An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly while being unconditionally energy stable. A rigorous error analysis is carried out to show that both velocity and pressure approximations are second-order accurate in time and space. Numerical experiments are presented to verify the theoretical results.

中文翻译：

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Navier--Stokes方程SAV-MAC方案的误差分析

为 Navier-Stokes 方程构建了基于标量辅助变量 (SAV) 和标记和单元格方案 (MAC) 的有效数值方案。该方案的一个特殊特征是在无条件能量稳定的同时显式处理非线性项。进行了严格的误差分析以表明速度和压力近似值在时间和空间上都是二阶准确的。给出了数值实验来验证理论结果。