for the simulation of the internal flow field in high performance rolling bearing, the gas-liquid two-phase flow model is adopted. In order to meet calculation requirements of the high precision and high resolution, discontinuous Galerkin numerical method with high precision is used. The interface state is solved by Riemann solver, and the gas and liquid phases are solved by two single-phase solvers respectively. The DG method is for the gas phase (first – order partial differential equation) and the LDG method is for the fluid phase (second– order partial differential equation). The shape function based on the Taylor series expansion is used widely for the simulation of gas phase and Riemann solver and it works well. But the shape function based on the Taylor series expansion is employed to the LDG method and the algorithm has low convergence rate and this needs take too much cost to convergence. We present the updated algorithm. The results show that the algorithm has low error, stable convergence order and fast convergence rate. The method is easy to achieve the high accuracy and has very good application prospects.