Nondimensionalization of variables in comp. flow

jinwon park

Hello! I am solving numerous compressible multi-fluid flow. In fact, the code was based on the ghost fluid method and the stiffened EOS was chosen to describe the fluid motion for both.

p=(gamma-1)*rho*I-gamma*PI where gamma=1.4 and PI=0 for gas and 5.5 and 4.9E6 for water.

Due to such large values, my code has suffered from the instability. However, when I solved a similar problem nondimensionalized, code worked excellently.

Can anyone explain about the performance or effectiveness of the nondimensionalized one and how to do it?

For example, density = 1200kg/m^3 velocity = 10 m/s pressure = 10GPa

And I also wonder that the gamma in the EOS is usually constant without any dimension so that it doesn't need to be nondimensionalized.

Please..

Thanks in advance.