@Article{JCM-21-3,
author = {Zi-Niu, Wu},
title = {Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems},
journal = {Journal of Computational Mathematics},
year = {2003},
volume = {21},
number = {3},
pages = {383--400},
abstract = {<p style="text-align: justify;">For nonlinear hyperbolic problems, conservation of the numerical scheme is important for convergence to the correct weak solutions. In this paper the conservation of the well-known compact scheme up to fourth order of accuracy on a single and uniform grid is studied, and a conservative interface treatment is derived for compact schemes on patched grids. For a pure initial value problem, the compact scheme is shown to be equivalent to a scheme in the usual conservative form. For the case of a mixed initial boundary value problem, the compact scheme is conservative only if the rounding errors are small enough. For a patched grid interface, a conservative interface condition useful for mesh refinement and for parallel computation is derived and its order of local accuracy is analyzed.</p>},
issn = {1991-7139},
doi = {https://doi.org/2003-JCM-10267},
url = {https://global-sci.com/article/85331/conservation-of-three-point-compact-schemes-on-single-and-multiblock-patched-grids-for-hyperbolic-problems}
}