On acceleration of Krylov-subspace Newton and Arnoldi iterations for incompressible CFD

Abstract eng:
Looking for an improvement of convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via a time-stepping, we propose two independent additions. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. Second, we propose to generate an initial guess of steady flow or eigenvalue and eigenvector using orthogonal projection on divergence free basis satisfying all boundary conditions. Both additions are illustrated on the solution of the linear stability problem for laterally heated square and cubic cav1t1es.

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