the Reinitialization of Level set
When solve the reinitialization equation of level set method,
phi,t+sign(phi_0)*(grad(phi)1)=0 in order to get a steady solution of the above equation. I used the 3order RungeKutta method for the time, and 3order upwind compact shceme or 5order WENO scheme, but i can't obtain the steady solution. thanks! 
Re: the Reinitialization of Level set
Is the first order upwind scheme converged? Is the pseudo time step appropriate, i.e. satisfy CFL constraint of RK2?

Re: the Reinitialization of Level set
In most cases, the first order upwind scheme converged, but the 3rd compact upwind scheme often did not converge. And as for my case, the ratio of time step to space step is 0.1 or 0.2. So I think it should satisfy the CFL condition.
thanks a lot for you concern! 
Re: the Reinitialization of Level set
In most cases, the first order upwind scheme converged, but the 3rd compact upwind scheme often did not converge. And as for my case, the ratio of time step to space step is 0.1 or 0.2. So I think it should satisfy the CFL condition.
Due to the too much dissipation of 1st order scheme, I try to use the 3rd ones thanks a lot for you concern! 
Re: the Reinitialization of Level set
The euqtions phi,t+sign(phi_0)*(grad(phi)1)=0 may not work well. sign(phi_0) should be replaced with some smoother functions, which can be found in the literatures.
The 3rd RK method is not necessary, you can use 1st order method if you only want the steady state solution. 
Re: the Reinitialization of Level set
thanks Here I had replaced sign(phi0) with the phi0/(phi0*phi0+dx*dx), where the dx is the space step.
And i have tried to use 1st order scheme in time. 
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