In my opinion, they are different. Conservative schemes are for hyperbolic equations while shock can occur in parabolic type problems too.
Dear Mittal, if one must then compute the parabolic shocks accurately, isn't it right that a conservative scheme must be used? Or
are there other schemes of capturing shocks numerically apart from conservative schemes?
I understand these concepts as follows: conservative means that the scheme discretizes the divergence form of the equations. Upon convergence the numerical solution will approach a weak solution. (The old paper by Lax and Wendroff) The general consensus is that this is necessary to catch a hyperbolic shock (not a viscous, parabolic, shock). It is not clear how to define a weak solution for other forms of the equation. Shock capturing schemes are hence conservative but usually have other properties as well. typically they contain artificial diffusion in some form to ensure stability and positivity.
I also agree with this; you need a conservative scheme to capture a shock, but not every conservative scheme does it ...
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