Finite-volume methods in Rust 🌪️

lib.rs:

Use Godunov's method to solve linear partial differential equations in 1D.

Godunov's idea:

1. Discretize domain into non-overlapping cells.
2. Compute average of the initial condition in each cell.
3. Solve a Riemann problem on each boundary to find the fluxes.
4. Advance each cell average.

This implementation uses simple convective upwinding.

Properties

Godunov's method is 1st-order in space and time. Twice as many cells cuts the error in half.

When would I use this?

This scheme was cutting edge in 1959. These days, it's used as a basis for more advanced methods.

That said, it's a classic result from one of the founding fathers of computational fluid dynamics.