论文标题
平衡阳性阳性的准拉格朗格移动网格DG方法，用于浅水方程
A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations
论文作者
论文摘要
为具有非平板底部形状的浅水方程式提供了一种高阶，平衡，具有阳性的准拉格朗格移动网格DG方法。井平衡特性对于模拟湖泊稳定状态（例如湖泊上的波浪或深海海啸波）的方案的能力至关重要。该方法结合了一种准拉格朗格移动的网格DG方法，一种静水重建技术和未知变量的变化。讨论了使用坡度限制，阳性保存限制和变量的变化以确保井平衡和阳性性能的变化的策略。与重新分区型方法相比，当前方法会及时处理网格运动，并且具有从旧网格到新网格的插值流量变量的优势，并且不需要为新网格上的底部地形选择更新方案所限制。提出了一维例和二维示例，以证明该方法的良好特性，阳性保存以及该方法的高阶精度及其根据流量和底层地形中的特征来适应网格的能力。
A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of an update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.
