Conservation of Three-Point Compact Schemes on Single and Multiblock Patched Grids for Hyperbolic Problems
Year: 2003
Author: Zi-Niu Wu
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 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 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JCM-10267
Journal of Computational Mathematics, Vol. 21 (2003), Iss. 3 : pp. 383–400
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Conservation Compact scheme Uniform grid Multiblock patched grid.