Do high grid resolution capture accurate shocks?
Please clarify my doubts...When solving Euler equations using finite difference method for compressible flows, the shock gets captured because of the implicit presence of numerical dissipation or due to the addition of artificial viscosity for obtaining a smooth and stable solution. However the shock obtained is much 'thicker' than the physical shock proportional to the amount of artificial viscosity. Can this solution be improved by refining the grid near shock region or is just independent of the grid resolution. I mean I want a smooth and stable solution with accurate capture of the shocks if possible by increasing the grid resolution. Thanks in advance.
Re: Do high grid resolution capture accurate shock
You can only accurately capture the inner structure of a shock with a NS solver, since it is a viscous flow structure. With an Euler calculation the shock is only calculated as a flow discontinuity (thus infinitely thin). The simulated shock thickness is merely a numerical artifact related to numerical dissipation (and therefore also grid size). So your shock will become thinner (more crisp) as you increase grid density, but this is by no means a more accurate solution of shock thickness.
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