Abstract: The convergence characteristics of the preconditioned Euler equations at low Mach numbers were studied in this article. An order analysis was conducted to search for the convergence characteristics of Euler equationswith Weiss-Smith preconditioner in low speed flow. The convergence characteristics of every equation were studied, and then a new preconditioning matrix was suggested. It is shown that excellent convergence rates and solution accuracy of Euler equations are obtained with the Weiss-Smith preconditioner, and the new preoconditioning matrix can improve the convergence characteristics of continuity equations considerably in ultra-low speed flow.

Key words: computational fluid dynamics, preconditioning, low Mach numbers, convergence, Euler equations