Abstract
In this paper, two modified QUICK schemes, namely Q-QUICK and UQ-QUICK, for improving the preci-sion of convective flux approximation are verified in advection-diffusion equation of pollutants on unstruc-tured grids. The constructed auxiliary nodes for Q-QUICK/UQ-QUICK are composed of two neighboring nodes plus the next upwind node, the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces. 2D unsteady advection-diffusion equation of pollut-ants is conducted for their verifications on unstructured grids. The numerical results show that Q-QUICK and UQ-QUICK have similar computational accuracy to the central difference scheme and similar numerical stability to upwind difference scheme after applying the deferred correction method. In addition, their corre-sponding CPU times are approximately equivalent to those of traditional difference schemes and their abili-ties for adapting high grid deformation are robust.
Highlights
The physical processes of pollutant transportation in flowing water are mainly consisting of advection and diffusion, which are usually governed by advection-diffusion equation of pollutants
The constructed auxiliary nodes for Q-QUICK/UQ-QUICK are composed of two neighboring nodes plus the upwind node, the later node is generated from intersection of the line of current neighboring nodes and their corresponding interfaces. 2D unsteady advection-diffusion equation of pollutants is conducted for their verifications on unstructured grids
The verification of Q-QUICK/UQ-QUICK has been investigated on three values of unstructured mesh numbers: 454, 1770 and 3955 with quadrilateral grids only
Summary
Another similar scheme named UQ-QUICK is introduced for comparative investigation. As for time discretization, the first-order and second-order schemes are taken into account. To this end, many compound schemes are formed and their corresponding numerical performances including numerical precision, stability and CPU time are fully demonstrated in 2D unsteady advection-diffusion equation of pollutants. In order to accelerate convergence speed for linear equations, generalized Minimum Residual (GMRES) [13] method with the Incomplete LU (ILUT) precondition is used
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