Dear sir,

I have read from some paper about the roundoff error caused by the sigular pressure gradient term in the momentum equations in low speed flow. It say that the pressure term is of order 1 over Mach number squared while the convective term is of order unity in the nondimensional momentum equations. I can prove this!

The paper suggest that we should decompose the pressure into a constant reference pressure part and a gauge pressure part.

presssure = constant reference pressure + gauge pressure Because the pressure term in momentum equations is the gradient of pressure then we have

gradient of pressure = gradient of gauge pressure The paper say that, with proper selection of reference pressure, the magnitude of the pressure gradient term in the nondimensional momentum equations becomes of order unity as the Mach number approaches zero. I cannot prove this part. And I do not understand why the decomposition of pressure can circumvent the pressure singularity problem.

Could you please

- suggest me how to prove that the order of pressure term is changed to unity?

- give me some idea how can this procedure remedy this problem?

Thank you very much sir.

Best regards,

Atit Koonsrisuk

As i can understand u are talking about preconditioning methods. Have u tried searching with that term in internet or libraries? Can u tell me the name of the papers u have read cause that methods interests me too

Thanks

p.s. as long as i find something specific i will try to send it

The name of my reference paper is "A Time-Accurate Algorithm for Chemical Non-Equilibrium Viscous Flows at All Speeds" by Shuen et. al. AIAA 92-3639.