A Note on Conservation Laws for Keplerian Flows

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Abstract
The straightforward use of numerical conservation laws in non-Cartesian coordinates for flows with strong gravitational/centrifugal forces may induce significant errors. The numerical error when computing a conservation law driven by a gravitational body force is examined and traced to an incompatible finite-differencing sequence similar to that found in applications involving rectilinear flows. An alternate form of the conservation law is presented and illustrated by computing shock wave motion in a model protoplanetary disk using a high-order finite-difference method.