An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus

We analyze the behavior of an ensemble time integrators applied to semi-discrete problem resulting from spectral discretization equations describing Boussinesq thermal convection in a cylindrical annulus. The are cast their vorticity-streamfunction formulation that yields differential algebraic equation (DAE). comprises 28 members: 4 implicit-explicit multistep schemes, 22 Runge-Kutta (IMEX-RK) and 2 fully explicit schemes used for reference. whose theoretical order varies 5 assessed 11 different physical setups cover laminar turbulent regimes. Multistep IMEX-RK methods exhibit expected convergence under all circumstances. higher-order show occasional reduction impacts both field variables. ascribe stiffness at hand and, larger extent, presence DAE. Using popular Crank-Nicolson Adams-Bashforth (CNAB2) integrator as reference, performance is defined by ratio maximum admissible step cost performing one iteration; determined inspection series viscous dissipation within system, which guarantees physically acceptable solution. Relative bounded between 0.5 1.5 across studied configurations. Considering accuracy jointly with performance, we find 6 consistently outperform CNAB2, meaning addition allowing more efficient calculation, they achieve operational, dissipation-based limit stability lower error. In our most setup, where almost entirely dictated component, 13 CNAB2 terms efficiency.