The velocity field is initialised with an exact stationary solution of the Euler equations in a periodic 2D domain. An exact Euler solver would not change this field, however any numerical solver will introduce numerical dissipation which will slowly dissipate the kinetic energy of the initial solution. By monitoring the evolution of the kinetic energy, the dissipative properties of the numerical scheme can be measured (see [20] for details).
Figures 35 and figure 36 illustrate the evolution of the divergence of the velocity field with time. This is a check of the stability of the approximate projection and should remain bounded.
Figures 37 and 38 illustrates the evolution of the kinetic energy and the corresponding equivalent Reynolds number as a function of resolution. The higher the Reynolds number, the less dissipative the scheme.
Same as the previous test but with a refined box in the middle and four modes of the exact Euler solution.
