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A stable and accurate convective modelling procedure based on quadratic upstream interpolation
A convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstreamExpand
The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection
Abstract Modeling of highly advective transport is embarrassingly difficult, even in the superficially simple case of one-dimensional constant-velocity flow. In this paper, a fresh approach is taken,Expand
Simple high-accuracy resolution program for convective modelling of discontinuities
SUMMARY For steady multi-dimensional convection, the QUICK scheme has several attractive properties. However, for highly convective simulation of step profiles, QUICK produces unphysical overshootsExpand
Conservative Explicit Unrestricted-Time-Step Multidimensional Constancy-Preserving Advection Schemes
Abstract The multidimensional advection schemes described in this study are based on a strictly conservative flux-based control-volume formulation. They use an explicit forward-in-time update over aExpand
Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection
TLDR
The new universal limiter and associated solution procedures form the so-called ULTRA-SHARP alternative for high-resolution non-oscillatory multidimensional steady-state high-speed convective modelling. Expand
Positivity-preserving numerical schemes for multidimensional advection
This report describes the construction of an explicit, single time-step, conservative, finite-volume method for multidimensional advective flow, based on a uniformly third-order polynomialExpand
Universal Limiter for Transient Interpolation Modeling of the Advective Transport Equations : The ULTIMATE Conservative Difference Scheme
steps and shock waves, for example; but progress has been unexpectedly slow. It seems that correction of one defect always introduces another, equally severe. Unphysical oscillations inherent inExpand
SHARP Simulation of Discontinuities in Highly Convective Steady Flow
For steady multidimesional convection, the Quadratic Upstream Interpolation for Convective Kinematics (QUICK) scheme has several attractive properties. However, for highly convective simulation ofExpand
Sharp monotonic resolution of discontinuities without clipping of narrow extrema
Abstract A strategy is presented for accurately simulating highly convective flows containing discontinuities such as density fronts or shock waves, without distorting smooth profiles or clippingExpand
Order of accuracy of QUICK and related convection-diffusion schemes
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 QUICKExpand
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