Error analysis and iterative methods in pseudospectral semi-implicit simulations: an application to compressible convection

摘要

Compressible convection is an interesting field for numerical experiments. Rapidly varying small-scale flow structures appear as the Rayleigh number Ra increases, demanding larger spatial resolution under more and more severe Courant stability conditions. Coupling a pseudospectral approximation in space to a semi-implicit scheme in time allows one to increase the size of ts, though at each time step a system of algebraic equations, whose size increases with the spatial resolution, must be solved by means of direct or iterative methods. The former allows one to minimize the consumption of CPU time but leads to unacceptable demand of memory. The efficiency and cost of the latter, on the other hand, depend heavily on the choice of the preconditioning operator and on the allowed error tolerance. In this paper we check the capabilities of iterative-like methods and we achieve the main goal of drastically reducing the memory storage with respect to direct methods, without increasing the CPU time.