Numerical simulation of underexpanded plumes using upwind algorithms

A high-resolution TVD (total variation dimishing) upwind scheme is applied to solve highly underexpanded plumes. The code features finite-volume type of metrics, Roe averaging with entropy correction and the MUSCL (monotonic upstream schemes for conservation laws) approach. The strategy for implicit methods in this paper is to use the existing approximate factorization schemes as a preconditioner and to apply the conjugate residual algorithm. The LU-AD1 (lower-upper factored alternating direction implicit) and LU-SGS (lower-upper factored symmetric Gauss-Seidel) methods are examined as a preconditioner as well as a straight implicit time marching method. In the present work, plumes are assumed to be axisymmetric and laminar. Although an ideal gas is assumed, the gas is allowed to be thermally incomplete. Using the foregoing approximations, simulations have been successfully carried out for the Space Shuttle main engine and the solid rocket booster plumes with near flight conditions.