论文标题
浅水方程
Structure-preserving finite volume arbitrary Lagrangian-Eulerian WENO schemes for the shallow water equations
论文作者
论文摘要
本文在任意的拉格朗日 - 欧拉（ALE）框架下，开发了具有结构性的有限体重加权（WENO）的混合方案（WENO）混合方案，称为ALE-WENO方案。 WENO混合重建是在移动网格上采用的，这可以通过简单的平滑度检测器区分光滑，非平滑和过渡模板。为了维持ALE-WENO方案的积极性和均衡性能，我们适应了保持阳性的限制器和静态网格上均衡的方法，以使其适应移动网格。严格的理论分析和数值示例证明了在啤酒框架下的方案的高阶精度和阳性性能。对于均衡的方案，它在独特的精确平衡保护中取得了成功，并且可以很好地捕获静水状态的小扰动，而在不连续性附近没有数值振荡。此外，由于流体运动的较高分辨率接口跟踪，我们的ALE-WENO混合方案比静态网格的模拟具有优势。
This paper develops the structure-preserving finite volume weighted essentially non-oscillatory (WENO) hybrid schemes for the shallow water equations under the arbitrary Lagrangian-Eulerian (ALE) framework, dubbed as ALE-WENO schemes. The WENO hybrid reconstruction is adopted on moving meshes, which distinguishes the smooth, non-smooth, and transition stencils by a simple smoothness detector. To maintain the positivity preserving and the well-balanced properties of the ALE-WENO schemes, we adapt the positivity preserving limiter and the well-balanced approaches on static meshes to moving meshes. The rigorous theoretical analysis and numerical examples demonstrate the high order accuracy and positivity-preserving property of the schemes under the ALE framework. For the well-balanced schemes, it is successful in the unique exact equilibrium preservation and capturing small perturbations of the hydrostatic state well without numerical oscillations near the discontinuity. Moreover, our ALE-WENO hybrid schemes have an advantage over the simulations on static meshes due to the higher resolution interface tracking of the fluid motion.
