Abstract
This paper describes a simple and efficient approach to ensure the bounded numerical solution with respect to the discretization of convective transport on unstructured numerical grids. The approach is based on the existing boundedness criteria that provide a straightforward way to design and implement bounded convective schemes on structured grids. We show that two popular steady-state criteria, Convection Boundedness Criterion (CBC) and Total Variation Diminishing (TVD), have a common origin and can be easily derived by enforcing local monotonicity and interpolative boundedness of the cell-face variable values. As these criteria require the far upstream value for each face under consideration, the bounded reconstruction of this value is tested. The reconstruction employs the cell gradient projection on a given direction. In addition, a new version of the SMART scheme (AVL SMART) is proposed. Several test-problem results obtained with various convective schemes validate the present approach and confirm good resolution and convergence properties of the modified SMART scheme.
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