Advection of a passive scalar in the setup described in Sect. 9.2. The left panels were computed using the unmodified Roe scheme. In the right panels, the flux preconditioning method from Eq. (35)was used with the matrix from Eq. (37). Top panels: low-resolution simulations (1282), bottom panels: same setup at higher resolution (10242). All panels show the state at a nondimensional time of 3.0. Initially, the central (rightward-flowing) region had a value of X = 1 and the upper and lower (leftward-flowing) regions had a value of X = 0.
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