A second-order Ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations

TL;DR

This paper introduces a second-order ensemble method for Navier-Stokes equations using a blended three-step BDF scheme, offering improved accuracy with minimal additional computational cost.

Contribution

The paper develops a novel second-order ensemble method based on a blended three-step BDF scheme, enhancing accuracy over existing methods with similar computational effort.

Findings

The new method is more accurate than existing second-order ensemble methods.

Stability and error analyses confirm the method's reliability.

Numerical examples demonstrate improved accuracy and theoretical validation.

Abstract

We present a second-order ensemble method based on a blended three-step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier-Stokes equations. Compared with the only existing second-order ensemble method that combines the two-step BDF timestepping scheme and a special explicit second-order Adams-Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method.