Project 1

Aim:-

1. Derive the FVM formulation for the 2D heat conduction equation.
2. Build a data structure in Python to read and store the unstructured mesh from a text file.
3. Estimate gradients and fluxes.
4. Solve the heat diffusion problem using the FVM.

1. Derive the FVM formulation for the 2D Heat conduction equation:

The heat conduction equation in 2D can be derived as:-

For steady-state problems, it simplifies to:

In the FVM, we integrate this equation over a control volume V:

Using Gauss's divergence theorem:

where S is the surface of the control volume and n is the outward-pointing unit normal vector on S.

Coding:-

Result:-