Hi guys, I have a one question expecially for compressible flows (mach number more than 2). I would like to know whether FDM (finete difference)or FVM (finete volume)is better for the above mentioned case. thanks in advance for your help. bye rajani.

Hi,

Finite difference methods are based on Taylor series approximation which assumes the contnuity of the function. WHen you are talking M>=2,all your physical variables are discontinuous. Does it answer your question? I have used FVM methods for supersonic cases. Regards gita

Hi, thanks for your answer. I understand that FVM provides local conservation. but i used to observe that many academic research persons prefer FDM methods for compressible flows. May be it is beacause of the easy implementation expecially for complex geometries. even in some recent papers expecially in LES related stuff i observed that people are using FDM (by using sanjeev leele method). thats why i am still not clear which one is beter.

Hi,

When you say compressible,you need to clearly specify your Mach No. In the case of shocks,the fn itself is discontinuous. So,you can't apply Taylor's series. Can you send me the ref of the papers? I would like to look at it. There are codes(I know)which are basically an incompressible code and they use it to solve some compressible problems. But I observed the results(by that code)for the simplest compressible test case(weak shock)known as Sod's problem,to be poor. As long as your fns are not discontinuous FD scheme should work fine. If I'm wrong anyone can update my knowledge. Regards

hi, the reason that u find some applications to finite difference is that it's simplicity. Another advantage when utilised for DNS or maybe LSE is the possibility to easily obtain high-order approximation, and hence, to achieve high-order accuracy of the spatial discretisation. That is the reason for using it in DNS.However, it has lots of disadvantages, one of them is that it can not be used in complex geometries (Numerical errors) and that is why it is not used in industrial application. If you wanna write a DNS code u'd better use Spectral Element Method. For all other applications the FVM is superior

Hi Michael,

Thanks. I've seen people using compact finite difference schemes(different from classical explicit FD schemes)in DNS. But I don't have any experience along these lines and wasn't sure what rajani meant by FD schemes(compact/classical FD chemes). Doesn't spectral method face problems in terms of boundary conditions? Regards gita

hi, yep the spectral method can not be applied except for simple domanes and this is the main drawback. However, the Spectral element method or the spectral hp combines the geometric flexibility of the finite element with the high order spacial accuracy and sustain a rapid convergence....there are lots of advantages using this method, treatment of complex geometries,non-diffusive and many more. the main drawback ( which personely I dun consider ) is that it needs much more effort ( Numerical) compared to the finite volume. Michel