Figure 2

Figure 2: Godunov’s scheme: local solutions of Riemann problems. At every interface, xj− 1 2, xj+ 1 2 and xj+3 2, a local Riemann problem is set up as a result of the discretization process (bottom panel), when approximating the numerical solution by piecewise constant data. At time n t these discontinuities decay into three elementary waves, which propagate the solution forward to the next time level tn+1 (top panel). The timestep of the numerical scheme must satisfy the Courant–Friedrichs–Lewy condition, being small enough to prevent the waves from advancing more than Δx ∕2 in Δt.