论文标题
具有可变地形和不连续数据的2D浅水方程的几何固有的Lagrangian-Eulerian方案
A geometrically intrinsic Lagrangian-Eulerian scheme for 2D Shallow Water Equations with variable topography and discontinuous data
论文作者
论文摘要
我们提出了一个Lagrangian-Eulerian方案，以在空间可变的底部几何形状的情况下解决浅水方程。使用固定在底部表面上的局部曲线参考系统，我们开发了无流量表面的有效的一阶和高分辨率的时空离散化，并解决了一个Lagrangian初始值问题，该问题描述了平衡法律的演变，该法律规定了几何学上固有的浅水水方程。然后将进化的溶液集投影回原始的表面网格，以完成所提出的拉格朗日 - 欧拉群配方。所得的方案保持单调性并捕获冲击，而在存在非自主通量的情况下，也没有提供过多的数值耗散，例如源于可变地形图上的几何固有浅水方程。我们提供了一组代表性的数值示例，以说明拟议的Lagrangian-Eulerian公式的准确性和鲁棒性，用于具有一般曲率和不连续的初始条件的二维表面。
We present a Lagrangian-Eulerian scheme to solve the shallow water equations in the case of spatially variable bottom geometry. Using a local curvilinear reference system anchored on the bottom surface, we develop an effective first-order and high-resolution space-time discretization of the no-flow surfaces and solve a Lagrangian initial value problem that describes the evolution of the balance laws governing the geometrically intrinsic shallow water equations. The evolved solution set is then projected back to the original surface grid to complete the proposed Lagrangian-Eulerian formulation. The resulting scheme maintains monotonicity and captures shocks without providing excessive numerical dissipation also in the presence of non-autonomous fluxes such as those arising from the geometrically intrinsic shallow water equation on variable topographies. We provide a representative set of numerical examples to illustrate the accuracy and robustness of the proposed Lagrangian-Eulerian formulation for two-dimensional surfaces with general curvatures and discontinuous initial conditions.
