Explanation
In shock-capturing approach the governing equations of inviscid flows (Euler equations) are cast in conservation form and any shock waves or discontinuities are computed as part of the solution. Here, no special treatment is employed to take care of the shocks themselves. This is in contrast to the shock-fitting method, where shock waves are explicitly introduced in the solution using appropriate shock relations (Rankine–Hugoniot relations).
The shock capturing methods are relatively simple compared to the more elaborate shock fitting methods. However, the shock waves predicted by shock-capturing methods are generally not sharp and smear over several grid points. Also, classical shock-capturing methods have the disadvantages that unphysical oscillations (Gibbs phenomenon) may develop near strong shocks.
Read more about this topic: Shock Capturing Methods
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