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Use Godunov's method to solve linear partial differential equations in 1D.
Godunov's idea:
- Discretize domain into non-overlapping cells.
- Compute average of the initial condition in each cell.
- Solve a Riemann problem on each boundary to find the fluxes.
- 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.