A new fractional-step scheme for the numerical solution to the incompressible Navier–Stokes equations with variable density is proposed. Compared with other known methods, the numerical velocity and pressure are determined by a generalized Stokes problem per time step. The stability and convergence rate \(\mathcal O(\tau )\) of the scheme are proved and the performance of the scheme is numerically illustrated.

中文翻译：

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变密度不可压缩Navier-Stokes方程分数阶新方法的误差分析

提出了一种新的分数步法，求解变密度不可压缩的Navier-Stokes方程。与其他已知方法相比，数值速度和压力由每个时间步长的广义斯托克斯问题确定。证明了该方案的稳定性和收敛速度\（\数学O（\ tau）\），并用数值方法说明了该方案的性能。