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

2025/07/02 by Huang, Fukeng, Shen, Jie · 3 citations
#65M12 #65M15 #76D05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2507.01296

Abstract

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 with β≥ 1 being a free parameter. It is shown that by choosing \colorblack β= 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. \colorblackThese 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 BDF (i.e. β=1) are not unconditionally stable while the new third- and fourth-order schemes with suitable β are unconditionally stable and lead to expected convergence rates.

Cited by

• Viscosity in error upper bound for a consistent splitting scheme of the Navier-Stokes equations
• A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations
• A Discontinuous Galerkin Consistent Splitting Method for the Incompressible Navier-Stokes Equations

Related

• A spectral-vanishing-viscosity stabilization of a higher-order consistent splitting scheme for the Navier-Stokes equations
• Error estimate of a consistent splitting GSAV scheme for the Navier-Stokes equations
• A Stable and High-Order Accurate Discontinuous Galerkin Based Splitting Method for the Incompressible Navier-Stokes Equations
• A Discontinuous Galerkin Consistent Splitting Method for the Incompressible Navier-Stokes Equations
• Stability and error analysis of a class of high-order IMEX schemes for Navier-stokes equations with periodic boundary conditions