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.
翻译:本文为所谓的ALE-WENO(ALE)框架下的浅水方程式制定了结构-保留有限量加权(WENO)混合计划,其结构-保留量主要是非螺旋性(WENO),称为ALE-Eulerian(ALE)框架下的浅水方程,称为ALE-WENO(ALE)计划。WENO混合重建在移动meshes时采用,将光滑、非脉冲和过渡性斜线区分为简单的光滑探测器。为了保持ALE-WENO计划的假设性保存和平衡特性,我们调整了静电模件的活性保护限制和平衡方法,以移动meshes。严格的理论分析和数字实例表明ALE框架下的计划具有高度的顺序准确性和活性保留属性。对于平衡性计划来说,它成功地实现了独特的平衡保护,并捕捉到流体状态的微扰动的微扰动。此外,我们的ALE-WE-WENO混合计划对静模层的模拟具有优势,因为对流体流体进行更高的分辨率接口跟踪。