Stability Analysis of Shock Wave/Boundary Layer Interactions - Jean ...

Compressible Case: SWBLIDNS Comparison (1)SWBLI - Global Instability X. MERLE SINUMEF - ENSAM Paris 2008-07-15 19/19The equations solved are the three-dimensional unsteady compressibleNavier-Stokes (N-S) equations in conservation form:∂∂t Q i + ∂ (F (c)ji∂x j)− F (v)ji= 0,where0Q i = B@ρρEρuρvρw10hCA , F (c) i=ji B@ρu j(ρE + p) u jρuu j + δ 1j pρvu j + δ 2j pρwu j + δ 3j p10hCA , F (v) i=ji B@01uτ 1j + vτ 2j + wτ 3j − q jτ 1jCτA2jτ 3j(x, y, z) : the Cartesian coordinates, (u, v, w) are the velocity components, ρ is the density, and p is the pressure. E is thetotal energy given by:“E = e + u 2 + v 2 + w 2” /2, e = c vT, p = ρrTe is the internal energy, and T is the temperature. The shear stress and the heat flux are given by:τ ij = µ∂u i+ ∂u j− 2∂x j ∂x i 3 δ ∂u kij∂x k!, q j =−κ ∂T∂x j.The viscosity µ : Sutherlandï¿ 1 2 s law.