When it comes to a second-order accurate finite volume discretization of Navier-Stokes equations, which one of the two following rationales is adopted?
1- Second-order accuracy is a direct consequence of how we eliminate higher order terms in the Taylor expansion of all the terms;
2- From the beginning, we assume that the dependent variable varies linearly between a pair of neighboring cell centers; with such an assumption, high-order terms won't appear at all.

  • $\begingroup$ With #2, why would it be second-order accurate, not third-order or higher? $\endgroup$ Jun 24 at 17:07

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