Volume 21, Issue 3
Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems

Zi-niu Wu

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J. Comp. Math., 21 (2003), pp. 383-400

Published online: 2003-06

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  • Abstract

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 pathed grids. Gor 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.

  • Keywords

Conservation Compact scheme Uniform grid Multiblock patched grid

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@Article{JCM-21-383, 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 = { 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 pathed grids. Gor 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. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10267.html} }
TY - JOUR T1 - Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems AU - Zi-niu Wu 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 KW - Compact scheme KW - Uniform grid KW - 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 pathed grids. Gor 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.
Zi-niu Wu. (1970). Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems. Journal of Computational Mathematics. 21 (3). 383-400. doi:
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