Modeling the Chimera Domain DecompositionApproach to Solving Conservation

The standard Chimera Domain Decomposition approach to numerically solving the conservation laws of uid dynamics can give rise to anomalous ow eld features near subdomain boundaries. Keeling, Tramel, and Benek hypothesized that these anomalous behaviors are caused by interpolation across shocks at the artiicial boundaries and can be eliminated by using the appropriate trace approximation near shocks. In this paper, we prove that such anomalous behaviors are impossible for one dimensional scalar conservation laws. In addition, we show computationally that for certain systems of conservation laws it is acceptable to interpolate across shocks at the artiicial boundaries provided there are no characteristics propagating away from the shock. If there is at least one outgoing characteristic near shocks, then the numerical solutions can lead to incorrect ow dynamics. We also show that this problem can be avoided by using proper trace approximation at the shock sites.