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 Tian Baolin April 17, 2003 05:31

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 3-order Runge-Kutta method for the time, and 3-order upwind compact shceme or 5-order WENO scheme, but i can't obtain the steady solution.

thanks!

 versi April 17, 2003 05:56

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?

 Tian Baolin April 18, 2003 03:15

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!

 Tian Baolin April 18, 2003 03:17

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!

 ptyue April 18, 2003 14:41

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 R-K method is not necessary, you can use 1st order method if you only want the steady state solution.

 Tian Baolin April 18, 2003 21:29

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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