A Second-Order Ensemble Method Based on a Blended Backward Differentiation Formula Timestepping Scheme for Time-Dependent Navier-Stokes Equations
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.
N. Jiang, "A Second-Order Ensemble Method Based on a Blended Backward Differentiation Formula Timestepping Scheme for Time-Dependent Navier-Stokes Equations," Numerical Methods for Partial Differential Equations, vol. 33, no. 1, pp. 34 - 61, John Wiley & Sons, Jan 2017.
The definitive version is available at https://doi.org/10.1002/num.22070
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; NavierÃ¢â‚¬â€œStokes equations
International Standard Serial Number (ISSN)
Article - Journal
© 2017 John Wiley & Sons, All rights reserved.
01 Jan 2017