The QUICK scheme is a third-order finite-volume scheme with point-valued numerical solutions

In this paper, we resolve the ever-present confusion over the Quadratic Upwind Interpolation for Convective Kinematics (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 economical high-order unstructured-grid schemes as we will discuss in a subsequent paper.