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• W1986689624 abstract "This paper explains significant differences in truncation error between finite-difference and finite-volume convection-diffusion schemes. Specifically, the order of accuracy of the QUICK scheme for steady-state convection and diffusion is discussed in detail. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 18-factor multiplying the “curvature” term) is indeed a third-order representation of the finite-volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 16-factor) is a third-order representation of the finite-difference single-point formulation; this can be written in a pseudo-flux-difference form. These are both third-order convection schemes; however, the QUICK finite-volume convection operator is 33% more accurate than the single-point implementation of SPUDS. Another finite-volume scheme, writing convective fluxes in terms of cell-average values, requires a 16-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages and then express this in pseudo-flux-difference form; for third-order accuracy, this requires a curvature factor of 524. Diffusion operators are also considered in both finite-difference and finite-volume formulations. Finite-volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite-volume formulation as it is in a finite-difference formulation." @default.
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• W1986689624 date "1995-11-01" @default.
• W1986689624 modified "2023-10-01" @default.
• W1986689624 title "Order of accuracy of QUICK and related convection-diffusion schemes" @default.
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• W1986689624 doi "https://doi.org/10.1016/0307-904x(95)00084-w" @default.
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