Lower-upper symmetric Gauss-Seidel scheme exhibiting asymmetric vortices over slender bodies

A perfect numerical simulation of asymmetric vortical flow around slender bodies at high angle of attack, which was observed experimentally, is extremely difficult to obtain accurately. Previous results has assumed that the steady-state solution that depends only on the right-hand side of the algorithm, which has been generally accepted, does not hold for the high angle-of-attack flows. In this paper, a recently developed lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm, has been applied without introducing any perturbation intentionally. The scheme does not symmetrically factorize the flux Jacobian of the left-hand side. Asymmetric vortical flows have been obtained numerically simply through direct application of LU-SGS scheme. The origin of the numerical asymmetry has also been investigated.