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

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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