Abstract

A comparative analysis of the accuracy of shock-capturing schemes, such as the RBM (Rusanov–Burstein–Mirin), CWA (Compact high order Weak Approximation), and A-WENO (Alternative Weighted Essentially Non-Oscillatory) schemes is carried out by numerically solving a gas-dynamic Cauchy problem with smooth periodic initial data. It is shown that, in the presence of shock waves, the RBM and CWA schemes (which do not involve nonlinear flux correction) have a higher order of integral convergence, which provides significantly higher accuracy to these schemes (compared to A-WENO) in areas of shock wave influence, despite the noticeable nonphysical oscillations at their fronts. This makes it possible to use the RBM and CWA schemes as basic ones in constructing combined schemes that monotonically localize shock fronts and, at the same time, maintain higher order accuracy in shock influence areas.

中文翻译：

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气体动力冲击波数值方案的积分收敛性研究

摘要

对 RBM (Rusanov–Burstein–Mirin)、CWA (Compact high order Weak Approximation) 和 A-WENO (Alternative Weighted Essentially Non-Oscilatory) 等冲击捕获方案的精度进行了比较分析使用平滑的周期性初始数据数值求解气体动力学柯西问题。结果表明，在存在冲击波的情况下，RBM ​​和 CWA 方案（不涉及非线性通量校正）具有更高阶的积分收敛性，这为这些方案提供了更高的精度（与 A-WENO 相比）尽管其前沿存在明显的非物理振荡，但仍存在冲击波影响的区域。这使得可以使用 RBM 和 CWA 方案作为构建组合方案的基本方案，该组合方案单调定位激波锋面，同时在激波影响区域保持较高的阶次精度。