Simulation of penetrative convection with adaptive spectral domain decomposition method Original Research Article

The penetrative convection problem with infinite domain is simulated by spectral collocation method. The single-domain formulation uses algebraic mapping while the multi-domain uses the C1 interface condition with adaptive domain boundaries. The test on the advection-diffusion equation shows that the adaptive method can reduce the error significantly. When the two methods are applied to the Navier–Stokes equations with Boussinesq approximation, they give similar statistical results. However, the multi-domain approach is approximately 2.5 times faster in CPU time. Furthermore, the two methods do not have the drawbacks of Hermite functions used in previous work.