Navier-Stokes time step size
 

Hi,

I have implemented a 2d/3d spectral/hp finite element solver for the Euler equations. I use an explicit Runge-Kutta time stepping with a variable step size calculated as the minimum over all elements of

dt = CFL*volume/((2p+1)(c+u))

where volume is the element volume, p the polynomial order used in the element, c and u being the local speed of sound and flow velocity (averages) in the element. This works fine.

But what time step should I use for NS? Due to viscosity it must be much smaller than for purely convective flows. Is there a formula for calculating the time step for NS for any polynomial order ?

Thanks, Niels

Re: Navier-Stokes time step size
 

Can I ask you something? Are you using a spectral element method or discontinuous Galerkin method?

Re: Navier-Stokes time step size
 

Glad you pointed that out. It is a discontinuous Galerkin solver.

Hello Niels,

I am delaing with a problem in time step size for solving Sod's Shock Tube using DGFEM code using 2D CNS equations. The code is from the book by Hesthaven & Warburton. I have tried to replace teh BCs and iCs of channel flow with that of Sod's BCs and ICs. But the problem lies with time step size. As soon as i reach 3rd order polynomial, the timestep diverges even if i start from a very small value. And also in case of 1st and 2nd order polynomial, the results are highly under evolved.

Do you think you can suggest me something that can work out a solution.

Thanks & Regards