Acceleration of nonlinear solvers for natural convection problems

Abstract This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. After analyzing fixed point operator associated with nonlinear iteration prove that certain stability regularity properties hold, we apply authors’ recently constructed theory acceleration, which yields convergence result accelerated system. The shows leading term in residual is improved by gain optimization problem, but at cost additional higher order terms can be significant when large. We perform numerical tests illustrate theory, show 2-stage choice depth advantageous. also consider Newton equations, observe allows converge significantly Rayleigh numbers it could without even standard line search.