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.
Cite
@article{arxiv.1701.04834,
title = {High-order schemes for the Euler equations in cylindrical/spherical coordinates},
author = {Sheng Wang and Eric Johnsen},
journal= {arXiv preprint arXiv:1701.04834},
year = {2017}
}