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1D shock instability with Roe FDS?
I recently used Roe's FDS TVD + MUSCL (3 order) to solve quasi-one-dimensional flow. The problem I considered involves a shock located at divergent section and an injection (mass addition) downstream the shock.
supersonic | ==> | (mass injection) ==> exit | (shock) The simulated flowfield, in some cases, display a stable oscillation from the shock to the exit. I checked the oscillation frequency -- it is much higher than the possible acoustic frequency. Thus the oscillation is unphysical. So is this "1D shock instability" resulted from the Roe Scheme? Any comment is appreciated. - ma |

Re: 1D shock instability with Roe FDS?
Can I ask how did you measure frequency of oscillation?
Are you sure about CFL condition, actually it limits the propagation of weak waves.The unphysical oscillation that I've got in my 1D modelling always decreased with denser grids. Do you have any source term in the numerical method (or non-potential forces in the equations)? |

Re: 1D shock instability with Roe FDS?
Be careful using Roe's scheme, specially close to sonic points, I advice to read laney's book on Gasdynamics.
Check if you got the oscillation when you turn your MUSCL scheme off. If yes, change scheme to a more "modern" one. If not, then your MUSCL scheme is not doing things properly |

Re: 1D shock instability with Roe FDS?
The oscillation frequency can be measured either by a FFT of the pressure history at some probe or a hand-calculation of the oscillation cycle period.
The oscillation is very small in simple cases such as 1D nozzle flow, but still can be detected if we enlarge the figure. Yes, I have source term -- the mass injection downstream of the shock, which is a source term in 1D model. Thanks. - ma |

Re: 1D shock instability with Roe FDS?
(1) I have tested the Mach 3 shock tube problem (see Wesseling's CFD book). There is an unphysical "expansion shock" for first order Roe Scheme, but it disappears for second and third orders. In addition, I also adopted the entropy fix for Roe scheme.
(2) I did compared 1st, 2nd, and 3rd orders. There is no oscillation with 1st order (1st order means turning MUSCL off). But I checked my MUSCL part very carefully, and it seems there is no coding error. Maybe I will check it again. I would be happy if the unphysical oscillation is due to my coding error. (3) What do you mean by "modern one"? Do you mean WENO or AUSM or ...? In fact, I did the same simulation with the recently developed "space-time CE/SE scheme", the results have no oscillation and are much better than Roe's scheme. (+) I checked the CFD literature, it is easy to found the shock instability of 2D TVD schemes, such as the well-known "carbuncle phenomenon". But for 1D, I only found one paper by Arora and Roe "on postshock oscillations due to shock capturing schemes in unsteady flows (JCP 1997, vol. 130)". I am not sure if this 1D oscillation a common phenomenon of Roe's TVD scheme, and if there is any cure to it. Thanks a lot. - ma |

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