Stabilized seventh-order dissipative compact scheme for two-dimensional Euler equations

Qin Jia-Xian, Chen Ya-Ming^†, Deng Xiao-Gang

Density contours of the vortex obtained by the scheme of Eqs. (6)–(14) with penalty coefficients τ 1 = τ 2 = τ 3 = τ 4 = 5 . Here N × M = 41 × 81 , the time step Δ t = 0.1 h x 1 h y 1 is chosen to implement the fourth-order Runge–Kutta scheme. (a) At the moment t=4.2. (b) At the moment t=6.3.