does the time step depend on constant source term?

Shenren_CN · April 18, 2011, 08:12

In 3D Euler FVM steady flow solver, the time step for local time stepping acceleration is scaled as

(1) cell_volume /( lambda1+lambda2+lambda3)

where lambda1,2,3 are spectral radii of the convective matrix.

I do understand how formula (1) is derived. My question is, if there's
a (constant) source term on the R.H.S. of the Euler equation, i.e.,

Original: du/dt + Flux(u)=0
Now: du/dt + Flux(u)=Constant

then, will this constant on the R.H.S. change the time step? Can I still
use formula (1) or should I formulate another time step to take into account the effect of the R.H.S term?

Thanks.

RameshK · April 18, 2011, 10:04

Hi

We know that CFL = (|U|*del_t)/delx, from which we get del_t = cfl*delx/IU| which can be written for 3D as delt = cfl * cell_volume / (|V.S|+c*|S|) . where S is the surface area vector.
If the constant you were referring to is the artificial dissipation terms then the time step doesnot depend on those terms. If I am wrong please correct me.

Thank you

April 18, 2011, 08:12	does the time step depend on constant source term?	#1
Shenren_CN Member Shenren Xu Join Date: Jan 2011 Location: London, U.K. Posts: 67 Rep Power: 15	In 3D Euler FVM steady flow solver, the time step for local time stepping acceleration is scaled as (1) cell_volume /( lambda1+lambda2+lambda3) where lambda1,2,3 are spectral radii of the convective matrix. I do understand how formula (1) is derived. My question is, if there's a (constant) source term on the R.H.S. of the Euler equation, i.e., Original: du/dt + Flux(u)=0 Now: du/dt + Flux(u)=Constant then, will this constant on the R.H.S. change the time step? Can I still use formula (1) or should I formulate another time step to take into account the effect of the R.H.S term? Thanks.

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April 18, 2011, 10:04		#2
RameshK Member Ramesh K Join Date: Dec 2009 Location: Bangalore Posts: 73 Rep Power: 16	Hi We know that CFL = (\|U\|del_t)/delx, from which we get del_t = cfldelx/IU\| which can be written for 3D as delt = cfl * cell_volume / (\|V.S\|+c*\|S\|) . where S is the surface area vector. If the constant you were referring to is the artificial dissipation terms then the time step doesnot depend on those terms. If I am wrong please correct me. Thank you