In order to reduce numerical diffusion associated with first-order upwind differencing schemes (UDS), higher order upwind differencing schemes are often employed in computational fluid dynamics (CFD) calculations. The two most popular higher order UDS are the second-order UDS (1) and the quadratic upwind interpolation for convective kinematics (QUICK) scheme (2).

It is well known that the use of either of the aforementioned two schemes results in a system of equations that may not converge when using an iterative solution method (3). Even for the one-dimensional advection-diffusion equation, since the stencil extends beyond three nodes, a single tridiagonal matrix inversion is not sufficient, and iterations are necessary to solve the resulting system of algebraic equations. Thus, one-dimensional calculations are sufficient for extracting meaningful information pertaining to the stability of these schemes in the context of iterative...

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