TY - JOUR
T1 - Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems
AU - Wu , Zi-Niu
JO - Journal of Computational Mathematics
VL - 3
SP - 383
EP - 400
PY - 2003
DA - 2003/06
SN - 21
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10267.html
KW - Conservation, Compact scheme, Uniform grid, Multiblock patched grid.
AB - <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>