  In this paper, we resolve the ever-present confusion over the QUICK scheme:
it is a second-order scheme or a third-order scheme. The QUICK scheme, as
proposed in the original reference [B. P. Leonard, Comput. Methods. Appl. Mech.
Eng., 19, (1979), 59-98], is a third-order (not second-order) finite-volume
scheme for the integral form of a general nonlinear conservation law with
point-valued solutions stored at cell centers as numerical solutions.
Third-order accuracy is proved by a careful and detailed truncation error
analysis and demonstrated by a series of thorough numerical tests. The QUICK
scheme requires a careful spatial discretization of a time derivative to
preserve third-order accuracy for unsteady problems. Two techniques are
discussed, including the QUICKEST scheme of Leonard. Discussions are given on
how the QUICK scheme is mistakenly found to be second-order accurate. This
paper is intended to serve as a reference to clarify any confusion about
third-order accuracy of the QUICK scheme and also as the basis for clarifying
third-order unstructured-grid schemes as we will discuss in a subsequent paper.
