Leap Frog Scheme
 

Hi I just want to know if leap frog scheme without any artificial viscosity would fetch good results in solving Sod's Shock tube(euler equation) problem. I was getting NaN's in solution after a few time steps..

Re: Leap Frog Scheme
 

For the Shock tube test you really need something that "captures" the shock. You will get oscillations near the shock and at the same time you will "smooth out" the profile of the shock using a simple method as the leap frog scheme. You need to use a method adapted for shocks.

Re: Leap Frog Scheme
 

If you do not use a shock capturing scheme ( Gud, roe, ENO etc.), you would need artificial viscosity to remove the oscillations observed on the leading and trailing edge. If you do not remove them, they would contaminate the solution. If you use macormack or leapfrog or other FD schemes add either an artificial damping or use wavenumber filtering to remove the oscillations.