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

• Published in: International journal for numerical methods in fluids 1997-10, Vol.25 (8), p.959-971
• Main Authors: Rubini, F., Taverne, V., Valdettaro, L.
• Format: Article
• Language: English
• Subjects: Approximation theory; Computational complexity; Computational methods in fluid dynamics; Computer simulation; Efficiency; Error analysis; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Iterative methods; Physics; semi-implicit simulations; Turbulent flow
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19971030)25:8<959::AID-FLD598>3.0.CO;2-0

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 Δ 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. © 1997 John Wiley & Sons, Ltd.