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An improved $r$-factor algorithm for TVD schemes. (English) Zbl 1206.76039
Summary: An improved $r$-factor algorithm for TVD schemes on structured and unstructured grids within a finite volume method framework is proposed for numerical approximation to the convective term. The new algorithm is tested by a problem of pure convection with a double-step profile in an oblique uniform velocity field. The computational results are then compared with the results of Darwish’s $r$-factor algorithm using Superbee and Osher limiters on both structured and unstructured grids. The numerical results show that the new algorithm can mitigate the oscillation behavior efficiently while still maintaining the boundedness of the solutions. When using a deferred correction technique to handle the non-linear term arising from the high resolution schemes, the proposed algorithm showed a smoother and faster convergence history on structured grids than Darwish’ $r$-factor algorithm, while on unstructured grids the presented one is more accurate with a similar convergence history.
##### MSC:
 76M20 Finite difference methods (fluid mechanics) 65M06 Finite difference methods (IVP of PDE) 65M50 Mesh generation and refinement (IVP of PDE) 76R05 Forced convection (fluid mechanics) 76R10 Free convection (fluid mechanics)