Ak. Verma et V. Eswaran, A BOUNDED CONVECTION SCHEME FOR THE OVERLAPPING CONTROL-VOLUME APPROACH, International journal for numerical methods in fluids, 25(10), 1997, pp. 1137-1161
This paper introduces a flux-limited scheme FLOCV for the overlapping
control volume (OCV) approach to 2D steady and unsteady convection-dif
fusion problems on structured non-orthogonal grids, FLOCV switches fro
m second-to first-order interpolation in the presence of extrema. Smoo
th switching between the two is ensured by weighted average second-and
first-order upwind differencing, with the weights being dynamically d
etermined. Five convective test problems are solved using this scheme
and results are compared with known analytical solutions. It is found
that FLOCV approximately retains second-order accuracy of the base dis
cretization scheme on uniform grids and smooth non-uniform orthogonal
grids. It is also found effective in removing oscillations for problem
s with discontinuities on both orthogonal and non-orthogonal grids, wi
th little degradation of accuracy. (C) 1977 John Wiley & Sons, Ltd.