Stability and error analysis of a new class of higher-order consistent splitting schemes for the Navier-Stokes equations

作者：Fukeng Huang, Jie Shen · 发表于：Mathematics of Computation · 年份：2025 · DOI：10.1090/mcom/4132 · 被引用次数：4 · 研究领域：Advanced Numerical Methods in Computational Mathematics、Computational Fluid Dynamics and Aerodynamics、Numerical methods for differential equations

A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at t n + β t^{n+\beta } with β ≥ 1 \beta \ge 1 being a free parameter. It is shown that by choosing β = 3 , 6 , 9 \beta = 3, \,6,\,9 respectively for the second-, third- and fourth-order schemes, their numerical solutions are uniformed bounded in a strong norm, and admit optimal global-in-time convergence rates in both 2D and 3D. These results are the first stability and convergence results for any fully decoupled, higher than second-order schemes for the Navier-Stokes equations. Numerical results are provided to show that the third- and fourth-order schemes based on the usual backward differentiation formula (BDF) (i.e. β = 1 \beta =1 ) are not unconditionally stable while the new third- and fourth-order schemes with suitable β \beta are unconditionally stable and lead to expected convergence rates.