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A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations

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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.

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  1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, 65409-0020, USA

    Nan Jiang

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This author was partially supported by the US National Science Foundation Grant DMS-1720001 and a University of Missouri Research Board Grant.

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Jiang, N. A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations. J Sci Comput 80, 315–350 (2019). https://doi.org/10.1007/s10915-019-00939-w

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