A comparison of high-order time integrators for highly supercritical thermal convection in rotating spherical shells

摘要: The efficiency of implicit and semi-implicit time integration codes based on backward differentiation extrapolation formulas for the solution three-dimensional Boussinesq thermal convection equations in rotating spherical shells was studied Garcia et al. (J Comput Phys 229:7997–8010, 2010) at weakly supercritical Rayleigh numbers R, moderate (10−3) low (10−4) Ekman numbers, E, Prandtl number σ = 1. results presented here extend previous study focus effect R by analyzing methods obtaining solutions \(E 1{0}^{-4}\), 0. 1 high R. In first case (quasiperiodic solutions) decrease one order magnitude does not change significantly. second (spatio-temporal chaotic differences behavior due to different treatment Coriolis term disappear because is dominated nonlinear terms. As 2010), methods, either with or without step control, increase integrators allow obtain more accurate solutions.