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

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.

Publication Date

15 Jul 2019

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