2017/01/17 by Sheng Wang, Wang, Sheng, Eric Johnsen +1
Engineering · Mathematics · #35L65 #35L67 #65M06 #Computational Fluid Dynamics and Aerodynamics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1701.04834
openalex publication_date 2017/01/17 · openalex created_date 2017/02/03 · openalex updated_date 2026/08/01
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.