This repository contains the Python implementation for Computational Fluid Dynamics , which solves the One-dimensional unsteady heat conduction equation in a homogeneous wall.
Implement and compare Three finite difference methods:
- ✅ Explicit FTCS
- ✅ Implicit Laasonen
- ✅ Crank-Nicolson
All methods are benchmarked against the analytical solution for six test cases to analyze accuracy, stability, and efficiency.
- Three Numerical Methods: Explicit FTCS, Implicit Laasonen, Crank-Nicolson.
- Analytical Benchmark: Compares numerical results to an analytical series solution.
- Multiple Test Cases: Six configurations with varying mesh sizes and Courant numbers.
- Automated Plots: Generates solution plots for visual comparison.
- Simple, Modular Python Code: Easy to extend or adapt.
∂T/∂t = α ∂²T/∂x²
- T(x, t): Temperature distribution
- α = 0.02 m²/hr: Thermal diffusivity
Initial & Boundary Conditions:
- Initial: Triangular profile — T = 0 K at x = 0 and x = 1 m; T = 100 K at x = 0.5 m
- Boundaries: T(0, t) = T(1, t) = 0 K
- Forward time, centered space.
- Solves a tridiagonal system.
- Averages time levels.
