Title: High-order schemes for the Euler equations in cylindrical/spherical coordinates,
Abstract: We consider implementations of high-order finite difference Weighted
Essentially Non-Oscillatory (WENO) schemes for the Euler equations in
cylindrical and spherical coordinate systems with radial dependence only. The
main concern of this work lies in ensuring both high-order accuracy and
conservation. Three different spatial discretizations are assessed: one that is
shown to be high-order accurate but not conservative, one conservative but not
high-order accurate, and a new approach that is both high-order accurate and
conservative. For cylindrical and spherical coordinates, we present convergence
results for the advection equation and the Euler equations with an acoustics
problem; we then use the Sod shock tube and the Sedov point-blast problems in
cylindrical coordinates to verify our analysis and implementations.