Evaluation of Different Krylov Subspace Methods for Simulation of the Water Faucet Problem
Nuclear Science and Techniques
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In this study, a one-dimensional two-phase flow four-equation model was developed to simulate the water faucet problem. The performance of six different Krylov subspace methods, namely the generalized minimal residual (GMRES), transpose-free quasi-minimal residual, quasi-minimal residual, conjugate gradient squared, biconjugate gradient stabilized, and biconjugate gradient, was evaluated with and without the application of an incomplete LU (ILU) factorization preconditioner for solving the water faucet problem. The simulation results indicate that using the ILU preconditioner with the Krylov subspace methods produces better convergence performance than that without the ILU preconditioner. Only the GMRES demonstrated an acceptable convergence performance under the Krylov subspace methods without the preconditioner. The velocity and pressure distribution in the water faucet problem could be determined using the Krylov subspace methods with an ILU preconditioner, while GMRES could determine it without the need for a preconditioner. However, there are significant advantages of using an ILU preconditioner with the GMRES in terms of efficiency. The different Krylov subspace methods showed similar performance in terms of computational efficiency under the application of the ILU preconditioner.
Water faucet problem; Krylov subspace methods; ILU preconditioner
Nuclear | Physical Sciences and Mathematics | Physics
Evaluation of Different Krylov Subspace Methods for Simulation of the Water Faucet Problem.
Nuclear Science and Techniques, 32(5),