Abt: Mach number.. Help! Plz!

jinwon park

Hi all. Recently, I posted the question about the low-mach number flow simualation by the density-based formaluation. Today, I found a presentation material mentioning about this issue. The title is "The Low Mach number approximation for multidimensional modelling of type I-ray bursts". In that material, time step was increased by replacing delT=CFL*((dx)/(U+C)) by delT=CFL*(dx/U) when Mach <0.1. It sounds good for me who does not want to modify the equation as in preconditioning methods.

Have anyone see this approach? They said that this can speed up the computation by a factor of 10 or more. If so, it is a good one for me. In implementing, I had some questions about the Mach number. I know its definition but I could not realize some situations.

I am solving compressible gas-water flows. In initial stage, the flow velocity in rest water is zero. Wonder if Mach number is zero whenever the flow velocity is zero.Could you help me to figure out the numerical meaning of Mach number in simulations?

Thanks in advance!