A Second-Order Ensemble Method Based on a Blended Backward Differentiation Formula Timestepping Scheme for Time-Dependent Navier-Stokes Equations

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Numerical methods; Viscous flow; Adams-Bashforth; Backward differentiation formulae; Computational costs; Ensemble methods; Second orders; Time-dependent Navier-Stokes equations; Time-stepping schemes; Uncertainty quantifications; Navier Stokes equations; Blended backward differentiation formula; Ensemble calculation; Navier–Stokes equations

International Standard Serial Number (ISSN)

0749-159X; 1098-2426

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 John Wiley & Sons, All rights reserved.

Publication Date

01 Jan 2017

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