高阶方案用于柱坐标/球坐标中的欧拉方程
High-order schemes for the Euler equations in cylindrical/spherical coordinates
AI总结：
本文研究了在柱坐标和球坐标系中使用高阶有限差分加权本质非振荡（WENO）方案求解欧拉方程的实现，分析了三种不同空间离散化方法的精度与守恒性，验证了新方法的高阶准确性和守恒性。
摘要：
我们考虑了在柱坐标和球坐标系统中仅具有径向依赖性的高阶有限差分加权本质非振荡（WENO）方案在欧拉方程中的实现。本文的主要关注点在于确保高阶精度和守恒性。评估了三种不同的空间离散化方法：一种高阶准确但不守恒，一种守恒但不高阶准确，以及一种新的方法，该方法既高阶准确又守恒。对于柱坐标和球坐标，我们给出了对传播方程和欧拉方程中声学问题的收敛结果；然后使用柱坐标中的Sod冲击管和Sedov点爆炸问题来验证我们的分析和实现。
英文摘要：
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.
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