“…We consider the vortex evolution problem[7] to test the accuracy. For this problem, the mean flow is ρ = p = u = v = 1 and is added by an isentropic vortex perturbation centered at (x 0 , y 0 ) in (u, v) withT = p/ρ, no perturbation in entropy S = p/ρ γ , (δu, δv) = ε vortex 2π e 0.5(1−r 2 ) (−ȳ,x), δT = − (γ − 1)ǫ 2 8γπ 2 e (1−r 2 ) , δS = 0,(4.2)where (x,ȳ) = (x − x 0 , y − y 0 ), r 2 =x 2 +ȳ 2 .The computational domain is taken to be [−5, 15] × [−5,15] and (x 0 , y 0 ) =(5,5). The boundary condition is periodic.…”