The QUICK scheme is a third‐order finite‐volume scheme with point‐valued numerical solutions
Hiroaki Nishikawa
Abstract
Abstract 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.