Penalty decoupled iterative methods for the stationary natural convection equations with different Rayleigh numbers

摘要: Abstract In this paper, we propose and analyze six combined schemes in the framework of penalty method to solve natural convection (NC) equations numerically. The key role technique is manage incompressibility constraint div u = 0 effectively improve positivity resulting system. For definiteness without loss generality, mainly explore a inf-sup stable finite element pair P 1 b - unstable one . Three efficient iterative are applied deal with nonlinear terms. Moreover, results discrete stability optimal convergence under exactly different conditions proved for given methods. Numerical simulations three benchmark problems explored illustrate theoretical findings.