High-order schemes for the Euler equations in cylindrical/spherical coordinates
Provides a practical solution for computational fluid dynamics simulations requiring both high-order accuracy and conservation in radially symmetric geometries.
This work develops a new high-order accurate and conservative finite difference WENO scheme for the Euler equations in cylindrical/spherical coordinates, addressing the trade-off between accuracy and conservation in existing methods. Numerical tests confirm high-order convergence and correct shock capturing.
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.