Comments on ‘equivalent versions of the quick scheme for finite‐difference and finite‐volume numerical methods’

Abstract

In Reference 1, Johnson and MacKinnon consider two convection schemes. For ease of reference, call these QUICK(l/8) and QUICK( 1/6). The authors state that the QUICK(1/8) scheme is only O(h2) accurate when used (as originally intended*) as a finite-volume method, and that the alternative QUICK(1/6) scheme is O(h3) in a finite-volume formulation. In fact, exactly the reverse is true: the QUICK(1/8) scheme is O ( h 3 ) accurate in a finite-volume formulation, but only O(hz) accurate in a single-point (finite-difference) formulation; whereas the QUICK (1/6) scheme is O(h3) accurate in the single-point formulation, but only O(h2) when used as a finite-volume method. This can easily be shown in two separate ways: (i) truncation-error analysis, and (ii) gridconvergence using exact diffusive fluxes.