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Table 1

Percentage of kinetic energy compared to the initial value after one revolution (t = 1.0) of the Gresho vortex for the Roe scheme with and without preconditioning.

Initial max. Mach number 10-1 10-2 10-3

Not preconditioned 94.47 74.52 49.24
Preconditioned 98.70 98.72 98.72
Preconditioned (explicit) 97.70 97.74 98.31

Notes. The tests were performed using implicit ESDIRK34 time discretization, except for those labeled “(explicit)”, which were made using the time-explicit RK3 scheme.

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