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International Journal for Uncertainty Quantification

Impact factor: 0.967

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2014007691
pages 273-301

AN ALGORITHM FOR FAST CALCULATION OF FLOW ENSEMBLES

Nan Jiang
Departament of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
William Layton
Departament of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

ABSTRACT

This report presents an algorithm for computing an ensemble of p solutions of the Navier-Stokes equations. The solutions are found, at each timestep, by solving a linear system with one shared coefficient matrix and p right hand sides, reducing both storage required and computational cost of the solution process. The price that must be paid is a timestep condition involving the timestep and the size of the fluctuations about the ensemble mean. Since the method is a one step method and the timestep condition involves only known quantities, it can be imposed to adapt the next timestep. The report gives a comprehensive stability analysis, an error estimate, and some first tests.