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8.7.3 Computational Efficiency: Broyden's Method
Fluid analyses produce a non-symmetric stiffness matrix and the resulting system of equations may be efficiently solved using Broyden's quasi-Newton method, where an approximation to the matrix inverse is produced at each iteration after the first full-Newton iteration of a time step. In fluid analyses, it is often possible to achieve convergence at each time step without having to perform additional full-Newton updates. Therefore, it is recommended to set max_updates (Section 3.3↑) to a large number (e.g., 50), along with setting diverge_reform to 0 (false), which leads to a more efficient solution scheme. A further advantage arises in fluid analyses since the mesh remains invariant over time: it is often possible to continue using Broyden updates even across time steps, without performing a full-Newton iteration at the start of that step, by setting reform_each_time_step to 0 (false). In that case, the solver will continue using Broyden updates up to the value of max_updates, before performing a full Newton update.