Abstract. In the second part of the paper, we compare the solutions produced in the framework of the conference "Mathematical and numerical aspects of low Mach number flows" organized by INRIA and MAB in Porquerolles, June 2004, to the reference solutions described in Part 1. We make some recommendations on how to produce good quality solutions, and list a number of pitfalls to be avoided.Mathematics Subject Classification. 65M50, 76M10, 76M12, 76M20, 76M22, 76R10.

SUMMARYIn this paper, a transient injection flow at low Mach number regime is investigated. Three different methods are used and analyzed. Two of them are based on asymptotic models of the Navier-Stokes equations valid for small Mach numbers, whereas the other is based on the full compressible Navier-Stokes equations, with particular care given to the discretization at low Mach numbers. Numerical solutions are computed both with or without the gravity force. Finally, the performance of the solvers in terms of CPU-time consumption is investigated, and the sensitivity of the solution to some parameters, which affect CPU time is also performed.