@Article{CiCP-2-5,
author = {},
title = {Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes},
journal = {Communications in Computational Physics},
year = {2007},
volume = {2},
number = {5},
pages = {933--963},
abstract = {<p style="text-align: justify;">This is the continuation of the paper &quot;Central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction&quot; by the
same authors. The hierarchical reconstruction introduced therein is applied to central
schemes on overlapping cells and to finite volume schemes on non-staggered grids.
This takes a new finite volume approach for approximating non-smooth solutions. A
critical step for high-order finite volume schemes is to reconstruct a non-oscillatory
high degree polynomial approximation in each cell out of nearby cell averages. In
the paper this procedure is accomplished in two steps: first to reconstruct a high degree polynomial in each cell by using e.g., a central reconstruction, which is easy to do
despite the fact that the reconstructed polynomial could be oscillatory; then to apply
the hierarchical reconstruction to remove the spurious oscillations while maintaining
the high resolution. All numerical computations for systems of conservation laws are
performed without characteristic decomposition. In particular, we demonstrate that
this new approach can generate essentially non-oscillatory solutions even for 5th-order
schemes without characteristic decomposition.</p>},
issn = {1991-7120},
doi = {https://doi.org/2007-CiCP-7933},
url = {https://global-sci.com/article/81345/non-oscillatory-hierarchical-reconstruction-for-central-and-finite-volume-schemes}
}