($b_{lh}$): Total height of the boundary layer mesh.
• $G$: The geometric growth ratio (unknown).

The relationship is defined by the sum of a geometric series:

$$\delta = y_H \frac{1 - G^N}{1 - G}$$

Since this equation cannot be solved algebraically for $G$, this tool implements the Bisection Method (a numerical root-finding algorithm) to solve for $G$ with high precision.

📥 Inputs

1. Number of Layers ($N$): Integer count of inflation layers.
2. First Cell Height ($y_H$): Height of the wall-adjacent cell (meters).
3. Total Boundary Layer Height ($b_{lh}$): The target total thickness of the inflation stack (meters).

📤 Output

• Growth Ratio ($G$): The constant expansion ratio between consecutive layers.
• Convergence Info: Number of iterations required to reach the solution.

🛠️ Build & Run

Prerequisites

• G++ Compiler (or any standard C++ compiler)

Usage

# Compile the program
g++ main.cpp -o InflationLayers

# Run the executable
./InflationLayers

✍️ Author

Kıvanç Apaydın – Aerospace Engineer