A comparison of segregated and coupled methods for the solution of the incompressible Navier-Stokes equations

Abstract

SUMMARYThree different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;-and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.

A Fully Coupled Numerical Solution of Water, Vapor, Heat, and Water Stable Isotope Transport in Soil

“…In our simulations (Sections 2.2.1), to ensure consistency, the time step for the isotope equation in the semi-coupled method was kept the same as that for the water and heat equations, but the time consumption of semi-coupled method was doubled compared to the fully coupled method, as shown in Figure 6. This contrasts with the theoretical expectation that the semi-coupled method should generally be faster due to its lower memory and computational requirements per iteration (Gee & Gracie, 2021;Pimenta & Alves, 2019). Several factors can contribute to this discrepancy.…”

“…Therefore, it is crucial for a semi-coupled method to rigorously manage mass balance errors (Zha et al, 2019). By contrast, when equations are solved using the fully coupled method, fewer mass balance errors are transferred between equations (Ammara & Masson, 2004;Panday & Huyakorn, 2004;Pascau et al, 1996), a fact that has been verified through temporal and spatial discretization tests (Figures 5 and 7). Consequently, MOIST outperformed rHZ under a coarse spatial discretization in the semianalytical test (Table 3).…”

“…First, the choice between using the semi-coupled method and the fully coupled method depends on the degree of coupling exhibited by the variables involved (Pimenta & Alves, 2019). In our study, all variables are tightly coupled due to intricate interactions between water and heat transport, which concurrently influence the movement of isotopes.…”

“…When Δz was 0.0005 m, the time consumption of both methods was similar (Figure 11b). Consequently, it is expected that for even finer discretization, such as Δz = 0.00005 m, the fully coupled method may spend more time than the semi-coupled method (Gee & Gracie, 2021;Pimenta & Alves, 2019). However, such a fine spatial discretization is uncommon in practice, and the resulting matrix size is extremely large (60,000 × 60,000 for the fully coupled method, 40,000 × 40,000 and 20,000 × 20,000 for the semi-coupled method), potentially causing an "out of memory" error.…”

MOIST: a MATLAB-based fully coupled one-dimensional isotope and soil water transport model

“…However, the coupled method links all variables and equations implicitly. Compared to segregated methods, isotope results from coupled methods are more stable and accurate (Pimenta and Alves, 2019;Pascau et al, 1996). A simplified example as described below mathematically illustrates the difference between the segregated and coupled methods.…”