how calculate the density in low mach number?
 

hi, i am working on euler eq in low mach number with preconditioning. in actual, the euler code is compressible code, so its unknown is density, velociy, tempreture. the computation code is like this.

dWv dE dF

T ---- + ---- + ---- = 0

dt dx dy

where Wv=(p,u,v,t)

E =(rho u, rho u u + p , rho u v, rho u e + u p)

F =(rho u, rho u v , rho v v + p, rho u e + u p)

T - arbitrary preconditioning matrix p - pressure rho - density u,v - velocity component e - total energy

* all veriables are non-dimensionilized.

for clatulating the flux term(E,F), we should know density but the density is not present explicitly.

as i know p/rho = gamma R T (prefect gas eq) is not avaible owing to imcompressible and non-dimension. i shouble use artificial mach number or something else but i don't know.

thanks ahead. Lee

Re: how calculate the density in low mach number?
 

Hello,

Getting an Euler code to work for low Mach numbers is a very crucial test of the numerical scheme. I have computed flow around a cylinder at Mach=0.1, which is in the region of incompressible limit. The compressible Euler equations are valid so long as Mach > 0. You can still use the same equation of state, p=rho*R*T. If you have trouble in getting the results, then the problem lies with your numerical scheme. Also, low Mach number cases take a lot of time to converge. Hope this helps.