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 -

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.