Rotated Hybrid Low Diffusion ECUSP-HLL scheme and Its Applications to Hypersonic Flows

In this paper, a hybrid numerical flux scheme of low diffusion ECUSP (LDE) and HLL scheme is proposed by decomposing the cell-face normal vector. In the direction normal to shocks, the HLL scheme is applied to suppress carbuncles, in the other direction, the ECUSP scheme is implemented to keep low numerical diffusion. The new scheme with fifth-order WENO reconstruction is tested by using several benchmark cases, and then is applied to simulate a three dimensional double cone hypersonic flow of Mach number 12.43. The numerical simulation results agree very well with experiments. Nomenclature ∗ Research Scientist † Associate Professor ‡ Professor 1 20th AIAA Computational Fluid Dynamics Conference 27 30 June 2011, Honolulu, Hawaii AIAA 2011-3545 Copyright © 2011 by all the authors of this paper. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Ck = optimal weight C±,D± = coefficients for E-CUSP scheme CI l , C c l ,D I l = coefficients for defferencing formulas of viscous terms ISk = smoothness estimator J = Jacobian of transformation M = Mach number n = direction vector Pr = Prandtl number Prt = turbulent Prandtl number p = pressure/power used for WENO scheme qk = heat flux in Cartesian Coordinates/3rd-order polynomial interpolation Re = Reynolds number t = time u, v,w = velocity components in x, y and z direction x, y, z = Cartesian coordinates ∆U = difference of the conservative variables ∆q = velocity difference vector α, β = coefficients γ = ratio of specific heats ρ = density μ = molecular viscosity μt = turbulent viscosity ε = parameter introduced in WENO scheme ξ, η, ζ = generalized coordinates ωk = weight τ = stress tensor Subscripts i, j, k, l = indices I = index of interface ∞ = freestream Superscripts I = index of interface L,R = left and right sides of the interface n = time level