A test case initially presented by Almgren et al [2]. The Euler equations are solved in a divergent channel for a unit inflow velocity on the left boundary and outflow on the right boundary.
Tables 7 and 8 illustrate the errors and convergence orders obtained for both components of the velocity when the resolution varies. Richardson extrapolation is used. The errors are computed either on the whole domain (All cells) or on the cells whose parents at level 5 are entirely contained in the fluid (Full 128 cells).
Close to second-order convergence is obtained in the bulk of the fluid, reducing to first-order close to the boundaries. The errors are small in all cases (with a maximum of .5%) and comparable to that obtained by Almgren et al using a different discretisation.
All cells Full 128 cells 128-256 Rate 256-512 128-256 Rate 256-512 L1 1.18e-04 1.21 5.08e-05 1.00e-04 1.54 3.46e-05 1.18e-04 1.21 5.08e-05 1.00e-04 1.54 3.46e-05 L2 2.89e-04 0.91 1.54e-04 2.57e-04 1.26 1.07e-04 2.89e-04 0.91 1.54e-04 2.57e-04 1.26 1.07e-04 L∞ 2.33e-03 0.53 1.62e-03 2.18e-03 0.68 1.36e-03 2.33e-03 0.53 1.62e-03 2.18e-03 0.68 1.36e-03
All cells Full 128 cells 128-256 Rate 256-512 128-256 Rate 256-512 L1 1.72e-04 1.81 4.91e-05 1.54e-04 2.18 3.42e-05 1.72e-04 1.81 4.91e-05 1.54e-04 2.18 3.42e-05 L2 5.27e-04 1.46 1.91e-04 5.01e-04 1.80 1.44e-04 5.27e-04 1.46 1.91e-04 5.01e-04 1.80 1.44e-04 L∞ 4.55e-03 0.91 2.43e-03 4.55e-03 1.00 2.28e-03 4.55e-03 0.91 2.43e-03 4.55e-03 1.00 2.28e-03