Title

A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations

Abstract

We study a pressure-correction ensemble scheme for fast calculation of thermal flow ensembles. The proposed scheme (1) decouples the Boussinesq system into two smaller subphysics problems; (2) decouples the nonlinearity from the incompressibility condition in the Navier-Stokes equations and linearizes the momentum equation so that it reduces to a system of scalar equations; (3) results in linear systems with the same coefficient matrix for all realizations. This reduces the size of linear systems to be solved at each time step and allows efficient direct/iterative linear solvers for fast computation. We prove the scheme is long time stable and first order in time convergent under a time step condition. Numerical tests are provided to confirm the theoretical results and demonstrate the efficiency of the scheme.

Department(s)

Mathematics and Statistics

Comments

Article in Press

Keywords and Phrases

Control nonlinearities; Linear systems; Boussinesq equations; Boussinesq system; Coefficient matrix; Ensemble methods; Fast calculations; Pressure correction; Pressure-correction methods; Uncertainty quantifications; Navier Stokes equations

International Standard Serial Number (ISSN)

0885-7474; 1573-7691

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Springer Verlag, All rights reserved.

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