Compressible flow has complex structures of wide-range scales such as vortices, turbulence, shock waves and contact discontinuities. In order to accurately capture the small fluid structures and discontinuous solutions, low-dissipation schemes have been developed so far. Meanwhile, the improvement of computational power enables simulations with high grid resolution. As a result, numerical simulations with extremely low dissipation can be obtained. However, in such high-resolution numerical simulations, errors of floating-point arithmetic may be amplified and result in asymmetric solutions even the physical configurations are symmetric. In this study, we have thoroughly examined the causes of symmetry-breaking and proposed numerical techniques to completely eliminate the numerical errors for asymmetric solutions.