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A Review of Domain Decomposition Methods for Simulation of Fluid Flows: Concepts, Algorithms, and Applications

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Abstract

Domain decomposition (DD) is a powerful approach to numerically solve partial differential equations, and it has become popular and indispensable in simulations of fluid flows, especially those that arise from models of the real world that require large-scale, parallel computation. Domain decomposition methods (DDMs) were originally introduced for problems on “complex” geometries, and they are now widely used as parallel algebraic solvers and preconditioners for solutions of various problems. Research in theory and practical application of DDMs for fluid flows has seen considerable progress with a substantial amount of work published in the past forty years. This paper makes a comprehensive review of the development and current status of the DDMs, and, for both beginners and experts in this area, it surveys the concepts, algorithms, and the utilization of DD to simulate compressible flows, incompressible flows, and flows in various applications. Along with numerical examples, difficulties are highlighted with potential methods to overcome them, and topics for future study are identified.

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Acknowledgements

This paper is support by NSF (DMS \(\#\)1543876 and \(\#\) 1622459) and the NSERC Discovery Grant Program (RGPIN-2018-04881).

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  1. Department of Civil Engineering, City College of New York, The City University of New York, 138th Street and Convent Avenue, New York, NY, 10031, USA

    H. S. Tang

  2. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NL, Canada

    R. D. Haynes

  3. Department of Computer Applications in Science and Engineering, Barcelona Supercomputing Center, 08034, Barcelona, Spain

    G. Houzeaux

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Tang, H.S., Haynes, R.D. & Houzeaux, G. A Review of Domain Decomposition Methods for Simulation of Fluid Flows: Concepts, Algorithms, and Applications. Arch Computat Methods Eng 28, 841–873 (2021). https://doi.org/10.1007/s11831-019-09394-0

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