This manuscript is devoted to investigating the conservation laws of incompressible Navier-Stokes equations(NSEs), written in the energy-momentum-angular momentum conserving(EMAC) formulation, after being linearized by the two-level methods. With appropriate correction steps(e.g., Stoke/Newton corrections), we show that the two-level methods, discretized from EMAC NSEs, could preserve momentum, angular momentum, and asymptotically preserve energy. Error estimates and (asymptotic) conservative properties are analyzed and obtained, and numerical experiments are conducted to validate the theoretical results, mainly confirming that the two-level linearized methods indeed possess the property of (almost) retainability on conservation laws. Moreover, experimental error estimates and optimal convergence rates of two newly defined types of pressure approximation in EMAC NSEs are also obtained.

翻译：本文致力于研究不可压缩Navier-Stokes方程（NSEs）在能量-动量-角动量守恒（EMAC）形式下，经两水平方法线性化后的守恒定律。通过适当的校正步骤（如Stokes/Newton校正），我们证明由EMAC形式NSEs离散化得到的两水平方法能够保持动量、角动量，并渐近保持能量。文中分析并获得了误差估计与（渐近）守恒性质，同时通过数值实验验证理论结果，主要证实两水平线性化方法确实具有（几乎）保持守恒定律的特性。此外，还获得了EMAC形式NSEs中两类新定义压力逼近的数值误差估计与最优收敛阶。