ENO Scheme in a Shock tube problem
 

I was solving a simple Sod's shock tube problem using third order convex ENO scheme and third order RK. When I used a coarser mesh (100X10) it worked fine. When I made the mesh finer in the transverse direction (along the y direction), the code blew up. The grid size now was 100 X 100. And This happened only if I solve for V velocity (although it is a one dimensional problem). I am adapting my time step based on teh CFL number at each time step. Anyone ever experienced anything like this before ? any ideas and suggestion will be of great help. I have looked at my code several times and I have not found a bug so far.

thank you in advance

Re: ENO Scheme in a Shock tube problem
 

i hope ur problem is with the cfl number. try reducing it to a safe value rather than considering it at each step. this may solve ur problem. also understand the philosophy behind cfl number. about the physical speed and computational speed and stuff like that. hope there is no error with ur code. thank u prapanj

Re: ENO Scheme in a Shock tube problem
 

Hi there,

Thanx a lot for your reply. Well, it works if I reduce my cfl number. But my point is that ENO schemes should take care of carbuncle phenomenon because of the LLF way of constructing the fluxes. Hence there should be enough dissipation in the transverse direction to dissipate any shock instabilities. Atleast this is my understanding. However I dont know if there is any well documented theories for the shortcommings of ENO. The code just works fine if I reduce the CFL number from 0.945 to say 0.4. What do you think ? But I have so far been unlucky in finding a bug in my code. I am still unsure..... Thank you once again for your reply

Re: ENO Scheme in a Shock tube problem
 

well i am too immature to give so much of explanation. i am just an undergraduate engg student. well i request u to understand the physical significance of CFL number. in hyperbolic systems, the speed of propogation of information should be less computationally than the physical speed. if the CFL number exceeds the limit, the computation tends to acquire information from regions that dont have a solution. and hence the blow up. hope u got some info... or may be u know this already. i dont think u had any bug in ur code.

Re: ENO Scheme in a Shock tube problem
 

Hey Thanx again for your reply. You are right. CFL number should always be less than one. In that way you ensure that the waves (characteristics) do not leave the grid cell in one time step. However maintaining a cfl close to one gives you solutions close to the exact solution. Reducing the cfl number certainly helps in many situation, (by adding some kind of artificial viscosity and hence smearing any spikes occuring in the solution) but I want to make this case to work for large cfl number close to one. The code blows up only when I make the mesh finer in the transverse direction. This has got to do with shock instabilities. I am not sure if this can occur with ENO schemes and I want to know if anybody has experienced this before.