• normalized variable diagram (NVD);
  • high-resolution scheme (HRS);
  • convection boundedness criterion (CBC);
  • convection discretization;
  • unstructured mesh;
  • normalized variable and space formulation (NVSF)


Three new far-upwind reconstruction techniques, New-Technique 1, 2, and 3, are proposed in this paper, which localize the normalized variable and space formulation (NVSF) schemes and facilitate the implementation of standard bounded high-resolution differencing schemes on arbitrary unstructured meshes. By theoretical analysis, it is concluded that the three new techniques overcome two inherent drawbacks of the original technique found in the literature. Eleven classic high-resolution NVSF schemes developed in the past decades are selected to evaluate performances of the three new techniques relative to the original technique. Under the circumstances of arbitrary unstructured meshes, stretched meshes, and uniform triangular meshes, for each NVSF scheme, the accuracies and convergence properties, when implementing the four aforementioned far-upwind reconstruction techniques respectively, are assessed by the pure convection of several scalar profiles. The numerical results clearly show that New-Technique-2 leads to a better performance in terms of overall accuracy and convergence behavior for the 11 NVSF schemes. Copyright © 2013 John Wiley & Sons, Ltd.