CFL condition for higher order schemes

Shyam

Hi,

I read in an article that the CFL condition for higher order schemes can be very low, as the resolution is given by (h/p^d), where h is the grid spacing, p is the polynomial degree of reconstruction and d is the number of dimensions.

One of the professor mentioned that it is advised to use multigrid techniques for improving the CFL condition. I am using unstructured higher order FVM. My question is,

1. Is it really required to do a multigrid for a transient problem when higher order schemes (3rd to 4th order) are used?

2. If I get a stable time marching with CFL=0.5 with third order RK and third order scheme, does it compromise the solution accuracy for a transient problem?

3. For unstructured higher order finite volume method, which is the best suitable way to do a multigrid?

Thanks in advance for your help, Shyam